kohler bathroom toilets dual flush toilet co dual flush toilet bathroom toilet pan download low flush toilet parts kohler bathroom toilet paper holder kohler bathroom commode.
kohler bathroom toilets best toilet kohler bathroom toilet seats kohler bathroom sinks and toilets.
kohler bathroom toilets best toilet colors images the bathroom ideas kohler co bathroom products toilets kohler bathroom toilet seats.
kohler bathroom toilets memoirs classic elongated toilet memoirs toilet memoirs stately pedestal bathroom sink design decor memoirs classic kohler bathroom commode kohler bathroom toilet seats.
kohler bathroom toilets memoirs stately k toilet kohler bathroom toilet colors kohler bathroom toilet parts.
kohler bathroom toilets toilet parts and also great remodel tank replacement commode lever service kit f toilet parts break down kohler bathroom commode kohler bathroom toilet parts.
kohler bathroom toilets get quotations a genuine toilet piece toilet bathroom toilet k kohler bathroom toilet seats kohler bathroom commode.
kohler bathroom toilets bathroom toilet seat cachet quiet close round closed front plastic white kohler bathroom toilet colors kohler bathroom sinks and toilets.
kohler bathroom toilets modern wall hung toilet modern kohler bathroom toilet colors kohler co bathroom products toilets.
kohler bathroom toilets main kohler bathroom sinks and toilets kohler bathroom commode.
kohler bathroom toilets toilet parts toilet parts dual flush toilet panache dual flush 3 two piece toilet toilet kohler bathroom commodes kohler bathroom toilet colors.
kohler bathroom toilets new toilet seat makes your poop smell green design innovation architecture green building kohler bathroom commodes kohler bathroom toilet seats.
kohler bathroom toilets toilet reviews farmhouse bathroom with toilet and white wall for small bathroom kohler co bathroom products toilets kohler bathroom commode.
kohler bathroom toilets enchanting one piece toilets of toilet bathroom products pacific kohler bathroom commodes kohler bathroom toilet colors.
kohler bathroom toilets kohler bathroom toilet parts kohler bathroom toilet colors.
kohler bathroom toilets toilets bathroom kohler bathroom commodes kohler bathroom sinks and toilets.
kohler bathroom toilets memoirs kohler bathroom toilet seats kohler bathroom sinks and toilets.
kohler bathroom toilets offers more than toilet options in black and company officials say the color kohler bathroom sinks and toilets kohler bathroom commode.
kohler bathroom toilets explore a wide selection of toilets from high efficiency to comfort and more kohler bathroom toilet colors kohler bathroom toilet seats.


Climate reconstruction aims to reconstruct a consistent record of the Earth's climate dating back to thousands of years. By understanding the long term history of Earth's climate, scientists can explain and project the planet's current and future climate trends. Scientists usually drill for sediments which can reveal the past state of the Earth's climate.
The new method of using studying algal deposits on the ocean floor is similar to the practice of using tree rings to track the passing of the time. With algae, these "rings" can be as small as 30 microns. Scientists study the magnesium levels in these layers which is dependent on the amount of sunlight and water temperature.
Past climate data only goes back 150 years but with the new method of using coralline algae, this record can go back to the life span of the algae which is more than a thousand years.
Almost 650 years of annual change in sea-ice cover can been seen in the calcite crust growth layers of seafloor algae, says a new study from the University of Toronto Mississauga (UTM).
"This is the first time coralline algae have been used to track changes in Arctic sea ice," says Jochen Halfar, an associate professor in UTM's Department of Chemical and Physical Sciences. "We found the algal record shows a dramatic decrease in ice cover over the last 150 years."
With colleagues from the Smithsonian Institution, Germany and Newfoundland, Halfar collected and analyzed samples of the alga Clathromorphum compactum. This long-lived plant species forms thick rock-like calcite crusts on the seafloor in shallow waters 15 to 17 metres deep. It is widely distributed in the Arctic and sub-Arctic Oceans.
Divers retrieved the specimens from near-freezing seawater during several research cruises led by Walter Adey from the Smithsonian.
The algae's growth rates depend on the temperature of the water and the light they receive. As snow-covered sea ice accumulates on the water over the algae, it turns the sea floor dark and cold, stopping the plants' growth. When the sea ice melts in the warm months, the algae resume growing their calcified crusts.
This continuous cycle of dormancy and growth results in visible layers that can be used to determine the length of time the algae were able to grow each year during the ice-free season.
"It's the same principle as using rings to determine a tree's age and the levels of precipitation," says Halfar. "In addition to ring counting, we used radiocarbon dating to confirm the age of the algal layers."
After cutting and polishing the algae, Halfar used a specialized microscope to take thousands of images of each sample. The images were combined to give a complete overview of the fist-sized specimens.
Halfar corroborated the length of the algal growth periods through the magnesium levels preserved in each growth layer. The amount of magnesium is dependent on both the light reaching the algae and the temperature of the sea water. Longer periods of open and warm water result in a higher amount of algal magnesium.
During the Little Ice Age, a period of global cooling that lasted from the mid-1500s to the mid-1800s, the algae's annual growth increments were as narrow as 30 microns due to the extensive sea-ice cover, Halfar says. However, since 1850, the thickness of the algae's growth increments have more than doubled, bearing witness to an unprecedented decline in sea ice coverage that has accelerated in recent decades.
Halfar says the coralline algae represent not only a new method for climate reconstruction, but are vital to extending knowledge of the climate record back in time to permit more accurate modeling of future climate change.
Currently, observational information about annual changes in the Earth's temperature and climate go back 150 years. Reliable information about sea-ice coverage comes from satellites and dates back only to the late 1970s.
"In the north, there is nothing in the shallow oceans that tells us about climate, water temperature or sea ice coverage on an annual basis," says Halfar. "These algae, which live over a thousand years, can now provide us with that information."


text:
Q: By Removing vim-minimal I removed sudo I'm on Fedora 25 gnome, I rarely use vim, so I decided to remove vim minimal
sudo dnf remove totem-1\:3.22.0-1.fc25.x86_64
bash: sudo: command not found...
Install package 'sudo' to provide command 'sudo'? [N/y] y

 * Waiting in queue...
The following packages have to be installed:
 sudo-1.8.18p1-1.fc25.x86_64    Allows restricted root access for specified users
 vim-minimal-2:8.0.194-1.fc25.x86_64    A minimal version of the VIM editor
Proceed with changes? [N/y] y

So I was forced to reinstall it to use sudo, no big deal but why? It doesn't make any sense

A: Usually sudo depends on the vi package to edit the sudoers file (visudo), but it seems like for Fedora it's vim minimal.
You can actually change the default editor used by visudo by setting the EDITOR variable to another editor and exporting it.

redpajama_set_name: RedPajamaStackExchange


text:
School of Mathematical Sciences School home
Taught programmes
Complex Systems & Networks
Dynamical Systems and Statistical Physics
Geometry, Analysis & Gravitation
Mathematical Foundations of AI
Probability & Applications
Our Research Seminars
Postdoctoral fellowship opportunities
Mathematics Society
Maths Ambassadors
Mental Health and Wellbeing Group (Me + We)
Dr Kostas Papafitsoros
Lecturer in Mathematical Data Science
Email: k.papafitsoros@qmul.ac.uk
Room Number: MB-117
Website: http://kostaspapafitsoros.weebly.com/
I am a Lecturer in Mathematical Data Science at the School of Mathematical Sciences, Queen Mary University of London. Prior to that (2017-2022), I was a research scientist at the Weierstrass Institute for Applied Analysis and Stochastics, in Berlin, Germany, working in the group Nonsmooth Variational Problems and Operator Equations. During the period September 2015-August 2017, I was an Alexander von Humboldt Postdoctoral Fellow, working initially at the Mathematical Institute of Humboldt University Berlin and later at the Weierstrass Institute. I completed my PhD in 2014 at the University of Cambridge, where I was also a member of the Cambridge Image Analysis group. I stayed in Cambridge six more months after my PhD, as an EPSRC Doctoral Prize fellow at the Department of Applied Mathematics and Theoretical Physics.
My main research area is mathematical imaging, in the interface of several areas of applied mathematics, like inverse problems, variational methods, calculus of variations, functional analysis, optimisation, optimal control, numerical analysis and deep learning. I have been particularly involved in the design, analysis and application of nonsmooth energy functionals incorporated in variational regularisation methods tailored for image processing. These functionals are at one hand discontinuity-preserving often stemming from their nonsmoothness, that is, they have the ability to preserve sharp edges in the images and on the other hand, they are adaptive to the specific structure of the given data. I am interested in combining these "classical" methods with modern data-driven and deep learning approaches.
I have a second research direction which is the result of my long-term involvement in environmental conservation with special focus on marine turtles, see the corresponding section of my personal website. I consider several applications of animal photo-identification (identification of individual animals via their unique morphological characteristics e.g. patterns/features), and in the same time consider various ways to enhance and automatise this process via modern imaging techniques. I am also looking at mathematical/statistical aspects of citizen science projects related to wildlife conservation.
Mathematical imaging
Inverse Problems
Calculus of variations
Deep learning and neural networks
Wildlife conservation (marine turtles)
Animal photo-identification techniques
Mathematical/statistical aspects of citizen science
Here are a few latest relevant publications of mine. For a complete list of publications, please visit my google scholar profile.
First-order conditions for the optimal control of learning-informed nonsmooth PDEs, Guozhi Dong, Michael Hintermüller, Kostas Papafitsoros, Kathrin Völkner, (2022) [arXiv preprint]
A social media-based framework for quantifying temporal changes to wildlife viewing intensity: Case study of sea turtles before and during COVID-19, Kostas Papafitsoros, Lukas Adam, Gail Schofield, (2022) [biorRxiv preprint]
Dualization and automatic distributed parameter selection of total generalized variation via bilevel optimization, Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg, Hongpeng Sun, Numerical Functional Analysis and Optimization, 43(8), 887-932, (2022) [DOI]
Bilevel training schemes in imaging for total-variation-type functionals with convex integrands, Valerio Pagliari, Kostas Papafitsoros, Bogdan Raita, Andreas Vikelis, SIAM Journal on Imaging Sciences, to appear, (2022) [arXiv preprint]
Optimization with learning-informed differential equation constraints and its applications, Guozhi Dong, Michael Hintermüller, Kostas Papafitsoros, ESAIM: Control, Optimisation and Calculus of Variations, 28(3), (2022) [DOI]
More aggressive sea turtles win fights over foraging resources independent of body size and years of presence, Gail Schofield, Kostas Papafitsoros, Chloe Chapman, Akanksha Shah, Lucy Westover, Liam C.D. Dickson, Kostas A. Katselidis, Animal Behaviour, 190, 209-219, (2022) [DOI]

redpajama_set_name: RedPajamaCommonCrawl


text:
BREAKING: No strike Wednesday; negotiations continue between BART, unions
OAKLAND, Calif.
There were a lot fewer fireworks than there were on Monday, perhaps both sides are tired, or maybe they are making some real progress.
BART General Manager Grace Crunican is at the table, which is something the unions have wanted all along. There are also three federal mediators working with the two sides and both have said the presence of George Cohen in particular has made a big difference.
Beyond that, BART is sticking to its last, best and final offer in terms of its $57 million total, but they are open to modifying the details within it.
Tuesday evening, Cohen announced that negotiations are continuing and there will be no strike Wednesday.
More about Federal mediator George Cohen
Cohen is known for finding common ground in several high profile cases. He's a lawyer by training and used to teach at Georgetown. He was appointed by President Obama in 2009 as Director of the Federal Mediation and Conciliation Service - to help end major disputes that are hurting the economy.
Cohen has mediated disputes between the National Basketball Association and the NBA Players Association, the National Football League and its players, as well as a labor dispute involving the Federal Aviation Administration.
Stay with ABC7NEWS.COM for updates on the looming BART strike and information on how to get around if the trains stop running. Follow us on Twitter, Facebook, and Google+ and download our news app for the latest news whenever and wherever you want.
The AP has contributed to this story.


, it's certainly not the only measure. In fact, the approval of a huge number of likes through social media can stunt your development, as it may well blind you to some of the mistakes you make when taking photos.
, and allow your photography to grow organically.
, and in the early day's it's worth trying out different techniques to see which is the one for you. But sooner or later though you'll need to decide whether you're a portrait, landscape or food photographer.
is one niche, will you choose this or something different?
. This can either be online or in person. The majority of photography groups or clubs have a mixture of levels and abilities, and it may well be you'll find your mentor by joining such a group.
. Everywhere has its point of interest, and training your photographer's eye to see that will help you become a better photographer.
Description: 9 Tips for Aspiring Young Photographers from the above which is part of the Tips category.
This 9 Tips for Aspiring Young Photographers is provided only for personal use as image on computers, smartphones or other display devices. If you found any images copyrighted to yours, please contact us and we will remove it. We don't intend to display any copyright protected images.


MUSINGS ON THE THIEF OF LIFE - DEATH!
MUSINGS ON THE THIEF OF LIFE – DEATH!
How does it feel like? There is always a word for every emotion felt except when our brain has seized functioning properly for a while, when we are consumed by too much grief, bewilderment, shock or that which cut across all these emotions to form a state of nothingness.
The tears from consolers made of friends, enemies and those who cared less. The ones who were clear-eyed but burst into loud cacophony of sounds at the entrance of the home of the bereaved, putting up a show of emotion, acting their sorrow and crying more than the bereaved. The shocked one who keeps talking about how she saw the deceased just minutes ago through shivers of doubt. The ones who are tough hearted and wouldn't shed a tear not even when the mother of the deceased starts a painful dirge. The ones who are there to preach and tell the mother of the bereaved to take heart and accept fate. Tell me would they accept fate when death becomes the unwanted visitor knocking on their door? Will they welcome fate when it enters uninvited even though it was told to wait a little while longer at the door? The ones who are only there just because they are meant to be there, who sigh deeply because sighing is what is done when people express their condolences and no one replied because everyone is shocked, sad and crumbled.
'E lo ra turare wa, who is getting the perfume?' Someone will call from where they bathed the deceased.
There are also those who are there to just observe, accepting it as one of those things 'verily, the dark times are here.' They will mutter.
Every one of them converge around the mother of the deceased without a care for the father. The father acts the way he must act, the way he should act, the way the society wants him to. He shouldn't cry when his wife is there to do that. He musn't cry when his wife is there to do that. So he swallows his grief like the hot pap forced down his throat because he must eat, he needs the strength they would say. Nobody cares about his feelings because he refused to wear it on his sleeve.
The deceased is getting prepared for the sojourn to another world, wrapped in white travel clothes waiting to be transported to the other side.
The deceased is transported in a wooden ship of death. No one followed, not even the Mother who ferried her to Earth in the beginning.


Equities start the day lower as bulls go all Russell Crowe here. I'll tell you what, I'm still wiped from Wednesdays move. I sat in the parking lot staring at my speedometer yesterday because I didn't want to muster the energy to drive. I haven't seen markets like that since Greek debt made the world tremble. To be honest, I'm not even sure the story was about equities, it was probably fixed income. Some bond short got taken out of business yesterday, the move in 10yr yields was an 8 std deviation event, something that happens once in thousand year...ok lemme stop right there. You know what, insane stuff happens in markets. Stocks, bonds, options, commodities, all will do things you can never plan for. Things that no rational human would expect. Standard deviation events are just fancy ways of saying "wow, this puppy did something crazy so now I need to sound smart about it". You just can't prepare for everything, especially in the equity world. But you know what? Days like yesterday are why equities have a risk premium over bonds. You can't have that without volatility/selloffs so learn to embrace the carnage. What really bums me out is the velocity of these moves. It took 262 days for the market to gain 9% and only 19 days for it to be wiped out. So where do we go from here? That's the real question. Unfortunately I don't think we race back to the highs, we're gonna need to mow this grass for a while before it regrows. Europe is going to need someone at the ECB to say something positive and we're gonna need a solid earnings calendar and juicy macro data to get going again. And that's not even addressing sentiment which really needs to get ugly. The damage is done people, bears are going to claim victory over the "stock market bubble". I saw a great quote on Twitter that said "yesterday there was blood in the streets, now we have to wait for the bodies to show up". So true.
After the open we buckled up for another wild ride. But you know what? I think everyone wore themselves out yesterday because it felt relatively calm. We spent most of the day rallying after Fed President Bullard said "yea, if we need to keep this QE thing going we can talk about that". I said this in a previous recap, and about a million times in 2011, but in these kind of headline driven markets all you need is one central banker or finance minister to say one random comment and things can turn rapidly. Which is what makes this kind of price action so incredibly frustrating, especially for people in our industry. Analyst work takes a back seat to macro, PMs get whipped around, traders chase VWAP all over the place, lunch delivery business soars, and headline writers can be both relevant and irrelevant in a 30 min span. The biggest loser was NFLX, which dropped 19% after godawful earnings guidance. If you are a high multiple stock in October 2014 you better not guide lower or your stock is gonna look like a Saw movie. Other losers were SWN, EBAY, GWW, and FITB. Winners were almost all energy stocks as Crude oil finally caught a small bid. CHK, QEP, DNR, NFX, and RRC to name a few. By lunch we had erased a 1.2% overnight decline and sat on 1,867 up 0.25%. Did I mention AAPL introduced new iPads today? No? Well they did, and they get thinner every year. Which is the opposite of me. Hey, at what point is AAPL gonnna stack 5 iPads together and sell them to Gillette as a new type of razor? I should work for Bain. Moving on.
The final hour brought absolutely no stock market movement. In fact the S&P went nowhere from 1130am to the close. Absolutely freaking nowhere. Which is a huge bummer right? It's like we were fed oatmeal after eating at one of those super fancy one name restaurants in NY where you drink $15 water.
As long as we hold yesterday's lows I think the market can start to repair itself. Make no mistake though, bears will try to push it thru there. We're gonna see some wicked selling again soon, today was nothing more than a rest day. Be prepared for it because you know it's coming. We just need to channel our inner Gladiator (or is it Braveheart?) and HOOOLLDDD.
Final Score: Dow -15bps, S&P500 flat, Nasdaq -55bps, Rus2k +125bps.
Succinct Summation of the Day's Events: Fed President talks about QE, markets embrace it, erase overnight losses then trade sideways most of the day. We're not out of the woods.
Glenview's Larry Robinson: "Our own checks with companies indicate that the economy is doing reasonably well in the US, clearly some challenges overseas. We don't believe that this a change in tone in the market that's likely to be here to stay. We believe that this is a transitory risk problem."
Why did the Stock Market Decline? "But I find this questioning misguided. Who cares why the stock market went down. Answering that question serves no purpose. You don't get your money back if you find the answer. You don't get a prize. All you get is some comfort knowing that you know why something happened after the fact. And that's not worth a whole lot.
I'm making it a life goal to camp right there.
If you recognize any of these characters you lived in the golden age of cartoons.
These are real shots right?
My final link tonight features the most disappointing ending to a video since Jar Jar binks won that battle by acting like a complete moron.


"A few weeks ago, I noticed that our heat pump didn't seem like it was putting out any heat. I gave Robben & Sons Heating a call. They had set me up with an appointment for one of the technicians to come out. My heat pump was at least 15 years old and I had an idea that it had probably reached the end of its life expectancy.
The technician, Josh arrived on time. I might add, I did reschedule from my original appointment. When I did reschedule, the staff, particularly Mary Jo at Robben & Sons were very professional, accommodating and was able to set me up with another appointment within a week. Josh ran some diagnostics and gave me the news that I was hoping not to hear….no refrigerant and weak heat strips. Josh recommended replacement and I agreed. He offered to have a project consultant to come out and give me an estimate. Fortunately, the consultant had an opening later in the day.
The consultant, whose name is Roz, arrived and looked over my situation. Roz asked some questions regarding our heating and cooling patterns of my wife and me. We were limited to options as we live in a manufactured home. Roz worked out a solution which included increasing the size of my unit to a Bosch 3-ton condenser from a 2-ton. I agreed with this as I always thought the 2-ton was undersized for this size house and the number of windows we have. I sold HVAC many, many years ago, so I have a little knowledge of the products. I was happy with the product and felt the price was within the reasonable limits. Sold!
So, I was set up for installation within a reasonable time. Matt and Anthony showed up on time and worked the entire day installing my new system. During the installation, Matt answered the questions that I had and provided valuable training on my new thermostat. The thermostat is very cool. It is a Bryant Housewise with wi-fi. Away from the house, I can check the current temperature and increase the heat or turn on the cooling side. It gives me a weather forecast as well as other options. The install team finished up and cleaned up leaving the area spotless.


Based on the Clark's trekker. The shoe is leather upper, with the stitching going through the middle of the shoe, which extends up the tongue. On this shoe, the sole crepe sole is replaced with a more trainer based rubber sole.
The leather upper is corded and so not plain suede. The cord lines does make the shoe look a little less wide. Some desert boots and shoes like this suffer from being wide at the front and clown looking. I think dj have done a great job of getting the shoe looking slimmer, but retaining the classic look.
On first inspection I like the interplay between the normal leather and suede. The two leather compliment well and the stitching is also compliments well to them.
Wearing wise, I have had them on for five solid days and worn them at the office, on several dog walks, and out at a gig. So each time it has never been less than 7 hours each time.
In terms of wear the shoes have buffed up a little in suede, making it look a little rough in texture, but only a bit. The suede has stretched just like desert boots do. I must say the shoes are extremely comfortable and even in the hot weather we have had in the UK my feet have been noticeably cooler than trainers and desert boots.
These shoes are becoming a fav of mine for day to day already. Looking good with jeans at work, is a requirement for me most days. Smart but casual is most days for me. I am not convinced that they would work with a suit or even trousers, I think they are just to causal. The really look to me as something an indie mod or Stone roses fan is going to love.
Anyways enjoy the videos and the pictures and if you think you want to try something different to a desert boot, then I would seriously ink about giving these a go.
This entry was posted in Uncategorized and tagged casual mod, happy mondays, madcester, madchester, stone roses shoes, suede mod shoes.
Everyday Mod shoes ? Or what to wear on your feet to work?


This exterior remodel features James Hardie fiber cement siding. The homeowners invested in 7" exposure individual shingle in Sail Cloth. Our expert team installed each shingle with varied keyways. Keyways are the spaces between each shingle. Varied keyways allow Hardie to mimic the look of traditional cedar siding while still providing all of the benefits of fiber cement. This particular project had keyways that varied from 0" to 1/8" to 1/16", giving this home a beautiful authentic look. The garage doors were also excentuated with 5 1/4" PVC crowns and Burr finished the look with crisp Arctic White window trim and corners.


It's time for the media to check its implicit biases. This past weekend, a deadly attack took place at a country music concert in Las Vegas Nevada. The culprit? Stephen Paddock, a 64 year old white man. 59 people died and at least 527 were wounded.
1. The media attempted to conceal the fact that Paddock was White.
I scrolled through articles struggling to find the face of the man that committed the attack. No physical description had been given except his age and his name, which was odd. News outlets are typically so quick to disclose such information. That was when I realized, without even seeing an image of Paddock, that the attack was committed by a white man.
RELATED: Let's Talk About Mass Gun Violence in U.S.
Because irrespective of whether or not a person of color is guilty or innocent, the media is known to be swift at disseminating incriminating photos of them.
And of course, when an image finally emerged, it was one of him smiling with a drink in hand.
2. The media attempted to humanize Paddock.
This man had just committed massacre, yet somehow he was being illustrated as a regular, friendly man. This is not the first time a white person has committed a vicious crime and the media has painted them in a positive light.
3. The media labeled Paddock as anything but a terrorist.
Under this definition, Paddock is a terrorist.
Yet countless media outlets are continuously describing Paddock as a "lone wolf" with "no motive." If social or political motive is what truly separates terrorists from non-terrorists, how come Dylann Roof, the white man who killed 9 Black people at a church, under the tenet of white supremacy, was not labeled or prosecuted as a terrorist?
SEE ALSO: A Nation Under the Gun: Nearly 47,000 Gun Incidents in 2017 Alone.
50 dead. Over 400 in the hospital. And we continue to call this a LONE WOLF? Call it TERRORISM because that's what it is.
The truth is, the media can play a powerful role in perpetuating or dismantling dangerous social narratives. It is only my hope that moving forward, more outlets will choose the latter.


text:
The Director: Crash Course Film Production #7
YouTube: https://youtube.com/watch?v=7lIpcJVbbSA
Previous: Cybersecurity: Crash Course Computer Science #31
Next: Herakles. Or Hercules. A Problematic Hero: Crash Course World Mythology #30
So... what do Directors even do? That's not an easy question to answer but today Lily will do her best. Generally, directors are the driving creative force behind a movie, deciding what kind of cinematic world the story will take place in, how the performances will fit into that, and how the camera will capture that world. But, there's a lot more to discuss on this episode of Crash Course Film Production.
Produced in collaboration with PBS Digital Studios: http://youtube.com/pbsdigitalstudios
The Latest from PBS Digital Studios: https://www.youtube.com/playlist?list=PL1mtdjDVOoOqJzeaJAV15Tq0tZ1vKj7ZV
Tumblr - http://thecrashcourse.tumblr.com
Support Crash Course on Patreon: http://patreon.com/crashcourse
So, I have a script to work off of, to tell you about directing. But what do you think we should do in this video? Should I show you what a director does? Should I explain everything a director does? Should I try to get you to guess what a director does?
People often assume that the director has all the answers, but directors also ask a lot of questions. According to American playwright and filmmaker David Mamet, directors only have two main questions to ask themselves: What do I tell the actors? and Where do I put the camera?
And that's a cheeky way of encompassing a lot of what the director should do. But maybe a better way of looking at it is that the director has a strong sense of where the answers are buried, and their job is to steer their team to where they can uncover those answers.
That might sound a little foofy, but it's the clearest way I can describe what the job of the director is. A director must use everything at their disposal to clearly communicate to their actors, their crew, and ultimately to us, the audience.
[Opening music]
What Do I Tell the Actors (1:00)
A director's job is to bring their vision to life in the film. So, a common misunderstanding is that the actors are just like puppets, illustrating the director's ideas. An actor's job is to bring a character to life. And we need actors to think real thoughts and feel real feelings to make the film relatable.
A good actor gives director options, by making informed choices about how a character would act in the various situations that the script puts them in. We've talked about the language of the camera, and how the way in which shots are framed can help convey a story. But the camera's most important job is to read the character's thoughts.
For that to happen, actors have to be vulnerable and think as the character. This is incredibly demanding work, so it's up to the director to ensure that the actors have a safe space to explore their character and to take risks. And the actor relies on the director to steer them in the right direction.
I joked earlier about having you guess what I would say in this video. That's because forcing an actor into a position where they're unsure about how to act in a scene is one way to ruin their performance. If an actor feels like they need to direct themselves in a scene, they won't risk losing themselves in the world of the film and it'll feel fake. To give an actor the confidence they need to inhabit a character, a director must give clear, actionable directions.
What do I mean by that? Well, let's say we're working on a scene about a breakup. A clear, actionable direction could be, "Since your character has been blindsided by this breakup, you want to keep the other person from leaving the room so you can get answers."
The actor receiving this direction now knows that their character has just learned that they were wrong about the other character and they have a goal of keeping the other person there. They know where they're coming from and where they're trying to go. Now, no matter what happens in the scene, this actor can feel confident in their decisions if they're working toward keeping the other person in the room.
On the flip side of that, an unclear or non-actionable direction in that breakup scene could be, "You wish this wasn't happening and it reminds you of when your parents got divorced." How do you act "wishing" or "being reminded" of something? That's way too vague. But if the director knew what they wanted, they could tell the actor something like, "You see this person as the father who left you when you were 10 and, just like then, you'll do anything to keep them here."
So now, this is a more actable note, because our actor understands the power dynamic of this relationship and knows that they're using the same tools a 10-year-old would. And, most importantly, the actor now has a goal: Keep the other person from leaving. So the director has a plan for how they'd like the scene to go, and the actor will add their own interpretations to that, and the hope is that they uncover the best possible scene.
It is possible to a director to get the scene they envision without allowing the actors to do their work, but this doesn't build trust or create conditions for a better film than the director is capable of imaging. This is something author and directing instructor Judith Weston calls result-oriented directing, and it's a common mistake of new directors who are focused on the surface-level aspects of acting instead of the true work that goes into it.
Instead of working with the actors to unpack what the line means and what the purpose of the scene is, a director will focus on outward emoting and try to control how an actor does things. You may have heard directions like, "On that line, laugh." or "When you see her, you start to cry." This tells the actor nothing about what their character is actually thinking and feeling.
A director might think they're helping the actor by telling them how they should say the line or where they should put the emphasis in the line, but this is called a line reading, and it limits the actor to just mimicking the director rather than communicating what the character is feeling.
A result-oriented direction will usually give the director what they think they want in that moment, but at a pretty high cost. These directors are only paying attention to what the characters look like outwardly instead of what's going on inside their minds. And when you're working with a good actor who's thinking real thoughts, the camera - and therefore the audience - can pick up on those thoughts. The result will be a deeper, more nuanced performance than when the actor is just pantomiming what the director tells them to do.
It's important to remember that filmmaking is collaborative by design, and while the director is the creative leader, insisting the film turn out exactly like the director imagines can severely limit the film. Result-oriented directing can also break trust that's been built between director and actor. After all, if a director can't trust an actor to experiment and discover what's needed from a scene, then why should the actor trust the director?
The detrimental short-cut of line readings can be avoided by making time for rehearsal. And rehearsal is a great way for the director and actors to build trust. Some directors, like Sydney Lumet, are subtle about it. Lumet would tell each person where to sit at the first read through of a script. This made it clear to the actors that he had a plan and was confident in his choices.
Directors like Mike Leigh are more overt about building trust in rehearsal. Leigh purposely works with actors who are willing to explore themes and ideas before they even have a script. They work through proposed scenes together, and then Leigh develops a script around what they've uncovered together in the rehearsal process.
By the time the cameras are rolling, the actors having been living and growing as these characters, so they know to approach every scene. From rehearsal to the final cut, a director's job always includes guiding the actors in their roles and shaping those performances, but the director also works with every creative department on a film.
Where to Put the Camera (5:33)
That's what Mamet calls "where to put the camera," but it involves much more than that. Just like with the actors, the director has to deeply understand the other departments so they can communicate clearly with everyone.
During pre-production, the director coaches the location scouts on what the film needs in its setting. They work with the Production Designer, set decorators, and props department to build the world and orchestrate everything in the mise en scene.
And before the actors even get to set, the director needs to understand the film's characters to communicate their personalities and struggles to the costume designer. Both before and during filming, the director works with the Hair and Makeup and special effects departments to perfect the details of the storytelling.
And yes, the director decides where to put the camera. There are an infinite number of ways to make a shot look cool or beautiful, but there's usually one best way to shoot a scene when you remember than every shot should be motivated by what the scene is trying to convey. What's motivating the camera placement and movement can be practical - like, if you need to show someone driving, we need to see who it is, and also see that they're in a car.
But how the director decides to use the camera can also help us understand something about the character or the themes of the film more deeply. Starting in pre-production, the director and cinematographer work together to design the shot list. They'll usually work with a storyboard artist to illustrate what the shots will look like and work off of the storyboards as a reference.
They can do this before the locations are nailed down, and it's possible to work on it even before the actors are cast, because what determines how a film is shot is that blueprint we talked about before: the script. Just like every line of dialogue, every shot should convey new information to the audience.
We should be able to watch a film with the sound off and still be able to get what's going on. We should be able to know things like who our protagonist is, what they want, what's standing in their way, and how they feel.
Post-Production (7:05)
Once we know what to tell the actors and where to set the camera, there's still one huge job left for the director: post-production. Just like all the other creative leads, the director needs to communicate the story with the editor and composers in order to tell the best version of the story.
The editing process introduces the final layer of discovery for the director. The director is the guiding force in uncovering the answers right up until the final cut. What the best version of the story is, depends on the director and the film. While a director leads their team in unlocking that best version, they're also the decision makers.
They're holding the whole film in their heads, and actors, cinematographers, designers, editors, and composers all give the director options they think are the right answers for the film. Then, the director chooses which are the best. Depending on the size of the production, the director might not be the one calling action or cut, but the director is always the one who says, "Yes, that's what I want."
Review and Credits (7:54)
Today, we explored the director's role as a leader and creative guide for everyone else working on the film. We learned that the director must have a strong vision and be able to communicate it clearly. And we talked about how one of the director's most important jobs is creating the safe space for the rest of the team to do their creative work. One of those people is the cinematographer, who we'll talk about next time.
Crash Course Film Production is produced in association with PBS Digital Studios. You can head over to their channel, check out a playlist of their amazing shows, like Eons, PBS Infinite Series, and PBS Space Time. This episode of Crash Course was filmed in the Dr. Cheryl C. Kinney Crash Course Studio with the help of all these nice people. And our amazing graphics team is Thought Cafe.
[Theme music]


text:
Newsletter: Tar sands crude-by-rail falls off a cliff
June 2, 2015By Matt MaioranaIndustry Analysis, Newsletter
As Kinder Morgan and Imperial Oil together opened the third tar sands unit train loading terminal in the Edmonton/Hardisty area, the business of sending tar sands crude to market by rail hit the skids.
Genscape monitors each of the three terminals and the latest figures show that two of the terminals loaded no crude whatsoever for a week, while the third loaded on only three out of seven days.
The three terminals have a combined rated loading capacity of 430,000 barrels per day (bpd) but only managed to load an average of 75,000 bpd between them over the past four weeks (see Table 1 and Figure 1). This is about 17% of their combined capacity and equivalent to about 1.1 unit trains per day between them.[1]
Table 1: Weekly Loadings at three tar sands unit train loading terminals
Source: Oil Change International and Genscape PetroRail Report.
Figure 1: Weekly Loadings at three tar sands unit train loading terminals
The low rates of utilization may come as a surprise to those that have heard so much about rail offering a solution to pipeline delays. However, we have extensively documented the problems with tar sands going by rail as well as the ongoing issues at the first tar sands unit train loading terminal, Canexus Bruderheim.
The current dive in utilization at these terminals is most likely linked to the lack of profitability in sending tar sands by rail when oil prices are low and the price differential between Canadian and U.S. crudes is narrow. Both of those factors are currently in play.
Loadings may pick up when prices rise and/or the differential widens again, but this merely confirms the stopgap status of crude-by-rail for tar sands producers. When the price differential widens it supports rail use because the extra cost of using rail is absorbed into the price the crude fetches at the destination. However, that does little to improve the netback (profit) for tar sands producers who will either have to sell at the loading end at a discount or pay the high cost of rail to sell at the destination and realize the higher price.
As the CEO of Imperial said when he announced the opening of the latest tar sands unit train terminal in Edmonton, "the jury is still out" on how much tar sands crude rail will ship by rail. If recent weeks are anything to judge by, the jury may have an answer.
[1] This assumes heavy oil loads at 550 barrels per tank car and 120 cars per train (66,000 barrels per train).


The curlicue placenames of Scotland give the impression that they were created with an eye on branding single malt whisky, so intriguing are the craggy mixtures of consonants and vowels. Consider the parish of Assynt, which is located on a remote corner of the northwest Highlands. It can boast a neighbourhood of Inverkirkaig, Baddidarach, Stoer, Quinag, Inchnadamph, Kylesku and Lochinver, to name but seven gems. No wonder, then, that Norman MacCaig adored it.
on its seven hills beside the Firth of Forth.
that looks across the Minch to the Hebrides.
giving me gifts wrapped in the ribbons of memory.
I store them away, greedy as a miser.


text:
Environmental Health News
Public Health and Protection
EH's role in enforcing lockdown still being clarified
EHPs race to work out practicalities of enforcement.
24 March 2020 , Katie Coyne
Update 25 March: the Government has issued guidance on business closures for local authorities. Download it here.
Confusion remains over some of the practicalities of enforcing the government's lockdown of businesses – but it's clear environmental health will play a key role.
On Saturday (21 March) enforcement powers and restrictions were enabled under the Government's Health Protection (Coronavirus, Business Closure) (England) Regulations 2020.
On Monday evening (23 March), all non-essential retail stores, including hair, beauty and nail salons and markets (excluding food markets), were ordered to close (the Government's guidance on this is here).
Responsibility for enforcing the shutdown lies with EH and trading standards officers with police backup where needed. This was a welcome change in direction from the previous week when London EHPs were told by PHE that they would not be involved in COVID-19 control measures – although this related to infected persons refusing to self-isolate rather than businesses refusing to close.
Originally, the Saturday announcement said prohibition notices could be used to shut down non-compliant businesses – but the HSE stepped in shortly afterwards to warn that existing notices, certainly one under the Health and Safety Act, should not be used in this way.
But it is still not entirely clear how EHPs should enforce. One EHP working said: "Reg 4 states 'a person designated by the secretary of state, may take such action as is necessary to enforce a closure or restriction imposed by regulation 2'.
"That reads as though a designated person can pretty much take any action to force closure. Draconian and non-specific stuff!"
A bigger practical problem may be police support. Depending on the numbers of police staff available, and the pressures and other incidents a local force may be dealing with, officers may not be readily available.
One EHP commented: "This is a grey area. There's no clarity on that. Will we get support from them when it's something that they might not deem essential? We would simply tell a business operator to close but it's up to them to make sure their customers go home immediately.
"But if we have an EHP in the corner and the operator points to them and tells everyone EH is closing them down, then potentially there could be a problem. That is worst-case scenario. I am hopeful that it is self-enforcing. I think we may get the odd occasion where the small village bar is having a regular lock-in, some places might think they are off the radar and choose to flout it."
Further guidance from Government on enforcement will follow, and CIEH will keep members fully updated.
CIEH Leadership Programme
Take your career to the next level with the CIEH Leadership Programme.


Green Galaxy Granite, Green Galaxy Granite Exporters, Green Galaxy Granite Suppliers, Green Galaxy Granite Slabs, Green Galaxy Granite Tiles, Green Galaxy Granite India, Green Galaxy Granite Price, Green Galaxy Granite factory, Green Galaxy Granite Factories India, Green Galaxy Granite Manufacturers, Green Galaxy Granite Mines, Green Galaxy Granite Blacks, Green Galaxy Granite wholesaler, Indian Green Galaxy Granite Supplier, India Green Galaxy Granite Supplier, India Green Galaxy Granite Exporter, indian Green Galaxy Granite Exporters, Green Galaxy Granite Banglore, Green Galaxy Granite Madurai, Green Galaxy Granite Chennai, Cheap Green Galaxy Granite India, Green Galaxy Granit, Green Galaxy Grani, Green Galaxy Exporter Rajasthan, Green Galaxy Udaipur, Green Galaxy Nakoda Marbles, Nakoda Granites, India.
We are indian exporters of Green Galaxy Granite Tiles, Green Galaxy Granite Slabs, Green galaxy Granite Blocks, Green galaxy granite cobbles and Pebbles. We also produce Kitchen top of green galaxy granite, Vanity top in Indian GREEN GALAXY COLOUR GRANITE. Steps and Risers, Basins and other interior products are also custom made in green granite. We also supply Graveyard stone and mosaic tiles made of Green Galaxy Indian Granites. Shree Nakoda Marbles is a reputed suppliers of Green Galaxy granite tile.
We are Green Galaxy Granite Exporters from India. Green Galaxy granite dealers from Russia, Germany, France, Italy, Spain, Sweeden, UK, USA, Nederland, Turkey, Poland, Albania, Romania and many other europian countries buy green galaxy granite slabs, tiles and other green galaxy granite products from us. Below are size details for export of green galaxy granite.
Green Galaxy granite Slabs are available in various size and thickness. we export two grades of green galaxy granite slabs, they are Best Quality green galaxy granite, and commercial grade. We process green galaxy granite and manufacture polished green galaxy granit slabs, Honed slabs and various other finish of this marvellous Indian green granit. The green galaxy granite slabs are one of the most demanded product of Indian Granite industry. We process both, the BIG SIZE blocks as well small size blocks. The large size slabs are little more expensive, but widely demanded by granite dealers and architect from Europe.
We are manufacturer of green galaxy granite tiles, also known as seaweed green granite, Pine green granite tiles or golden Green Granite Tiles. These tiles are made in various thickness ranging from 12 mm to 50 mm and customised. The most demaded product is 18 and 20 mm thick polished green galaxy granite tiles.
Most of our company revenue is generated by sales and supply of green galaxy granite products. In years, with our best product and timely delivey, we have established ourselve as othe of the most promissing green galaxy granite suppliers from India. No matter, what size, thickness or finish of material you need...we can process it for you.
We determine Green Galaxy granite price, based on two factors; first - size and thickness of product and second - quantity required. Please fill in the online enquiry form, so that we can quote the best price of our green galaxy granite.
Being one of the major exporter of green galaxy granites from India...we are committed to provide best product at resonable price. Be assured, we always charge wholesale price...but still large orders attract some additional discounts.
Although India is known for various colours of granites, the most demaded are green granites from India. Green Galaxy granite has the largest sales share among all Green granites. Infact, it is also one of the major source of our revenue. Looking for Green Galaxy granite from India, just send us a mail and be relaxed. We have all necessary infrastructure to make green galaxy granite products as per your requirement.
We, Shree Nakoda Marbles, are producer of green galaxy granite slabs, tiles, polished maple leaf granite floorings. The Indian green galaxygranite is mined from south India. our specialisation in chamfered green galaxy granite kitchen tops tiles makes us a better choice as supplier of green galaxy granites for projects. we are exporter of green galaxy indian granite to usa, uk, europe, australia and middle east. If you have any querry for green galaxy granite floorings, green galaxy granite slabs tiles blocks, green galaxy granite uses, just send us an Enquiry for Green Galaxy Granite India.


text:
The Return of Sherlock Holmes is a play written by J. E. Harold Terry and Arthur Rose and originally starring Eille Norwood as Sherlock Holmes. The play premiered at Princes Theatre on October 9, 1923.

Based on the work of Sir Arthur Conan Doyle, the play incorporated aspects of four stories: "The Adventure of the Empty House", "The Adventure of Charles Augustus Milverton", "The Disappearance of Lady Frances Carfax", and "The Red-Headed League". Actor Eille Norwood had previously portrayed Holmes in the Stoll film series from 1921 to 1923.

Cast
Eille Norwood as Sherlock Holmes
H. G. Stoker as Dr. Watson
Molly Kerr as Lady Frances Carfax
Arthur Cullin as Reverend Doctor Shlessinger
Noel Dainton as Hon. Philip Green
Paul Gill as Inspector Lestrade
Lauderdale Maitland as Colonel Sebastian Moran
Eric Stanley as Charles Augustus Milverton
Ann Desmond as Jenny Saunders
Esmé Hubbard as Mrs. Hudson

References

1923 plays
Works based on Sherlock Holmes
British plays
West End plays

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}
 Traditional approaches like \cite{fikes1994strips} considered the long-horizon manipulation as a strict decomposition of symbolic sub-tasks to be solved by motion planners independently. However, in most cases dependencies are unneglectable between symbolic and geometric levels. Consider a toy problem (Fig\,\ref{fig:toy_problem}) with its TAMP solutions  (Fig\,\ref{fig:toy_problem}), it is obvious that the success of the motion planners depends on the outputs of the task planner. On the other hand, the task planner should be aware of how its outputs are evaluated by motion planners to avoid spending too much time on infeasible skeletons. Therefore, planning techniques are required to integrate both task planning and motion planning. We are interested in an integrated planner that is able to search in both a large action space and a large motion space while addressing the infeasible skeleton issue resulting from the combination of the two spaces.

 \begin{figure}
    \centering
    \begin{subfigure}[b]{0.49\textwidth}
        \centering
        \includegraphics[width=0.9\textwidth]{toy_problem.png}
            \vspace{-0.18cm}
        \caption{\small The Unpacking problem}
        \label{fig:toy_problem}
    \end{subfigure}
    \vfill
    \begin{subfigure}[b]{0.49\textwidth}
        \centering
        \includegraphics[width=0.9\textwidth]{candidate_sk.png}
            \vspace{-0.18cm}
        \caption{\small A hierarchical (or "search-then-sample" \cite{garrett2021integrated}) TAMP workflow}
        \label{fig:candidate_sk}
    \end{subfigure}
        \vspace{-0.45cm}
    \caption{\small The unpacking problem. The taller red body in the environment must be relocated before the green one can be reached without collision.}
    \label{fig:1}
\end{figure}

\textit{\underline{Large task spaces.}}
In comparison to multi-modal motion planning (MMMP) \cite{hauser2010multi,barry2013hierarchical} that mainly extends the classic motion planning (for collision avoidance) to include changing the state of other objects in the domain, a TAMP problem features large abstract state spaces with additional state variables that have no geometric meaning, such as whether the food is cleaned in a cooking task \cite{garrett2021integrated}. To make this large action space tractable, the communities usually take relational representations such as PDDL \cite{mcdermott1998pddl} to compactly describe the planning domain by exploiting its underlying regularities \cite{garrett2018stripstream,garrett2020pddlstream,dantam2016incremental}.
Thus, task planning in TAMP are generally more complex and universal than in MMMP, and they require substantial search effort with dedicated AI planners.

\textit{\underline{Large motion spaces.}}
A skeleton must have its symbolic actions grounded by concrete motion values (\textit{bindings}) so that it can be executed by physical robots. Therefore, low-level motion planning with high-dimension variables are ultimately unavoidable. The motion space depends on both the parametrization of the abstract actions and the length of the skeleton. For example in Fig.\,\ref{fig:candidate_sk}, we have $\langle x_1,y_1,w_1 \rangle \in \mathbb{R}^3$ to search for the $x$- and $y$-position of \texttt{body1} and its orientation $w_1$ in \texttt{skeleton1}. While in \texttt{skeleton2}, the dimension of the motion space gets doubled: $\langle x_1,y_1,w_1,x_2,y_2,w_2 \rangle \in \mathbb{R}^6$. Since even larger motion spaces in robot manipulation are expected, an efficient motion planner is highly desired.

\textit{\underline{Infeasible task skeletons.}}
The state abstraction of TAMP inevitably prevents the task planners from accessing the detailed features of the environment that are possibly vital to the problem's solution, For example in Fig\,\ref{fig:toy_problem}, since the task planner receives no information from the symbolic initial state about the blockade of the taller body, thus it will probably generate \texttt{skeleton1} as the first attempt.
In AI planning research, this issue is commonly described as an \textit{incomplete domain description} \cite{weber2011planning,zhuo2013refining} in the sense that the task planner does not have enough domain knowledge to generate absolutely correct results.
To recover from such a deal end, the task planner in TAMP must provide alternative skeletons. Further, it must optimally select skeletons for further examination based on the binding search report from motion planning.

This paper proposes extended tree search for TAMP (\textit{eTAMP}) that is able to address the above challenges in a single framework with a simple pipeline~\footnote{The code is online available at \href{https://github.com/ttianyuren/eTAMP}{https://github.com/ttianyuren/eTAMP}}. In eTAMP, the first step (Sec.\,\ref{sec:topk-sk}) is to solve the task planning problem with a top-k planner and acquire diverse high-level plans. A skeleton space is build on these diverse plans for the following skeleton selection. In the second step (Sec.\,\ref{sec:extended-tree-search}), a decision tree is built with its first decision node for skeleton selection. From the second decision nodes on, a motion planner start binding search for each skeleton branch. After a preset number of roll-outs, eTAMP takes the tree branch of the highest value as the output plan. We summarize the eTAMP algorithm in Sec.\,\ref{sec:etamp}.
The main contribution of this work is twofold:
\begin{itemize}
    \item we propose a top-k skeleton planner based on generic top-k algorithms that generates diverse high-level plans in large task spaces;
    \item we propose an extended decision tree that models the skeleton selection under infeasible task skeletons and binding search in large motion spaces within the same optimal decision process.
\end{itemize}

We evaluate the proposed method on challenging robotic tasks defined in various domains, using both a 7-degrees-of-freedom (dof) robot and a 10-dof mobile manipulator. Our empirical results prove the ability of eTAMP to find feasible plans under various difficulties.

\section{Related Work}

Broadly speaking, TAMP contains also multi-modal motion planning problems that have been frequently approached as an optimization problem using logic geometric programming \cite{toussaint2015logic}, or multi-modal motion planning with motion-modes switches for various tasks \cite{kingston2020informing,mordatch2012discovery,mordatch2012contact}. However, these methods are designed for particular robot domains, e.g., desktop manipulation \cite{toussaint2015logic}, in-hand manipulation \cite{mordatch2012contact} and humanoid locomotion \cite{mordatch2012discovery}. They are applicable to neither problems with large action space such as the game of Hanoi Tower nor those with non-geometric actions. On the other hand, general-purpose TAMP systems generically use symbolic AI planners for  efficient problem solving in task spaces, where the relational language PDDL is used for the description of the symbolic domain and problem. A comprehensive review over integrated TAMP approaches can be found in \cite{garrett2021integrated}. Here we discuss only those that are closely
related with our method.

In in the earliest approaches such as \textit{aSyMov} \cite{cambon2009hybrid} and \textit{SMAP} \cite{plaku2010sampling}, the TAMP framework is more of a single-direction flow from task planning to motion planning. Based on the established links between symbolic descriptions and their geometric counterpart, high-dimension motion planning can be effectively guided by symbolic action plans. Nevertheless, these TAMP systems become less efficient when the problems are insufficiently constrained by symbolic descriptions and infeasible skeletons arise. By allowing action planners to validate preconditions of the
symbolic actions in the geometric space when computing action plans, TAMP methods such as \textit{FFRob} \cite{garrett2018ffrob} and \textit{PDDLStream} \cite{garrett2020pddlstream,garrett2018stripstream} strengthen the interplay between action planning and motion planning. These methods, however, require users to craft carefully the symbolic description that includes specifications of the geometric constraints in all high-level actions.

Without the explicit specification of geometric constraints, the TAMP system will expect more infeasible skeletons and a large motion space to search. Since the feasibility of a skeleton is ultimately evaluated via motion planning, the task planner must be able to take feedback from the motion planning results and react accordingly.
Approaches as proposed in \cite{srivastava2014combined}, \cite{dantam2018incremental} and \cite{shah2020anytime} incrementally refine the high-level representations using the
feedback from the low-level planning while searching for the motion bindings. Failures in motion planning are symbolized into logical predicates that are used to update the high-level models. Then new skeletons can be generated based on these updated models and they could possibly bypass those geometric failures. However, symbolization and expression of the geometric failures in high-level models are difficult when the low-level decisions are continuous. Therefore, it is a common practice for these methods to discretize some dimensions of the motion spaces that are considered to potentially contribute to the high-level models. This partial discretization of the motion space demands human expertise and makes the completeness of their planners questionable.

In this work, we build on current advances in TAMP and generic AI planning.
To integrate search in both large task spaces and large motion spaces while minimising human inputs, we explore a new method in this study.
Unlike the above-mentioned TAMP approaches, our method explicitly models the skeleton selection process. An optimal skeleton selection is achieved by (i) maintaining an explicit skeleton space and (ii) evaluating consistently the value of each skeleton.

We construct a skeleton space with various high-level plans by using a generic top-k planner as the task planner.
Top-k planning is one way of obtaining such a set, by finding a group of diverse solutions of size $k$. With a variety of candidate skeletons, it is possible to make a detour to avoid infeasible skeletons. Based on \textit{FastDownward} \cite{helmert2006fast,torralba2014symba}, \cite{speck2020symbolic} presents a complete top-k planner \textit{SYM-K} that scales efficiently to large sizes of $k$.

For value estimation of each skeleton, we rely on the back-propagation mechanism of MCTS from the binding search of this skeleton.
Specifically, we use \textit{PW-UCT} (Upper Confidence bounds for Trees with Progressive Widening) \cite{coulom2007computing,auger2013continuous,chaslot2008progressive}, to solve the sequential binding problem over large motion spaces.

\section{Preliminaries}

\begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{fig_enrich.png}
    \caption{\small An example implementation of OPTMS-EXPD. At each level, streams whose precondition is satisfied generate new optimistic objects. The enrichment of the state is not shown in this figure.}
    \label{fig:enrich}
    \vspace{-0.5cm}
\end{figure}

\noindent\textit{\underline{PDDLStream description.}}
PDDLStream \citep{garrett2020pddlstream,garrett2018stripstream} attempts to increase the universality of PDDL by incorporating \textit{streams} into PDDL operators in addition to actions. A PDDLStream task can be represented as a tuple $T_{stream}=\langle Objects,S,G,Actions,Streams \rangle$. $Objects$ is a finite set of objects associated to the task, e.g., \texttt{body1} and \texttt{region2}. $S$ and $G$ are the initial and goal state of planning task respectively, each of which consists a set of literals. For the operators, $Actions$ contain all actions that can be used to update the environment; $Streams$ are operators that give out new objects as black-box generators of any kind.
A skeleton $\pi_s$ composed of both actions and streams can be found as
\begin{align}\label{eq:5}
    &\langle \texttt{Sample-pose}(\texttt{body1},\texttt{region2}) \to \texttt{\#poseA},\nonumber\\ &\texttt{Plan-motion}(\texttt{body1},\texttt{pose1},\texttt{\#poseA)} \to \texttt{\#trajA}, \nonumber\\
    &\texttt{Pick-place}(\texttt{body1}, \texttt{region1}, \texttt{region2}, \texttt{\#trajA)} \rangle.
\end{align}
Objects marked by $\#$ (e.g., \texttt{\#poseA}) are generated by streams and they demand \textit{bindings} of concrete values during binding search.
These objects are described as \textit{optimistic} in the sense that they may not ever find their bindings under the geometric constraints.

\noindent\textit{\underline{Optimistic Expansion of Objects.}} In the PDDLstream description,
optimistic objects can be generated either at one stroke in the beginning or in incrementally across search rollouts \citep{garrett2018stripstream}. Here we take the first approach and summarize this optimistic enrichment procedure as $\#Objects,\#S=\text{OPTMS-EXPD}(Objects,S,Streams,level)$, as illustrated in Fig.\,\ref{fig:enrich}. $\#Objects$ and $\#S$ are the enriched objects and state respectively by applying $Streams$. For its detailed implementation we refer to \cite{garrett2018stripstream}.

\section{Top-k skeleton planning}\label{sec:topk-sk}

In task planning, we generate diverse skeletons via top-k planning.
Let $P_T$ be the set of all symbolic plans (possibly infinite) for a planning task $T$. The objective of top-k planning is to determine a set of \textit{k} different plans $\{\pi_1,\pi_2,...,\pi_k\}=P \subseteq P_T $ with the lowest costs for a given planning task \citep{speck2020symbolic}. We call a top-k algorithm \textit{complete} iff it could find the set of all plans as required. A standard top-k planner can be described as $P=\text{TOP-K}(Objects,S,G,Operators,k)$.

\subsection{Search for top-k action plans}
The planner firstly searches for the top-k action plans $P_a$ based on the optimistically enriched objects $\#Objects$ and initial state $\#S$. Those action plans are composed purely of actions.
\begin{equation}
    P_a=\text{TOP-K}(\#Objects,\#S,G,Actions,k)
\label{eq:top-k}
\end{equation}

\subsection{Search for top-k skeletons}
Then the streams that generate those involved optimistic objects $\#Objects \setminus Objects$ are retracted and integrated to the action plans. Finally we have the top-k skeletons $P_s$ which are composed of both actions and streams. Each of these skeletons only relies on the original objects $Objects$ and initial state $S$.

\begin{equation}
\begin{aligned}
    \pi_s=\text{TOP-K}(Objects,S,G_s(\pi_a,G),
    Actions \cup Streams,1)
\end{aligned}
\label{eq:stream_retrace}
\end{equation}

$Actions$ and $Streams$ constitute the operator set of this planning problem. Informally, by setting $k=1$, the top-k algorithm reduces to a classical PDDL planner.
To ensure that the sequences of actions maintain from $\pi_a$ to $\pi_s$, we add extra constraints to the goal state. By assuming $\pi_a=\langle a_1,a_2,...,a_n \rangle$, we define the updated goal state $G_s$ as below.
$(a_1\prec a_2)$ is a literal asserting that $a_1$ is the predecessor of $a_2$.

\begin{equation}
    G_s(\pi_a,G)=\{(a_1\prec a_2),...,(a_{n-1}\prec a_n)\} \cup G,
\label{eq:10}
\end{equation}

\subsection{Algorithm summary}

\begin{algorithm}
\DontPrintSemicolon
\KwInput{$Objs,S,G,Actions,Streams,k$}
 \For{$level \in [0,1,...,max\text{-}level]$}
 {
  $\#Objs,\#S=\text{OPTMS-EXPD}(Objs,S,Streams,level)$, \\
  $P_a=\text{TOP-K}(\#Objs,\#S,G,Actions,k)$, \quad see \eqref{eq:top-k}\\
  \If{$|P_a|<k$}
  {
  \textbf{continue for}
  }
  $P_s=\{\,\}$\\
  \For{$\pi_a \in P_a$}
  {
    $Operators=Actions \cup Streams$\\
    $\#G=G_s(\pi_a,G)$, \quad see \eqref{eq:10}\\
    $\pi_s=\text{TOP-K}(Objs,S,\#G,Operators,1)$, see \eqref{eq:stream_retrace}\\
    $P_s \leftarrow \{\pi_s\} \cup P_s$
  }
  \textbf{return} $P_s$
 }
 \caption{\small TOP-K-SKELETON} \label{alg:topk-skeleton}
\end{algorithm}

An overview of the above skeleton planning algorithm is shown
in Alg.\,\ref{alg:topk-skeleton}. The inputs of the algorithm include the
original initial state $S$, goal state $G$, available $Streams$ and $Actions$, and a desired number of skeletons $k$. The output $P_s$ is the list of the top $k$ skeletons.
The size of $\#Objects$ ramps up quickly with increasing $level$. To address this, in Alg.\,\ref{alg:topk-skeleton} we regulate the number of optimistic objects by progressively increasing $level$.
Here we choose the SYM-K algorithm as our top-k planning subroutines in \eqref{eq:top-k} and \eqref{eq:stream_retrace} due to its proved completeness and soundness  \citep{speck2020symbolic}. Accordingly we can derive the completeness property of our top-k skeleton planning algorithm.

\begin{property} Probabilistic completeness in the top-k skeleton planning.\label{property:1}
    Given a complete top-k planner, any potentially feasible skeleton will be contained by the result set of Alg.\,\ref{alg:topk-skeleton} as $k$ goes to infinity.
\end{property}

After applying Alg.\,\ref{alg:topk-skeleton} to the toy planning problem task (Fig.\,\ref{fig:toy_problem}), we get a feasible skeleton as shown in Table\,\ref{tab:skeleton_layer}.

\begin{table}
    \caption{\small An example skeleton to the toy problem in Fig.\,\ref{fig:toy_problem} with its operators grouped by tree node layers.} \label{tab:skeleton_layer}
\centering
\begin{tabular}{c|c}
    \hline
    \makecell{Layers} & \makecell{Operators}\\
    \hline
    \textbf{decision1} & \makecell[l]{$\texttt{Sample-pose(body2,region1)}$
    $\to \texttt{\#poseB}$}\\
    \hline
    \textbf{transition1} & \makecell[l]{$\texttt{Plan-motion(body2,pose2,\#poseB)}$
    $\to \texttt{\#trajB}$ \\
    $\texttt{Pick-place(body2,region1,region1,\#trajB)}$} \\
    \hline
    \textbf{decision2} & \makecell[l]{$\texttt{Sample-pose(body1,region2)}$
    $\to \texttt{\#poseC}$} \\
    \hline
    \textbf{transition2} & \makecell[l]{$\texttt{Plan-motion(body1,pose1,\#poseC)}$
    $\to \texttt{\#trajC}$ \\
    $\texttt{Pick-place(body1,region1,region2,\#trajC)}$} \\
    \hline
    \end{tabular}
    \vspace{-0.5cm}
\end{table}

\section{Tree search in the extended decision space}\label{sec:extended-tree-search}
Based on the top-k skeletons generated above, we must search for feasible concrete plans that are geometrically feasible and further find the optimal plan with the highest reward. To achieve this, firstly, we have to choose from the candidate skeletons (\textit{skeleton space}) the one that we would like to continue with in binding search (Sec.\,\ref{subsec:skeleton_selection}); secondly, we must search for concrete bindings of its symbolic variables (e.g., \texttt{\#pose12} in \eqref{eq:5}) in a \textit{motion space} (Sec.\,\ref{subsec:binding_search}). In this study, we define a reward function  \eqref{eq:reward_fun} as the optimization target for both skeleton selection and binding search. For a skeleton $\pi_i$ with $H_i$ symbolic variables to bind (\textit{binding horizon}), we have

\begin{equation}
r = p_t\left(\frac{1+d_\text{end}}{H_{i}}+\frac{p_m}{motionCost+1}\right)+r_\text{end}.
\label{eq:reward_fun}
\end{equation}

$d_{end}$ is the number of symbolic variables that have already found their feasible bindings, and $motionCost$ is proportional to the swept volume of the robot from its initial state to the terminal state. The first term in \eqref{eq:reward_fun} encourages the planner to avoid choices where less bindings are found. The second term makes the planner prefer choices with motions that have less occupation in the workspace. For the third term, $r_\text{end}=1$ when all bindings are successfully found, otherwise $r_\text{end}=0$. For the hyper parameters, we set $p_t=0.1$ and $p_m=1.0$.

\subsection{Optimal search in the binding space} \label{subsec:binding_search}

A skeleton describes logically a path
to the goal state. However, its geometric feasibility must be evaluated
along with the sequential binding of its symbolic variables to
concrete values. We describe the binding search problem as a Markov Decision Process (MDP) and address it as a classical finite-horizon stochastic optimal search problem.

We propose using PW-UCT to systematically explore this decision space. Since we have a mixtured motion space with both discrete and continuous decisions, we employ a UCT variant with progressive widening (PW) techniques \citep{coulom2007computing,auger2013continuous,chaslot2008progressive}. Its basic idea is to limit the number of visits for existing nodes artificially. When the value of the existing nodes is estimated sufficiently well, new nodes will be expanded to explore the unvisited regions of the decision spaces. At a decision node $z$, if $\text{PW-TEST}(z)$ is true, a new child (or binding decision) of $z$ will be sampled and thereby the tree will grow a new branch; otherwise, one of its existing children will be selected by UCB.

\begin{equation}
\text{PW-TEST}(z)=\floor{\text{visits}(z)^\alpha}>\floor{(\text{visits}(z)-1)^\alpha}
\label{eq:expandable-by-pw}
\end{equation}

In \eqref{eq:expandable-by-pw} index $\alpha$ is the corresponding PW constant for balancing expansion with evaluation \cite{auger2013continuous}. With a large $\alpha$, the planner will expand eagerly its skeleton space; when $\alpha$ is small, the planner will be reluctant to take new skeletons and will spend more time evaluating the existing ones.

The search tree of PW-UCT is structured with interleaved layers of decision nodes and transition nodes. We group our skeleton by these two node types as illustrated in Table.\,\ref{tab:skeleton_layer}. Decision nodes are responsible for the independent bindings (e.g., \texttt{\#pose21a} in \textbf{decision1}); while transition nodes decides on the dependent bindings (e.g., \texttt{\#traj211a} in \textbf{transition1}) and update the environment state (e.g., \texttt{Pick-place} from \textbf{transition1}). Since transition nodes contain sample-based generators (e.g., RRT \cite{lavalle1998rapidly} in \texttt{Plan-motion}), their resulting states can be different (see \textbf{state2.2} and \textbf{state2.3} in Fig.\,\ref{fig:tree}) even with the same starting state and the same binding decisions.

\subsection{Optimal search in the skeleton space} \label{subsec:skeleton_selection}

We model skeleton selection as a multi-armed bandit problem with the reward function of \eqref{eq:reward_fun}, and solve it via UCB1~\citep{auer2002finite}. With a UCB criterion, we are able to maintain an optimal balance between exploring new skeletons and exploiting existing skeletons with high rewards. The regrets of each skeleton selection are therefore kept to minimum.

Before any binding search, we have $d_{end}=0$, $r_\text{end}=0$, and $motionCost=0$. In this case, the bandit agent would prefer skeletons with small binding horizons. It is a reasonable behaviour in the absence of other heuristics, since less bindings  indicates not only less chance of failing in the binding search, but also less actions included in the skeleton. When some binding search results are available, this reward function takes more factors into consideration when evaluating a skeleton. It will prioritize skeletons that have been proved geometrically feasible (the third term), skeletons with high percentage of bindings found (the first term), and skeletons whose motion cost is low (the second term).

To ensure complete search in task planning, we should have $k$ in TOP-K-SKELETON in Alg.\,\ref{alg:topk-skeleton} sufficiently large.
When $k \rightarrow \infty$, a continuum-armed bandit instead of a multi-arm one should be used to model the extended root. Inspired by the solution to the continuous motion space, we use the progressive widening trick again at the decision node (noted as $e\_root$) for skeleton selection. As shown in \eqref{eq:expandable-by-pw}, if $\text{PW-TEST}(e\_root)$ is true, then a new skeleton is added to the skeleton space $P_s$, otherwise the bandit will continue searching the existing skeletons.

\subsection{The extended decision tree}

\begin{figure}
    \centering
    \includegraphics[width=0.46\textwidth]{extended_tree.png}
    \caption{\small The extended decision tree: an integration of optimal skeleton selection and binding search.}
    \label{fig:tree}
    \vspace{-0.5cm}
\end{figure}

Based on a given skeleton, we can build a decision tree for binding search as shown in the lower part of Fig.\,\ref{fig:tree}. The motion planner take a skeleton as the input and search for its bindings by PW-UCT. At each decision node (e.g., \textbf{d1}), the planner samples a binding for a symbolic variable (e.g., \texttt{\#pose21a}) and update the simulator correspondingly through a transition node (e.g., \textbf{t1.1}). If the resulting state is geometrically feasible (e.g., \textbf{state1.1}), the planner is able to continue binding the next symbolic variable (e.g., \texttt{\#pose12a}). Otherwise, a bad binding decision leads to a geometrically infeasible state (e.g., \textbf{state1.2}) and the current branch must terminate here.
Whenever a terminate node is created, it propagates its reward through its parents all the way back to the root of the current skeleton branch  \cite{coulom2006efficient}.

In this way, the value of selecting of that specific skeleton (e.g., \texttt{skeleton4}) is updated (orange arrows in Fig.\,\ref{fig:tree}) and it can be used by the multi-arm bandit in skeleton space (the upper part in Fig.\,\ref{fig:tree}). Further observation of Fig.\,\ref{fig:tree} reveals that the skeleton selection process is no more than an extended decision node before bind search and it can be readily included into the UCT structure. By having the bandit of skeleton selection as an extended root, we define an extended decision tree that is able to search in both the skeleton space and the motion space.

\subsection{Algorithm summary}

We can summarize the extended tree search algorithm in Alg.\,\ref{alg:tree_search}. It largely remains the structure of a standard PW-UCT algorithm. The children of the extended root node $e\_root$ that represents the skeleton space is initialized with empty set.

\begin{algorithm}
\DontPrintSemicolon
\KwInput{$P_s,t_{ts}$}
$new\_skeletons=P_s-e\_root.\text{CHILDREN}$\\
$e\_root=e\_root.\text{ADD-CHILDREN}(new\_skeletons)$\\
$node \leftarrow e\_root$\\
\While{$timeCost()<t_{ts}$}
{
    \While{$node$ is not terminated}
    {
        ADD-VISIT($node$)\\
        \eIf{PW-TEST$(node)$}
        {
            $node \leftarrow \text{EXPAND-NEW-CHILD}(node)$,
        }
        {
            $node \leftarrow \text{SELECT-CHILD-BY-UCB}(node)$,
        }
    }
    $\text{BACK-RPOPAGATE}(node)$\\
    \vspace{1.0mm}
    $node \leftarrow e\_root$\\
}
$\pi_c=e\_root.\text{BEST-CHILD}$\\
\textbf{return} $\pi_c$
\caption{\small EXTENDED-TREE-SEARCH}\label{alg:tree_search}
\end{algorithm}

The inputs of Alg.\,\ref{alg:tree_search} include the top-k skeletons $P_s$ from Alg.\,\ref{alg:topk-skeleton} as new children of the extended root, and a user-defined time budget $t_{ts}$. Its output is a single concrete plan $\pi_c$ that is the best child of the extended root in terms of branch value.
On ADD-VISIT$(node)$, $node$ will increase its visit number by 1. Meanwhile, the environment will be set to the initial state of $node$. By complying with UCB and PW criterion, a consistent value estimation of each node (e.g., \textbf{d1} in Fig.\,\ref{fig:tree}) is guaranteed.

\begin{property} Consistent value estimation in extend tree search.\label{property:2}
     The value estimation of each tree node will convergence to its real value as the search time goes infinite.
\end{property}

The above property can be perceived  straightforwardly via a recursive analysis from the leaf nodes to the root, we refer to \citep{auger2013continuous} for the detailed proof.
Based on the consistent estimation of decision value, a global convergence of the output $\pi_c$ to the optimal plan is expected.

\begin{property}Probabilistic completeness of extended tree search.\label{property:3}
     The optimal concrete plan within the given skeleton space (implied by $P_s$) can be found after $t_{ts}$ goes infinite.
\end{property}

\section{The eTAMP algorithm}\label{sec:etamp}
We introduce some techniques to make the proposed method more efficient in practice (Sec.\,\ref{subsec:incremetal_skeleton} and Sec.\,\ref{subsec:delay_binding}), and summarize the final algorithm (Sec.\,\ref{subsec:etamp}).

\subsection{Incremental skeleton space} \label{subsec:incremetal_skeleton}

In theory, a TAMP framework as presented in Fig.\,\ref{fig:tree} is capable to explore the all combinations of skeletons and their bindings when the skeleton space $P_s$ is exhaustive. However, we have found that the even for state-of-the-art top-k planners like sym-k, a large $k$ normally means significantly elongated planning time. To balance efficiency with completeness in task planning, we propose to incrementally expand the skeleton during search. We divide the whole TAMP into sessions with incremental skeletons.
In each session, a batch of new skeletons is added to the skeleton space. The TAMP system searches the current skeleton space for a given time period and then comes to the next session.

\subsection{Delayed binding of of new skeletons} \label{subsec:delay_binding}

By enabling knowledge sharing across skeleton branches, we can improve the overall planning efficiency.
Although the candidate skeletons are different from each other, they may share the same operator sequences at their initial parts. For example in Fig.\,\ref{fig:candidate_sk}, \texttt{skeleton1} and \texttt{skeleton3} have the same first high-level action \texttt{action1}. If the binding of \texttt{action1} in \texttt{skeleton1} is not found at the moment, there is no reason to start binding it in \texttt{skeleton3}. The binding of \texttt{skeleton3} should be delayed in this case so that the skeleton space can be kept as small as possible.
On the other hand, whenever a feasible binding is found for this operator in \texttt{skeleton1}, it should be shared with \texttt{skeleton3} and thus gives the binding search of \texttt{skeleton3} a warm start.

\subsection{Algorithm summary} \label{subsec:etamp}

\begin{algorithm}[h!]
\DontPrintSemicolon
\KwInput{$T_{stream},k_{batch},t_{ts},t_{d}$}
$i=1$\\
$P_s=\{\,\}$\\
$e\_root.\text{CHILDREN}=\{\,\}$\\
\While{$timeCost()<t_{d}$}
{
$k=k_{batch}\cdot i$\\
$P_s=P_s\,|\,\text{TOP-SKELETON}(T_{stream}, k)$, see Alg.\,\ref{alg:topk-skeleton}\\
$\pi_c=\text{EXTENDED-TREE-SEARCH}(P_s,t_{ts})$, see Alg.\,\ref{alg:tree_search}\\
$i=i+1$\\
}
\textbf{return} $\pi_c$
\caption{\small eTAMP}\label{alg:etamp}
\end{algorithm}

A serial combination of Alg.\,\ref{alg:topk-skeleton} and Alg.\,\ref{alg:tree_search} gives out the overall eTAMP algorithm, as summarized in Alg.\,\ref{alg:etamp}. It takes as input a PDDLStream problem description $T_{stream}=\langle Objects,S,G,Actions,Streams \rangle$, and three hyper-parameters: $k_{batch}$, $t_{ts}$ and $t_b$. $k_{batch}$ is the number of new skeletons added to the skeleton space in the next extended tree search session, and $t_{ts}$ is the time cost allocated to each session. $t_b$ limits the total planning time of eTAMP.
Given sufficiently large $t_b$, $k$ in Alg.\,\ref{alg:etamp} will grow to infinity, and the extended root will have all possible skeletons as it children (\textit{property \ref{property:1}}).
Meanwhile, as the visit number of the extended root increases, the resultant concrete plan $\pi_c$ will converge to the optimal one with respect to the reward function \eqref{eq:reward_fun} (\textit{property \ref{property:3}}).

\section{Empirical evaluation}
\label{sec:evaluation}

We empirically evaluate the proposed eTAMP algorithm in four domains: Kitchen, Hanoi Tower, Unpacking and Regrasping. Wherein Kitchen and Hanoi Tower are adapted from the framework-independent benchmarks for TAMP system proposed by \cite{lagriffoul2018platform}, and the other two are based on the existing robot hardware of our lab. We list the recognizable difficulties that  each task represents for testing the planner in Table\,\ref{tab:4}. In addition to those criteria listed in \cite{lagriffoul2018platform}, we add another dimension \textit{large motion spaces} to measure the difficulty in binding search. This criterion will be satisfied if the underlying motion planning problem of the domain requires substantial search effort. It applies to tasks with many bindings to be decided or some of their bindings have tight feasible spaces.

\begin{table}
    \caption{\small The difficulties reflected by the evaluation domains} \label{tab:4}
\centering
\begin{tabular}{c|c|c|c|c}
    \hline
    \makecell{Difficulty} & \makecell{Kitchen} & \makecell{Tower} & \makecell{Unpacking} & \makecell{Regrasping} \\
    \hline
    Infeasible task actions &  &  & \checkmark & \checkmark \\
    \hline
    Large task space &  & \checkmark &  &  \\
    \hline
    Large motion space* & \checkmark & \checkmark &  & \checkmark \\
    \hline
    Non-monotonicity &  &  &  & \checkmark\\
    \hline
    Non-geometric actions & \checkmark &  &  & \checkmark\\
    \hline
    \end{tabular}
    *An extra criterion in addition to those of \cite{lagriffoul2018platform}.
    \vspace{0.0cm}
\end{table}

 The Adaptive algorithm from \cite{garrett2020pddlstream} represents the best performance of existing PDDLStream methods, and it serves as a baseline in evluating eTAMP. The two algorithms share one internal simulator that is implemented with PyBullet \cite{coumanspybullet} for hosting the environment state. Both planners are terminated after a 300-second timeout for each of the three tasks. For eTAMP we set $k_{batch}=50, t_{ts}=250$. In the extened tree search (see Alg.\,\ref{alg:tree_search}),  The MCTS rollout policy is random and no heuristics is used to guide the search. PW-TEST (see \eqref{eq:expandable-by-pw}) takes $\alpha=0.26$ for regulating the growth of new branches. The performance of each algorithm is evaluated over 100 instances for each task. Whenever a feasible concrete plan is found, the algorithm is stopped and the computation time is calculated. These instances are diversely generated by randomly initializing the initial geometric state. It is noteworthy that both algorithms employ the same set of random stream generators for motion bindings, which have zero heuristics.

 \begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{fig_results.png}    \vspace{-0.5cm}
    \caption{\small The average time cost with std indicators of the TAMP methods in solving the evaluation tasks.}
    \label{fig:results}
    \vspace{-0.5cm}
\end{figure}

\subsection{Kitchen domain}

\begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{Kitchen.png}    \vspace{-0.5cm}
    \caption{\small Kitchen domain. Given an initial number of bodies to be  cooked, the mobile manipulator should cook by first placing the body on the sink for cleaning, and then place it on the stove for cooking.}
    \label{fig:kitchen_domain}
    \vspace{-0.5cm}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{Kitchen2.png}    \vspace{-0.5cm}
    \caption{\small The \textit{large motion space} of the Kitchen domain. The feasible space (the yellow zone) for the pose of coming bodies shrinks significantly by each placement. Binding search for these poses is challenging given zero heuristics.}
    \label{fig:kitchen_difficulty}
    \vspace{-0.5cm}
\end{figure}

Compared to the original Kitchen task in \cite{lagriffoul2018platform}, this domain reduces the complexity in task planning but meanwhile becomes more demanding to the motion planner. As shown in Fig.\,\ref{fig:kitchen_domain}, the mobile manipulator must "cook" a given number of food blocks initially placed on \texttt{table}. Food must be cleaned before it can be cooked. It can be cleaned when placed on \texttt{sink} and cooked when placed on \texttt{stove}. The metric decisions left to the motion planner is the body pose of each placement. The actions of \texttt{Clean} (via \texttt{sink}) and \texttt{Cook} (via \texttt{stove}) are non-monotonic from the robot's perspective. The main difficulty of this task lies in the tight stove region, where several bodies need to be placed. The search of the feasible pose for the newly coming body becomes exponentially challenging after each placement. In this way, this domain evaluates the planners' performance in \textit{large motion space}. As the planners are not provided with this potential congestion in their symbolic knowledge, they must search for the feasible decisions through trial and error. During binding search, the consistent value estimation of each decision is critical for this delayed-reward case.

We show the evaluation results in Fig.\,\ref{fig:results} where Kitchen2, Kitchen3, Kitchen4 indicate three different settings with the number of bodies to be cooked equals to 2, 3, 4, respectively. eTAMP scales better than Adaptive to more complicated settings and even has some chance solving the problem in Kitchen4. More specifically, in terms of the successful rates, both methods achieved 100\% for Kitchen2. eTAMP achieved 100\% and 60\% for Kitchen3, Kitchen4, respectively, while Adaptive achieved 36\% and 0\%.

\subsection{Hanoi Tower domain}

\begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{hanoi.png}
    \caption{\small Hanoi Tower domain. The robot must move all discs from \texttt{peg1} to \texttt{peg3} without causing any collision in motion spaces while complying to the game rule in task spaces.}
    \label{fig:hanoi_domain}
    \vspace{-0.5cm}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{hanoi2.png}
    \vspace{-0.5cm}
    \caption{\small The \textit{large motion space} of the Hanoi Tower domain. The feasible grasp direction (the yellow zone) is small compared to the whole decision space. Binding search for these poses is challenging given zero heuristics. The motion planner has to bind \texttt{\#graspDir1},\texttt{\#graspDir2},...,\texttt{\#graspDir8} to ground values (degrees) for the task completion.}
    \label{fig:hanoi_difficulty}
\end{figure}

This domain remains mostly same to its original version expect that here only one arm of the PR2 robot is allowed to manipulate (Fig.\,\ref{fig:hanoi_domain}). A stack of three discs of different sizes must be relocated to a target pole via a intermediate pole while obeying the game rule that the upper disc should always be smaller than the lower one. After generating a skeleton in the \textit{large task space}, the motion planner is tasked to do binding search for the grasping direction of each pick-place operation. Due to the confined work space and joint limitations, the robot must search carefully this \textit{large motion space}.

As shown in Fig.\,\ref{fig:results}, eTAMP got a successful rate of 99\% in the evaluation while Adaptive got 0\% and could not give a solution within the time limitation. We attribute the poor performance of Adaptive in this domain to the tight decision space in binding search. As shown in Fig.\,, the feasible binding area is small compared to the large search space ($[-\pi,\pi]$ in this example) due to the obstruction of nearby entities and the kinematic configuration of the robot arm. The robot has to make eight successive decisions like this to complete the task. Thus this domain is quite challenging to TAMP methods that are not dedicated to optimize the exploitation-exploration behaviour in motion planning such as Adaptive.

\subsection{Unpacking domain}

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig6.png}
    \caption{\small The 3-body Unpacking task. To reach the green body, taller bodies must be relocated by the robot at first.}
    \label{fig:unpacking}
\end{figure}

This task comes directly from the motivation example of Fig.\,\ref{fig:1}. When more than one body is involved in the scene, the problem becomes challenging since the task planners are not informed of the geometric constraints, as imposed by the taller red body in Fig.\,\ref{fig:toy_problem} (\textit{infeasible task actions}). In addition the 2-body scenario (Unpack2), we also tested the TAMP algorithms in a 3-body scenario (Unpack3) as shown in Fig.\,\ref{fig:unpacking}, where two taller bodies must be relocated before the target one can be reached.

Both methods solved Unpack2 and Unpack3 with a successful rate of 100\%. However, when look into the details in Fig.\,\ref{fig:results}, the two methods showed different characters. When motion planning is simple as the Unpack2 setting, eTAMP cost more time than Adaptive since it has to generate the top-k skeletons at the first place while most of them are unnecessary in this case. However, in Unpack3, when the the motion planning space gets larger (though not as large as the the other evaluation domains), eTAMP gave better performance due to its more efficient binding search.

\subsection{Regrasping domain}

\begin{figure}
    \centering
    \includegraphics[width=0.49\textwidth]{regrasp.png}
    \caption{\small Regrasping domain. The only way the robot could move the cuboid body from the drawer to the shelf is by regrasping it with a different direction after taking it from the drawer.}
    \label{fig:regrasp_domain}
    \vspace{-0.5cm}
\end{figure}

As illustrated in Fig.\,\ref{fig:regrasp_domain}, the robot must transport the red block from the drawer to the shelf, where it should still be placed upright. After each displacement, the location of the block must be measured by a camera. We have \texttt{locate-object} as a \textit{non-geometric action}. Due to the geometric constraints of the environment, the robot cannot move the block to its target area directly without regrasping it from a different direction.
The robot can choose from 5 directions to grasp the block: along the normal vectors of the top surface and four side surfaces. The block at its initial pose is limited to top grasping by \texttt{drawer}, while it must be grasped from the side when being placed on \texttt{shelf}, as depicted in Fig.\,\ref{fig:regrasp_domain}. This domain is difficult for task planning since a regrasping behavior must be composed. Otherwise, the problem cannot be solved (\textit{infeasible task actions}). Moreover, this task is geometrically challenging. Even if a correct skeleton is given, the motion planner must search the hybrid decision space (discrete grasping directions and continuous body poses) for bindings (\textit{large motion space}).

Fig.\,\ref{fig:results} shows eTAMP in this challenging task performs better than Adaptive. eTAMP presented a successful rate of 86\% compared to that of 22\% from Adaptive.

\subsection{Summary}
In the above experiments, we evaluate the time cost of the considered TAMP algorithms for finding the first feasible plans. Optimality (e.g., motion cost) of these plans is not considered in this study.
Evaluation results show competitive performance of eTAMP in solving challenging TAMP problems as summarized in \cite{lagriffoul2018platform}. We have to admit that most state-of-the-art TAMP methods such as Adaptive is satisfying in solving tasks with \textit{infeasible task actions} and \textit{large task space}, as shown in the Unpack domain in Fig.\,\ref{fig:results}. On the other hand, the unique tree search in the extended decision space makes eTAMP especially efficient when the motion space gets large and existing binding search practices start to suffer, which is proved by the experiments with the Kitchen domain, the Hanoi Tower domain and the Regrasping domain.

\section{Conclusion}
\label{sec:conclusion}

We propose eTAMP as a general-purpose planner of robot manipulation tasks with long horizons that demand symbolic sequencing of operators and binding search of motion parameters under geometric constraints.
Similar to other general-purpose TAMP frameworks, eTAMP relies on its internal symbolic planner to deal with the \textit{large task space} and \textit{non-geometric actions}. What makes it unique is that it derives its capability of addressing the \textit{infeasible task actions} from the diverse backup skeletons generated by a top-k planner and an optimal selection process of those skeletons. By modeling the binding search as MDPs, eTAMP utilizes PW-UCT to find ground values for the symbolic variables in skeletons and thus it is more prepared for the \textit{large motion space} that is ubiquitous in realistic robotic manipulation.

redpajama_set_name: RedPajamaArXiv