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Citizen participation could leverage public action to improve access to water in remote areas and address second-string subjects such as sanitation. However, this still very incantatory notion with its variable configurations first needs to be empirically explored and defined if it is to have the
The end of apartheid and Nelson Mandela's election as President of the Republic turned a page in the history of South Africa. In 1994, some 60,000 (white) farmers held around 87 million hectares of land, while 14 million (Black) South Africans confined to the homelands shared the remaining 13
Weather and seasonal forecasts give African farmers the information they need to prepare for climate shocks and change their practices.These changes are generally economically beneficial. Yet consideration of the business model, forecast dissemination institutions and target users is key to service
It's a big boost for small businesses and entrepreneurs. To help support and finance African start-ups, AFD is launching a new €15 million seed fund. It's part of a growing commitment to expanding the continent's digital ecosystem
The "Energy Access in the G5 Sahel Countries" Conference is the first edition of an annual meeting organized by the Energy Group of the Sahel Alliance, which aimed at strengthening the coordination of the various actors and contributing to experience sharing and innovation. Coordinated by AFD in
The sanitation challenge in Mauritania
In Mauritania, only 15% of the rural population has access to sanitation. As part of the Sahel Alliance, AFD and the European Union are supporting the Mauritanian authorities to raise awareness of good practices. With the help of an NGO, in the south of the country, village hygiene committees have
Inequality trends in South Africa: A multidimensional diagnostic of inequality
This report on inequality trends in South Africa is a joint publication produced by Statistics South Africa (Stats SA) in partnership with the Southern Africa Labour and Development Research Unit (SALDRU) based in the School of Economics at the University of Cape Town and the Agence Francaise de
Minka Lake Chad Initiative
The violence linked to the Boko Haram crisis has had an impact far beyond the birthplace of the movement in northeast Nigeria, its combat zones and the areas to which its fighters have withdrawn. The multidimensional consequences of this crisis have affected the entire sub-region of the countries
Minka CAR Initiative
The Central African Republic (CAR) is experiencing a situation of chronic conflict, with militant activity by armed groups spreading over a large swath of the country, including violent attacks against civilian populations. The situation is volatile and made further complex by institutional and
The security, humanitarian, and sociopolitical situation in the Sahel has continued to deteriorate since the 2012 crisis in Mali, with a significant increase in conflict hotspots. More than one million people, according to OCHA reports, have been forcibly displaced in the G5 Sahel countries, due to

redpajama_set_name: RedPajamaCommonCrawl


Enquiry from Online Galleries regarding "Two Sèvres style porcelain and gilt bronze vases"
These Sèvres style vases are elegant works of decorative art, which have been finely painted, gilded and mounted in gilt bronze (ormolu). The vases are designed in a graceful Rococo style, which was characteristic of porcelain goods produced by the Sèvres factory in the 18th-Century. Crafted in the late 19th-Century, these vases are exquisite revival style works, which will add vibrancy and beauty to an interior.
The porcelain vases feature ovoid bodies, with waisted necks, which are covered by domed lids with gilt bronze egg-and-dart edges, and pineapple finials. The lids and necks are painted navy (or 'bleu Sèvres) and decorated with gilt cartouches, scrollwork, stylised foliage, flowers and trophy motifs. On their fronts, the vase bodies feature Rococo style paintings of young lovers in garden settings, and their reverses are decorated with landscape paintings. These pictures are set within wonderfully-ornate gilt frames, against navy grounds. Each vase is fitted with two gilt bronze handles, which terminate in classical masks. The vases stand on splayed navy feet, decorated with gilt stylised foliate motifs. They are set on square gilt bronze bases, which have shaped sides and canted corners and are ornamented with leafy forms.


text:
Q: Div is positioned lower in Firefox than in other browsers I've got a cart drawer that slides in from the side and multiple divs in it for products. One of the divs is positioned lower in Firefox and it overflows its container but it's all fine in other browsers (Chrome, Opera, IE, Edge). I can't tell what causes it since I don't even have any positioning done on it other than a margin-left of 10px. Can anyone help?

A: Float your cart image to the left
header .cart-container #drawer-products .product-elements {
float: left;
}

and then clear this div by adding float left and width 100%
header .cart-container #drawer-products #drawer-indiv-product {
    border-bottom: 1px solid #e0e0e0;
    padding-bottom: 10px;
    height: 80px;
    float: left;
    width: 100%;
}

adding these changes will make both firefox and chrome carts look the same

redpajama_set_name: RedPajamaStackExchange


text:
Bold burglar startles Spokane Valley family
Kyle Simchuk
Updated: December 19, 2019 11:52 AM
by Kyle Simchuk
SPOKANE VALLEY, Wash. — The Spokane County Sheriff's Office believes they are close to identifying a woman who allegedly walked into a Spokane Valley house while the family was home.
Eric Sewell and his wife were in the backyard of their home near the 14900 block of East Broadway on the morning of April 22 – their nine-year-old son was inside watching T.V.
Sewell noticed a white car pull into his neighbor's driveway. He had no idea the female passenger had exited the car and entered his home through an unlocked front door.
Sewell's son, Aiden, 9, was playing videogames with a friend and thought the woman was there to see his parents. Aiden said she went into his mom's bedroom and spent a few minutes inside the home. He became suspicious and yelled for his parents when the woman walked out the door with his mom's purse.
"My son came running out and saying 'someone had taken mom's purse!'" Sewell said. "I didn't think it was true, you know, who was going to walk into someone's house on a Sunday afternoon and steal stuff out of their bedroom."
Sewell chased after the woman but she managed to get away with several items including electronics, car and house keys, his wife's purse, and several credit cards.
Spokane County Sheriff's deputy Mark Gregory said the victim's credit cards were used at several businesses. The woman using them was caught on at least one store's security cameras.
The Sheriff's Office is investigating the burglary, but Sewell said he got a call on Monday from the Spokane Police Department, saying they recovered some of his stolen property from a woman arrested during a residential burglary.
The Sheriff's Office is still investigating to determine if the woman arrested by SPD is the same woman that entered Sewell's home.


text:
HEALTH CARE REFORM BILL HR 3200 PDF
So, is there anything that can be done to fix HR so that it would provide affordable universal health care coverage without increasing federal deficits or halting the recovery from the recession? The answer is that major changes—some paralleling those in the Wyden-Bennett Healthy Americans Act—are needed in four areas of the bill, those relating to the proposed insurance exchanges, the individual mandate, Medicare, and costs and financing. The proposed insurance exchanges should be redesigned to maximize the size of the resultant pools and to achieve the benefits of price-competition. Insurers should be required to offer "best value" to the exchanges -- with exchange participation a requirement for selling any insurance -- to discourage "cherry picking" outside the exchanges through direct marketing to selected employers. Basic coverage should be set by a board independent of Congress to minimize the impact of provider lobbying. Insurers, in turn, should be protected from extreme adverse selection, through exchange-sponsored reinsurance or risk-adjustment.
Author: Yonos Fenrirn
Country: Algeria
Uploader: Kajimuro
Congressional Budget Office is a non-partisan organization that analyzes the effect on the federal budget of proposed and existing legislation on behalf of the Congress. The cutoff changes to twenty or fewer employees the next year. The legislation does not specify any further phases, leaving that up to the officer to decide. Employers that currently offer insurance have a five-year grace period after the act begins before they would be subject to the standards.
Individuals would be free to purchase their own private insurance, or work with the public option, in this period and afterward. It will consist of 9 more individuals who are not federal employees that are appointed by the President of the United States. It will also consist of 9 members who are appointed by the Comptroller General of the United States. Also, up to eight more members will be appointed in even numbers by the President of the United States who are federal employees and officers.
Each member of the committee will serve three year terms. Debate and controversies[ edit ] Main article: Health care reform debate in the United States Reimbursement for counseling about living wills[ edit ] One often-cited provision of the un-passed bill would have authorized Medicare reimbursement for physicians who provide voluntary counseling about such subjects as living wills. Boustany, a heart surgeon, said the end-of-life legislation was a "good medical practice".
Bush was President. Rationing exists now, and will continue to exist with or without health care reform. I have received a large amount of high-quality treatment without which I would not have survived. He has written: When my father was dying, my mother and brother and I had to decide how much treatment to pursue. This may then lead to a situation where most people end up being covered by the public insurance option.
The Lewin Group , a research firm that is part of a subsidiary of UnitedHealth Group but is run independently, [52] has estimated that over million people would join the public plan if it were structured like Medicare , which would then make it the dominant insurer. The health insurance subsidy is available to anyone with a qualifying level of income buying insurance from the exchange regardless of whether they choose a public or private plan.
The Service Employees International Union SEIU , a labor union, has been accused by opponents of the reform bill of busing paid operatives into town halls to demonstrate in support of the measure. The group denies the accusation. He argued that, as a result, an odd but potent political alliance has emerged with Republicans arguing to protect the existing Medicare program despite its position historically which has been to oppose Medicare as an entitlement.
Orszag , the then director of the CBO , argued in June that the Medicare program as currently structured is unsustainable without significant reform, as tax revenues dedicated to the program are not sufficient to cover its rapidly increasing expenditures.
He argued that it is necessary to cut wasteful spending which is known to exist over-testing, no IT, lack of co-ordination, hospital re-admissions in order to cut costs in order to protect Medicare in the future and cut the projected national deficit. It reduces projected future increases in Medicare spending such as inpatient hospital service payments and ambulatory care payments that would otherwise undergo annual re-adjustments.
Republicans have stated that there is nothing in the bill to enforce this. Michael M. Honda, are trying to change those requirements. He has argued that the restriction "will only add to uncompensated care costs and costly emergency room visits.
Costs due to such visits will be shifted and distributed among all those who have been mandated to carry insurance. With skyrocketing health care costs, legislators should do all that we can to contain costs for working American families".
After rejecting Democratic Rep. Although the group gets funding from the drug lobby PhRMA as well as from the Service Employees International Union , it does not disclose this fact in the ads themselves.
The vice chairperson of PhRMA has disputed the allegation and referred to the campaign as completely "transparent".
EZW ALGORITHM PDF
The University of Chicago The Law School
So, is there anything that can be done to fix HR so that it would provide affordable universal health care coverage without increasing federal deficits or halting the recovery from the recession? The answer is that major changes—some paralleling those in the Wyden-Bennett Healthy Americans Act—are needed in four areas of the bill, those relating to the proposed insurance exchanges, the individual mandate, Medicare, and costs and financing. The proposed insurance exchanges should be redesigned to maximize the size of the resultant pools and to achieve the benefits of price-competition. Basic coverage should be set by a board independent of Congress to minimize the impact of provider lobbying. Insurers, in turn, should be protected from extreme adverse selection, through exchange-sponsored reinsurance or risk-adjustment. A public plan option should be implemented only in states where insurers fail to control the premium rates offered through the exchange.
CONFIGURATION MODEM ZTE DJAWEB PDF
Twenty-six Lies About H.R. 3200
Congressional Budget Office is a non-partisan organization that analyzes the effect on the federal budget of proposed and existing legislation on behalf of the Congress. The cutoff changes to twenty or fewer employees the next year. The legislation does not specify any further phases, leaving that up to the officer to decide. Employers that currently offer insurance have a five-year grace period after the act begins before they would be subject to the standards. Individuals would be free to purchase their own private insurance, or work with the public option, in this period and afterward.
BHAJ GOVINDAM SANSKRIT PDF
Can HR 3200 be fixed?
COUPERIN LE ROSSIGNOL EN AMOUR PDF
BULLINGER APOCALYPSE PDF
ANTIHYPERTENSEURS CENTRAUX PDF
ADVANCED PYQT4 TUTORIAL PDF
ABRAHAM SILBERSCHATZ DBMS PDF
ELOGIO DEL AMOR BADIOU PDF
BT134 DATASHEET PDF
ENSAIOS RACIONALISTAS CIRO FLAMARION CARDOSO PDF


text:
Q: Rename header of table ClosedXML I am creating a workbook with a worksheet and a table. Afterwards I want to change the title of the header for each column. I have already tried different ways, but when I open the xmls file, excel shows an error message(after pressing repair file it opens). Maybe someone can give a hint. Here is a sample where I produce 2 files, one opens and the other has problem. I am using the latest version of the lib:
public class Test
{
    public string Test1 { get; set; }
    public string Test2 { get; set; }
}

public void MyTest()
{
    List<Test> testList = new List<Test>
    {
        new Test{Test1 = "T1",Test2 = "T2"},
        new Test{Test1 = "T1",Test2 = "T2"}
    };

    var wb1 = new XLWorkbook();
    var ws = wb1.Worksheets.Add("Mysheet");
    ws.Cell(1, 1).InsertTable(testList);
    wb1.SaveAs(@"C:\Test\Test1.xlsx");

    var wb2 = new XLWorkbook();
    var ws2 = wb2.Worksheets.Add("Mysheet");
    var tb2 = ws2.Cell(1, 1).InsertTable(testList);
    const string newHeader = "TestNew";
    for (int i = 0; i < tb2.Fields.Count(); i++)
    {
        tb2.Field(i).Name = string.Format(
            "{0} {1}",
            newHeader,
            i
            );
    }
    wb2.SaveAs(@"C:\Test\Test2.xlsx");
}

A: There seems to be a bug in ClosedXML. When you change Field(...).Name it only changes the displayed value of the cell with the column header but not the field name in the actual table code. (You can check that by opening Test2.xlsx as a zip file and look at xl\worksheets\sheet.xml and xl\tables\table.xml.)
Here is a discussion of that bug. The author of ClosedXML claims that it is fixed but I tested it with the latest version and still got the bug.
You should post there and clarify with the author.

A: I have contacted them and it seems that they fixed this bug in the source code but not in the release. Thank you very much for your interest on this question.


Deliverable 2.1 "Scenarios, Use cases and Requirements Deliverable"
Deliverable 2.3 "Report on SPECIFI Methodology Workshop"
This documents provides a brief description of the workshop organized as part of task 2.2 Living Lab Methodological Approach.
DELIVERABLE 2.5 "Final set of use cases"
Deliverable 3.1.1 "Intermediate Conceptual Architecture Blueprint for the European Creative Ring"
The aim of this deliverable D3.1.1 is to provide the "blueprint" of the European Creative Ring Architecture (ECRA).
deliverable 3.1.2 "Final Conceptual Architecture Blueprint for the European Creative Ring"
The aim of this deliverable D3.1.2 is to provide the final "blueprint" of the European Creative Ring Architecture (ECRA).
DELIVERABLE 3.2 "Technical specification of scenarios"
This deliverable aims to collect technical requirements form Pilots in view of next WP3 activity, target to define the European Creative Ring (ECR) Architecture definition and realizations.
DELIVERABLE 3.4 "Adaptation Requirements to the Platform"
This deliverable assesses the adaptation requirements to platforms and use cases in order to allow a replication or an extension through interpiloting activities or exchanges through Creative Hubs.
This deliverable describes the early planning for the adoption process of services in the city.
Deliverable 4.4 "Co-producing Creative Industries applications & Apps for Kortrijk events"
DELIVERABLE 4.6 "Integration of Kortrijk Creative Ring Into the European Creative Ring Architecture"
This document describes the first interpiloting activities involving the Kortrijk pilot, focusing on the adaptation requirements that are needed specifically for each interpiloting activity.
The objective of WP5 is to organize and follow trainings to instruct the different stakeholders on how to use the Distributed Real Time Cultural media platform.
DELIVERABLE 5.6 "Integration of Barcelona Creative Ring Into the European Creative Ring Architecture"
The pilot in the Barcelona Hub is focused on the development and testing of a Digital Media Platform.
This deliverable describes the early contents ready for services experimentation in the Trento Piloting phase of the SPECIFI project and the process of their definition.
DELIVERABLE 6.6 "European Creative Ring Testing - Trento"
The Trento Pilot is involved in defining and organizing interpiloting actions as the first step of the European Creative Ring Architecture.
Deliverable 8.1 "Service Customisation and Adaptation Framework"
Deliverable 8.2 "Abstraction Layer for Service Management and Inter-pilot Scenarios"
D8.2 elaborates on object-level models for the detailed representation of the platforms considered for piloting activities and updates models for the rest framework components (i.e.
DELIVERABLE 8.4 "Service provisioning and adaptation, solutions and evaluations"
D8.5 concludes WP8 work on inter-piloting and provides assessment of the implemented procedures based on the respective inter-piloting scenarios evaluation findings.
Deliverable 9.2 "Dissemination Materials Including Website"


text:
\section{Introduction}

Item picking arises in many robot manipulation applications. It involves the integration of perception and planning for recognizing the target item and then computing the motion of a robot arm for picking it. Clutter, however, can significantly complicate the challenge as it introduces occlusions and partial views.  It reduces the fidelity of object recognition and introduces uncertainty, both for the target item as well as surrounding objects. One solution - given access to an RGB-D sensor - is to compute a picking path which does not collide with the point cloud. In clutter, however, considering only the visible point cloud frequently results in collisions as it does not include the back side of objects, which may be close or attached to the target item.

\vspace{-0.03in}
\subsection{Setup given Uncertainty in Perception}
\vspace{-0.02in}
This work focuses on the case where models of objects are available but it is unknown which of these objects are present in the scene except the target item. Given object models, object recognition and 6D pose estimation algorithms allow to identify which objects are present and their poses. Many 6D pose estimation algorithms \cite{Narayanan:2017aa, Mitash:2018aa, xiang2017posecnn} depend on point cloud registration
\cite{Mellado:2014aa}. This process first generates pose hypotheses for the object, which are then scored on how well they align with the observed point cloud.  They typically return the most likely pose hypothesis.  This process, however, ignores the effects of clutter, which introduces uncertainty in pose hypothesis generation and point cloud alignment. Ambiguities arise due to occlusions as well as imperfect learning-based prior models. For instance, when training only over simulated data, which is often a necessity as it scales
better over many object models.

\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{figures/intro_rui.png}
\vspace{-.2in}
\caption{Left: An RGB image for a scenario considered in
  this work. The target ``Jell-o'' object is located between and in
  close proximity to other objects. Center: Point cloud obtained from
  the RGB-D sensor highlighting the occlusions and partial object
  views. Right: Example output of pose estimation returning a discrete
  set of poses for objects in the scene.}
\label{fig:uncertain scene}
\end{figure}

Experiments in this paper show that using only the most likely
pose estimate for each surrounding object frequently results in
collisions. The idea is to consider a discrete set of pose hypotheses
per object and define the likelihood for each hypothesis given how
well they match with the point cloud. This gives rise to a discrete
distribution of object poses. Figure \ref{fig:uncertain scene} gives a
real scene example and uses 6D pose estimation based on prior work \cite{mitash_ijrr} to define a discrete distribution of object poses.  Then, the planning problem is to compute a path of low collision risk that attaches the arm to the target given this discrete pose distribution and the likelihood of each object being in the scene.

\begin{figure*}[ht]
  \centering
  \includegraphics[width=0.95\textwidth]{figures/perception_pipeline.png}
  \vspace{-.1in}
\caption{ Perception pipeline developed to return the likelihood of each
  object existing in the scene and a discrete distribution of object
  poses.}
  \label{fig:perception_pipeline}
\end{figure*}

\vspace{-0.01in}
\subsection{Relation to the Motion Planning Literature}
\vspace{-0.02in}

Planning under uncertainty is often formulated as a Partially
Observable Markov Decision Process (POMDP) \cite{Kaelbling:1998aa},
where a solution is a policy.  Finding an optimal policy can be
intractable \cite{papadimitriou1987complexity}, which motivates
approximations, such as computing a plausible open-loop plan and
updating it as more information is acquired
\cite{Platt:2010aa}. Updating the scene, however, can be
computationally expensive and, for the considered task, new
observations do not necessarily provide additional information. This
motivates open-loop planning for the safest path, which does not consider future observations, such as conformant probabilistic planning ({\tt CPP}) \cite{Taig:2013aa}. {\tt CPP} approaches have been used in
robotics task such as rearrangement under uncertainty
\cite{dogar2012planning, koval2015robust, anders2018reliably}.  Recent
work formalizes manipulation under uncertainty as the
blindfolded robot setting \cite{saund2019blindfolded} where the
obstacles are only sensed through contact. A pick-and-place system has been designed \cite{zeng2018robotic} to enable manipulation on novel objects with little prior knowledge. The current paper has the objective of finding safe, open-loop solutions. It focuses on discrete distributions for the presence of collision volumes and also tackles the case where the target itself is uncertain.

A heuristic way to achieve safety is to stay sufficiently away from
obstacles by growing the robot's shape by an uncertainty bound
\cite{Bry:2011aa}. If the obstacles' geometry is uncertain, the area
around estimated obstacles can be expanded into a shadow whose size
depends on uncertainty \cite{lee2013sigma}. Often the model of uncertainty assumes
a continuous Gaussian probability distribution
\cite{Park:2016aa,Sun:2016aa}.  Recent work computes obstacles geometric bounds with only partial shape information, assuming Gaussian distributed faces \cite{axelrod2018provably,
  axelrod2018hardness}. There has not been much prior work, however,
which focuses on discrete sets of object poses, which can be an
effective way to model multi-modal distributions.

\vspace{-0.03in}
\subsection{Contributions}
\vspace{-0.02in}
{\bf A.} This paper proposes a perception pipeline to predict object
existence in a scene and return the corresponding pose hypotheses with
associated probabilities on top of modern 6D pose estimation algorithms \cite{mitash_ijrr}. It integrates this perception output with a planning approach to maximize the probability of finding collision-free and successful picking paths.

{\bf B.} This paper identifies the connection between planning under
discrete models of uncertainty with failure-explanation planning problems, such as Minimum Constraint
Removal ({\tt MCR}) problems \cite{hauser2013minimum,
hauser2014minimum},
which are known to be computationally hard. While typical motion planning assumes a
collision-free solution can be found, tasks considered
here can result in no obvious collision-free solution. For instance,
if all possible object poses are avoided, then the target item is not
reachable. {\tt MCR} paths minimize the number of constraints to be removed to admit a constraint-free solution
\cite{hauser2014minimum, Erickson2013A-Simple-but-NP,
  krontiris2015computational}. The planning challenge of this work can
be seen as a stochastic version of {\tt MCR}, where instead of
minimizing the number of constraints, the
objective is to minimize the sum of the constraints' weights, i.e.,
the probabilities of the objects occupying poses along the solution
path. In this way, this work promotes the use of failure-explanation
planning in solving planning problems under uncertainty.

{\bf C.}  Experiments have been performed in simulation and with
real data in different setups (table or
shelf) and scenarios (clutter, narrow
passage, an ``arch'' of objects).  The experiments show the importance of considering multiple object poses in contrast to most
likely pose alternatives and
the benefits of the
stochastic formulation of {\tt MCR} proposed here, which is more
effective than a conservative adaptation of {\tt MCR}, which avoids all
possible object poses.

\section{Problem setup and notation}
\label{Problem setup and notation}

\textbf{Path Robustness.} The robustness of a path in this paper is
defined based on two aspects:

1) \textit{Minimum collision probability with objects:}
The scene will be re-sensed and replanning is performed if a collision occurs. Thus, a path with minimum collision probability reduces overall execution time to complete a task.

2) \textit{Maximum probability of reaching the target item:} Since the
target $O_t$ also carries uncertainty, a safe path may end up having low probability to pick the object, which necessitates replanning. Therefore, maximizing the probability of reaching the target object is also important for task completion.
\vspace{-0.2in}
\begin{definition}
    \label{C-space Definition}
    ($C$-space): The configuration space ($C$-space) $\mathbb{C}$ of
    the robot arm is the set of all arm
    configurations. $\mathbb{C}_{p}$ is defined as the set of arm
    configurations, which end up in collision with an object pose $p$.
\end{definition}
\vspace{-0.15in}
\begin{definition}
    \label{Goal configurations}
    (Goal configurations): $\mathbb{Q}_{goal}$ is a set of
    configurations where the arm can pick the target object at
    poses $p_t^j$.
    $\mathcal{T}=[1,\dots,K]$ is the set of indices of
    all $K$ target poses.
    Each goal configuration $q_g \in
    \mathbb{Q}_{goal}$ is associated with a set $J(q_g) \subseteq
    \mathcal{T}$ indicating which target poses $q_g$ can pick. Then,
    the probability that a path $\pi$ from the initial configuration
    $q_s$ to any goal configuration $q_g$ leads to a successful picking
    of $O_t$ is $Pr(q_g) = \sum_{j \in J(q_g)}
    Pr(P_t^j)$, i.e., equal to the probability that the target $O_t$
    is at one of the poses $q_g$ can pick.
\end{definition}
\vspace{-0.12in}
\begin{definition}
    \label{Survivability Definition}
    (Survivability of a path) A path $\pi: [0, 1] \rightarrow
    \mathbb{C}, \pi(0)=q_s, \pi(1) \in \mathbb{Q}_{goal}$
    \textit{survives} an object $O_i$, if it does not collide with
    $O_i$. The \textit{survivability} of a path $\pi$, denoted as
    $S_{\pi}$, is the probability that $\pi$ survives all the objects.
\end{definition}

Define $E_i$ as the event that $\pi$ collides with object $O_i$ and $\overline{E_i}$ its
complementary event. Then, $E_i^j$ is defined as the event that $\pi$
collides with object $O_i$ when $O_i$ is at pose $p_i^j$.  Then $E_i =
\bigcup_{j=1}^{K} E_i^j$. The events that $O_i$ appears at different candidate poses are mutually exclusive, which indicates mutual exclusiveness of $E_i^j$. Thus, the probability that $\pi$ does not collide with $O_i$
is:
\begin{equation}
    Pr(\overline{E_i}) = 1 - Pr(E_i)
    = 1 - Pr(\bigcup_{j=1}^{K} E_i^j) = 1 - \sum_{j=1}^{K} Pr(E_i^j).
\end{equation}
Then, the survivability of a path for all objects $O_i \in
\mathcal{O}_{obj} (i=1,\dots,N)$ is computed as:
\begin{equation}
    \label{survivability of path}
        S_{\pi} = Pr(\bigcap_{i=1}^N \overline{E_i}) =
        \prod_{i=1}^N Pr(\overline{E_i}) =
        \prod_{i=1}^N (1 - \sum_{j=1}^{K} Pr(E_i^j)).
\end{equation}

$S_{\pi}$ represents the first aspect of path robustness, i.e., minimum collision probability with objects. The higher $S_{\pi}$ is, the less risky the path is in terms of collision.

\begin{definition}
    \label{Success probability value}
    (Success probability): Define $E$ as the event that the path
    survives all objects and $F$ as the event that the robot arm
    reaches the target item. Both events E and F must occur for a path
    $\pi: q_s \rightarrow q_g$ to successfully reach the target.
    Define the success probability of a path to be $Succ(\pi) = Pr(E,
    F)$.  Then, $Succ(\pi)$ can be rewritten as:
    \begin{equation}
        Succ(\pi) = Pr(E, F) = Pr(E) \cdot Pr(F) = S_{\pi} \cdot Pr(q_{g}|\pi).
    \end{equation}
\end{definition}

The events $E$ and $F$ are
independent with one exception, which leads to
defining $Pr(F)=Pr(q_g|\pi)$.  When a path leading to a goal $q_g$
collides with the target pose $p_t^j$ with which $q_g$ is associated, $q_g$ is no longer considered for the path as a valid
goal configuration for $p_t^j$, since: (1) if the target item $O_t$ is
at pose $p_t^j$, the path will be in collision with $O_t$ or (2) if
the target item $O_t$ is not at pose $p_t^j$, then $q_g$ does not
allow picking $O_t$ at pose $p_t^j$.

This means that $Pr(q_{g})$ should be conditioned on the path. Define
${\overline{J}}_{\pi}$ as the target poses intersected by the
path. Then, the remaining valid target poses for $q_g$ should be
$\hat{J}_{\pi}(q_g) = J(q_g) \setminus {\overline{J}}_{\pi}$ and
$Pr(q_g|\pi)$ is set to be:

\vspace{-.15in}
\begin{equation}
    \label{conditional definition of Pr(q_{g})}
    Pr(q_g|\pi) = \sum_{j \in \hat{J}_{\pi}(q_g)} Pr(P_t^j).
\end{equation}

Define the path space $\Pi$, which includes the set of candidate paths
$\pi: q_s \rightarrow q_g$, where $q_g \in \mathbb{Q}_{goal})$. The
overall objective is to find a path $\pi^*$:

\vspace{-.15in}
\begin{equation}
    \pi^* = \argmax_{\pi \in \Pi} Succ(\pi).
\label{eq:max_success}
\end{equation}

\vspace{0.1in}

\section{Algorithmic Framework}
\label{Algorithmic Framework}

Consider a roadmap $G(V, E)$, where $q \in V$ corresponds to an arm configuration and $e \in E$ the transition between two arm configurations.
If an edge $e$
connecting $q_1$ and $q_2$ intersects with a pose $p^j_i$, a label $l^j_i$  is
assigned to that edge and the weight for the label $w(l^j_i) = Pr(p^j_i)$.

The survivability $S_{\pi}$ depends on the probability
that the objects will appear at any pose that the path
intersects.  So $Pr(E^j_i)$ in Eq.\ref{survivability of path}
depends on whether there is an edge $e$ along the path $\pi$ that has
a label $l_i^j$. If such an edge exists along the path, then
$Pr(E_i^j)=Pr(p_i^j)=w(l_i^j)$.  Otherwise, $Pr(E_i^j)=0$.  An
indicator random variable $\mathds{1}_{\pi}(j,i)$ for each pose $j$
of each object $i$ is defined as
\begin{equation}
    \label{indicator random variable}
        \mathds{1}_{\pi}(j,i) =
        \begin{cases}
            1, & \text{if}\ \pi \ \text{carries label}\  l_i^j \\
            0, & \text{otherwise}.
        \end{cases}
\end{equation}
Then $S_{\pi}$ in a labeled roadmap can be
computed as
\begin{equation}
    \label{survivability in labeled roadmap}
    S_{\pi}
    = \prod_{i=1}^N (1 - \sum_{j=1}^{K} Pr(E_i^j))
    = \prod_{i=1}^N (1 - \sum_{j=1}^{K} w(l_i^j)\mathds{1}_{\pi}(j,i)).
\end{equation}

Eq. \ref{survivability in labeled roadmap} computes
$S_{\pi}$ for a path from $q_s$ to any currently examined
state $q_{curr}$ by checking the labels $L_{q_{curr}}$ the path $\pi:
q_s \rightarrow q_{curr}$ carries.  To compute the prospect of the
path $\pi$ accurately reaching the target, two situations are
considered:

{\em (i)} If $q_{curr}$ is a goal configuration $q_g$, the
probability that the path leads to the goal is computed according
to Eq. \ref{conditional definition of Pr(q_{g})}.

{\em (ii)} If $q_{curr} \notin {Q}_{goal}$, the
path is not complete and $T_{q_{curr}} \subseteq \mathcal{T}$ indicates the indices of remaining target poses
the path $\pi:
q_s \rightarrow q_{curr}$ can reach.
If the current path $\pi:
q_s \rightarrow q_{curr}$ carries a label $l_t^j$,
then the path and its extensions can no longer treat $p_t^j$ as a valid target pose. In this case, $T_{q_{curr}}$ is updated by removing pose index $j$ from $T_{q_{curr}}$.
An example is given in Fig. \ref{fig:alpha}(left).
Then the probability for the current path $\pi: q_s \rightarrow q_{curr} $ leading to the true target will be
\vspace{-.01in}
\begin{equation}
    \label{reaching_probability}
    Pr(q_{curr}|\pi) =  \sum_{j \in (T_{q_{curr}}\setminus{\overline{J}}_{\pi})} Pr(p_t^j)
\end{equation}

\begin{figure}[h]
  \begin{center}
    \includegraphics[width=0.25\textwidth]{figures/alpha.png}
    \includegraphics[width=0.21\textwidth]{figures/gamma.png}
  \end{center}
  \vspace{-.1in}
  \caption{(Left) A path $\pi: q_s \rightarrow q_{curr}$ intersects pose $p_t^1$, which makes $q_{g^1}$ no longer valid for this path.
    The remaining goals will be $\{q_{g^2}, q_{g^3}\}$ and $T_{q_{curr}} = [2,3]$
    (Right)
    The goal $q^\prime_{g^1}$ is not
    available since the path from $q_{curr}$ to $q^\prime_{g^1}$
    collides with pose $p_t^1$.  But it is still  available if being reached via $q_n$.  $q_{g^1}$ can also be treated as an intermediate
    configuration to reach a potentially more promising goal
    $q_{g^2}$. The child node for the path ending at $q_{g^1}$ will be
    added to search twice, once as a goal node, once as a non-goal node. \vspace{.1in}}
\label{fig:alpha}
\end{figure}

With Eq. \ref{conditional definition of Pr(q_{g})}, \ref{survivability in labeled roadmap} and \ref{reaching_probability}, the success probability $Succ(\pi)$ of a path $\pi : q_s
\rightarrow q_{curr}$ can be computed, which is used as the objective function during the search.

\subsection{Challenge - Lack of Optimal Substructure}

Consider the setup in
Fig. \ref{fig:beta}(left) where the locally optimal path is not globally optimal, i.e., the search algorithm cannot just remember  the locally optimal path (greedy search). For the related {\tt MCR} problem,  it has been argued that greedy search (where only the best local path is stored at each node) still guarantees an optimal solution if the optimal path encounters each obstacle once \cite{hauser2014minimum}. Even with this assumption for the current problem, greedy search still has a chance of failing to find the optimum (Fig. \ref{fig:beta}(right)). A straightforward reduction of the problem to the computationally hard {\tt MCR} problem can be found in the Appendix.

\begin{figure}[h]
  \begin{center}
    \includegraphics[width=0.48\textwidth]{figures/beta.png}
  \end{center}
  \vspace{-.1in}
  \caption{(Left) There are 2 poses
  $Pr(p_1)=0.3$ and $Pr(p_2)=0.4$. Two paths are considered: the
  pink path $q_s \rightarrow q_a \rightarrow q_m$ is favored vs. the blue one
  $q_s \rightarrow q_b \rightarrow q_m$ locally as it has a lower
  collision probability. Nevertheless, both paths go through
  pose $p_2$ afterwards ($q_m \rightarrow q_g$). Thus, the optimal path to $q_g$ is actually the
  blue one, which only collides with pose $p_2$ with probability 0.4.
  (Right) There are 3 poses: $p_1^1$ and $p_1^2$ for object $O_1$ with
  $Pr(p_1^1)=0.3$ and $Pr(p_1^2)=0.3$, while $p_2^1$ belongs to $O_2$
  with $Pr(p_2^1)=0.4$. Again the pink path $q_s \rightarrow q_a
  \rightarrow q_m$ is locally favored since it has higher
  survivability $1-Pr(p_1^1)=0.7$ than that of the blue path $q_s \rightarrow
  q_b \rightarrow q_m$ ($1-Pr(p_2^1)=0.6$).  But when both paths reach
  $q_g$, the pink path has survivability $1-Pr(p_1^1)-Pr(p_1^2)=0.4$,
  which is lower than that of the blue path $(1-Pr(p_2^1))(1-Pr(p_1^2))=0.42$.}
\label{fig:beta}
\end{figure}

\subsection{MaxSuccess Search}
Since greedy search is not guaranteed to be optimal,  a complete search method is proposed here, which follows the exact search for the {\tt MCR}
problem but adapts it to address the survivability objective
defined here. The algorithm stores a path to a
node only if the label set of the path is not a superset of that of
any path found reaching the same node. It theoretically guarantees optimality
since a path with a superset of labels cannot have a higher
$Succ(\pi)$ value than that of a path reaching the same node
with a subset of labels.

\begin{algorithm}
\label{alg:MSE Algorithm}
    \DontPrintSemicolon
    \KwIn{$G(V,E), q_s, \mathbb{Q}_{goal}, \mathcal{T}=[1,\dots,K]$}
    \KwOut{$\pi^*$}
        $ Q \leftarrow \text{{\sc Add}}(q_s, L_{q_s}=\emptyset, T_{q_s} = \mathcal{T}, \mathds{1}_{q_s}=false) $\;
        \While{$\textit{goal not found}$}{
            $q_{curr} \gets Q.top()$\;
            \If{$\mathds{1}_{q_{curr}} = true$}{
                \KwRet{$\pi: q_s \rightarrow q_{curr}$}
            }
            \For{$\text{each } q_{neigh} \in \text{Adj}(G, q_{curr})$}{
                $L_{q_{neigh}} = L_{q_{curr}} \cup L_e(q_{curr}, q_{neigh})$\;
                \If{$ \text{not } \textsc{IsSuperSet}(L_{q_{neigh}}) $}{
                    $q_{neigh}.{\pi} \gets q_{curr}.{\pi} \cup e(q_{neigh}, q_{curr})$\;
                    $S_{q_{neigh}.{\pi}} \gets \textsc{GetSurvival}(L_{q_{neigh}})$\;
                    $T_{q_{neigh}} \gets \textsc{UpdateGoals}(L_{q_{neigh}})$\;
                    $Pr(q_{neigh}|\pi) \gets \textsc{GetReach}(T_{q_{neigh}})$\;
                    $Succ(q_{neigh}.{\pi}) \gets S_{q_{neigh}.{\pi}} \cdot Pr(q_{neigh}|\pi)$\;
                    $Q \gets \text{{\sc Add}}(q_{neigh},L_{q_{neigh}}, T_{q_{neigh}},false)$\;
                    \If{$q_{neigh} \in \mathbb{Q}_{goal}$}{
                        \If{$\text{{\sc IsValid}}(q_{neigh}, T_{q_{neigh}})$}{
                        $Q\gets\textsc{Add}(q_{neigh},L_{q_{neigh}},T_{q_{neigh}},true)$
                        }
                    }
                }
            }

}
\caption{MaxSuccess Exact Search}
\end{algorithm}

\begin{figure*}[t]
  \centering
  \includegraphics[width = 0.9 \textwidth]{figures/legends_methods.pdf}

  \begin{tabular}{cccc}
      \includegraphics[width = 0.23 \textwidth]{figures/nhypo_nobs_b1.pdf} &
      \includegraphics[width = 0.23 \textwidth]{figures/nhypo_nobs_b2.pdf} &
      \includegraphics[width = 0.23 \textwidth]{figures/nhypo_nobs_b3.pdf} &
      \includegraphics[width = 0.23 \textwidth]{figures/nhypo_nobs_b4.pdf} \\
      \includegraphics[width = 0.23 \textwidth]{figures/noiseLevel_nobs_b1.pdf} &
      \includegraphics[width = 0.23 \textwidth]{figures/noiseLevel_nobs_b2.pdf} &
      \includegraphics[width = 0.23 \textwidth]{figures/noiseLevel_nobs_b3.pdf} &
      \includegraphics[width = 0.23 \textwidth]{figures/noiseLevel_nobs_b4.pdf} \\
      \includegraphics[height=1.2in, width = 0.23 \textwidth]{figures/table_1.png} &
      \includegraphics[height=1.2in, width = 0.23 \textwidth]{figures/table_2.png} &
      \includegraphics[height=1.2in, width = 0.23 \textwidth]{figures/shelf_1.png} &
      \includegraphics[height=1.2in, width = 0.23 \textwidth]{figures/shelf_2.png} \\
      \small Table 1 (narrow passage) & \small Table 2 (clutter) & \small Shelf 1 (narrow passage) & \small Shelf 2 (clutter) \\
  \end{tabular}
  \caption{Results on 4 tests (2 for tabletop and 2 for
    shelf) evaluating the number of objects collided for (top) different number of pose hypotheses    under uncertainty level 4 and (middle) different uncertainty
    levels for 4 poses per object. Each column corresponds to the
    benchmark shown below it. The target object is the baseball in
    the tabletop and the water bottle in the shelf. The dots are average values and the background color indicates variance.}
 \label{fig:experimental scenarios}
\end{figure*}

The method is outlined in Alg. \ref{alg:MSE Algorithm}.  It receives as
input the roadmap $G(V,E)$, the start arm configuration $q_s$, a
set of goal configurations $\mathbb{Q}_{goal}$ and a list of all target poses indices $\mathcal{T}$.  A priority queue $Q$ (line 1) prioritizes
nodes with higher $Succ(\pi: q_s \rightarrow q)$.  Each
state $q$ is specified with a label set $L_q$ indicating the labels
the path $\pi: q_s \rightarrow q$ carries and the set of indices of the target poses $T_q \subseteq \mathcal{T}$ the path $\pi$ can
reach.
An indicator $\mathds{1}_q$ is assigned to a node to indicate
whether it is a goal. If it is a goal, then it is found with the highest
$Succ()$ (line 4-5).  If not, it computes
the labels that the path from $q_s$ to all adjacent nodes $q_{neigh}$ via $q_{curr}$
carries (line 6-7).
If the set of labels is not
a superset of that of any previously stored paths $\pi: q_s
\rightarrow q_{neigh}$ (line 8), the path $\pi: q_s \rightarrow
q_{curr} \rightarrow q_{neigh}$ is stored, with corresponding $S_{\pi}$ and $T_{q_{neigh}}$ computed (line 9-11).
The probability for the path to reach the target is computed in line 12 using Eq. \ref{reaching_probability} and $Succ()$ value of the path can be computed (line 13).
The node is then added to
$Q$ as a non-goal node ($\mathds{1}_q=false$) (line 14). Then the algorithm
checks if it is a goal node and whether the path $\pi:q_s
\rightarrow q_{curr} \rightarrow q_{neigh}$ still treats this goal
$q_{neigh}$ as a valid one (line 15-16).  If $q_{curr}$ meets both
conditions, it is added to $Q$ as a goal
($\mathds{1}_q=true$) (line 17).
The search terminates when a goal $q_g \in \mathbb{Q}_{goal}$ has
been found (line 5) or there is no solution.

A key observation is that each node has a chance to be added to $Q$
twice in a single iteration (line 14 and line 17). If it is a non-goal
node, it will only be added once (line 14).  A goal node can be
treated as a goal configuration to grasp an object, but it can also be treated as
an intermediate node to reach a more promising goal configuration. For
that reason, the node is added as a non-goal node (line 14) as
usual. Then, the node is only added as a goal node (line 17) if it is still valid
(Fig. \ref{fig:alpha}(right)).

\vspace*{-.01in}

\section{Experimental Evaluation}
\label{Experimental Evaluation}
The proposed planning framework in \ref{Algorithmic Framework} is evaluated on (A) simulated sensing data and (B) data from a real-world setup. The following alternatives are also considered:
\begin{enumerate}
\item an $\tt Optimistic\ Shortest\ Path$ ($\tt OSP$) planner -
  which ignores the presence of the movable objects
  $\mathcal{O}_{obj}$,
\item an $\tt MCR$ search (Exact and Greedy) - which aims to minimize the
  number of collisions with all poses, and
\item an $\tt MCR \ Most\ Likely\ Candidate\ (MCR-MLC)$ search, which
  considers only the most likely pose for each object and aims to
  minimize the number of collisions.
\end{enumerate}

The methods are evaluated on two robot manipulators (1) a 7-DoF Kuka LBR iiwa14 and (2) a 7-DoF Yaskawa Motoman SDA10F, each of which with a suction-based gripper. The evaluation metrics used here are
(1) the number of objects colliding in the ground truth scene and
(2)
success rate in reaching the true target.
\vspace{-0.05in}
\subsection{Simulations}
\vspace*{-0.03in}
Large-scale experiments with simulated sensing data are performed first to evaluate the algorithms with different levels of uncertainty. Four benchmarks are created (Fig. \ref{fig:experimental scenarios} bottom), where
benchmarks 1-2 are tabletop scenarios while benchmarks 3-4 are highly-constrained shelf scenarios. The target object is either placed in a narrow passage or in clutter.

\begin{figure}[t]
    \centering \includegraphics[width = 0.45
      \textwidth, height = 0.13 \textheight]{figures/success_rate.pdf}
    \vspace{-.1in}
\caption{\footnotesize
    \label{fig:success rate}
    Success rate for different algorithms in all 4 benchmarks.}
\end{figure}

\begin{figure*}[t]
  \centering
  \includegraphics[width=0.9\textwidth, height=0.35\textheight]{figures/iros_paper_fig7.pdf}
  \vspace{-.1in}
  \caption{Experimental results on real vision system in 3 scenarios (1) target in objects clutter (top row) (2) target in narrow passage (middle row) (3) target in front of objects arch (bottom row). The second and third column demonstrate the number of objects collided during path execution and the success rate of reaching the target, respectively, as the evaluation metrics for 6 methods (including both exact and greedy version of {\tt MaxSuccess} and {\tt MCR}).}
 \label{fig:experiment on real vision system}
   \vspace{.05in}
\end{figure*}

Pose
hypotheses (sampled between 1-7) are generated according to probability distributions
centered at the ground truth pose. Different levels of uncertainty are defined (Level 1: $\pm0.5$
cm for translation error and $\pm5$ degrees for orientation error; level 7: $\pm3.5$ cm and $\pm35$ degrees noise). Intermediate levels (2-6) are linearly interpolated between
levels 1 and 7.  The pose probability is assigned based on its
distance from ground truth. 35 roadmaps are generated for each ground truth using a Probabilistic Roadmap ({\tt PRM}) \cite{kavraki1996probabilistic}. The details of the roadmap generation are provided in the Appendix. Fig. \ref{fig:experimental scenarios} provides the number of objects collided during path execution under different uncertainty.

In the tabletop benchmarks, the $\tt OSP$ paths collide with $1.54$
objects on average and $\tt MCR-MLC$ with $0.74$. In contrast, both $\tt MCR$ and $\tt MSE$ work well with much fewer collisions.  As the
uncertainty increases, the number of collisions for ${\tt
  MCR}$ methods start to increase, while the $\tt MSE$ algorithm
remains almost down to zero collisions.  Overall, $\tt MCR$ and $\tt
MSE$ result in few collisions but
Fig. \ref{fig:success rate} shows that $\tt
MCR$'s success rate is not as high (68.4\% for table 1 and 56.2\% for table 2), since it does not reason about target uncertainty. As a
result, $\tt MCR$ may avoid collisions but does not
lead to the true target.  Since the $\tt MSE$ methods take both safety
and goal reachability to form the success function $Succ(\pi)$, the
corresponding success rate is high on the tabletop scenes ($99.5\%$).

The shelf benchmarks are more challenging, as the objects must be
reached from the side in a limited space, which increases the collision risk.
Despite that, $\tt MCR$ and $\tt MSE$ remain safe
($0.34$ and $0.22$ collisions, respectively). Again, the $\tt MCR$ method is conservative
in terms of collisions at the expense of failing to reach the true
target pose.  In Fig. \ref{fig:success rate}, the success rate for
$\tt MCR$ drops to ($42.6\%$) in benchmark 4 (clutter, shelf), while
$\tt MSE$ is still able to succeed $83.6\%$ of the trials.

\vspace{-0.06in}
\subsection{Real-world Experiments}
\vspace{-0.03in}

After verifying the effectiveness of the proposed $\tt MaxSuccess $ algorithm with simulated sensing data, an evaluation with real data took place. Fig. \ref{real robot setup} shows the sensing setup used. An Azure Kinetic camera is mounted on top of a humanoid Motoman SDA10F robot to enable an overhead view of the objects on the table. The experiment focuses on overhand picks in a tabletop setup. 33 images have been taken from the camera with diverse scenarios:

\begin{wrapfigure}{R}{0.24\textwidth}
\vspace{-.1in}
    \begin{center}
        \includegraphics[width=0.24\textwidth, height=0.16\textheight]{figures/real_motoman_setup.jpg}
\vspace{-.25in}
        \caption{Real system setup}
\vspace{-.1in}
        \label{real robot setup}
    \end{center}

\end{wrapfigure}

\noindent \textbf{(1) target in clutter} - Target surrounded by multiple objects. The robot has to reason about the objects' uncertainty to reach the target without collision. \textbf{(2) target in narrow passage} - Target placed between 2 or 3 tall objects to create a narrow passage. The arm has to reach deep to pick the target. \textbf{(3) target under an obstacle arch} - An arch is created by three objects, where an object is put on top of the other two. The target is placed a little bit ahead of the arch. The robot is reaching the target with overhand picks, so the relative location of the arch to the target has to be carefully examined to succeed.

10 YCB objects are selected and the "pudding box", "gelatin box" and "meat can" are selected as the target in different scenes. All  images went through the perception pipeline as in Section \ref{Perception pipeline}. An object is treated as present if the probability prediction is over 0.3. Given this threshold, the accuracy of object recognition is analyzed in the Appendix. For each detected object, $K=5$ object poses have been returned with corresponding probabilities as the outcome of pose estimation and pose clustering\footnote{All the data of the 6D pose hypotheses can be found at \url{https://robotics.cs.rutgers.edu/pracsys/projects/planning_under_discrete_uncertainty/}}.

The proposed planner takes these poses as input. The process generates 5 roadmaps for each scene to produce the picking paths for each method. The paths are then executed in simulation using ground truth poses to evaluate their performance. The same metrics are used: (1) number of colliding objects; and (2) success rate of reaching the target.

\begin{figure}[t]
  \centering
  \includegraphics[height=1.025in]{figures/bad_picking.png}
  \includegraphics[height=1.025in]{figures/good_picking.png}
  \vspace{-.05in}
\caption{\footnotesize
    \label{fig:MCR vs MaxSuccess}
Left image shows the grasping configuration chosen by the $\tt MCR$ method. It avoids any risk of colliding with the arch but has a large chance to miss the target. The right one shows the grasping configuration chosen by $\tt MaxSuccess$. It reasons about the uncertainty of the sugar box and the target pudding box together and comes up with a better solution which can reach the target accurately with low risk of collisions.}
\end{figure}

Fig. \ref{fig:experiment on real vision system} demonstrates the performance of different methods with real vision data. As the scenarios have no obvious risk-free picking path, $\tt OSP$ suffers from many collisions. $\tt MCR-MLC$ also has a relatively high number of collisions, which confirms that the distribution of object poses have to be considered instead of only the most likely pose. The true pose for an object may not be the top response of pose estimation. In every scenario, the methods $\tt MSE$ and $\tt MSG$ outperform $\tt MCR-G$ and $\tt MCR-E$, which are good at finding safe paths but have low success rate of reaching the target. The $\tt MCR$  methods tend to find conservative paths to avoid obstacles, sacrificing the reasoning about target poses. This observation is highlighted in the arch scenario (Fig. \ref{fig:experiment on real vision system}, bottom-right bar graph). Fig. \ref{fig:MCR vs MaxSuccess} shows the advantage of the proposed method over $\tt MCR$ in the arch scenarios.

\section{Discussion and Future Work}
\label{Discussion and Future Work}

This paper tackles the problem of picking a target item in the presence of multiple objects, where there is uncertainty for both obstructing objects and the target item. Perception and planning pipelines have been proposed to address this challenge. Both simulated and real-world experiments demonstrate effectiveness of the proposed framework, which minimizes collision probability while maximizing the probability of reaching the target.  An interesting direction to extend this work is safe object retraction, as well as potentially clearing an entire bin of objects with uncertain poses, where the robot also needs to decide the order with which to reach the target items.  A computational improvement can be achieved by reducing the overhead of collision checking as the number of pose hypotheses increases.  One heuristic is to delay the collision checking \cite{hauser2015lazy} before finding a plausible path and check afterwards to save computation.  An important extension is to deal with unknown objects or scenarios where object models are not available. In such cases a perception system can predict a volumetric representation for the objects' poses and shape uncertainty \cite{mitash2020task}, which can be incorporated into the proposed planning framework.

\section{Generation of Discrete Pose Distributions}
\label{Perception pipeline}

The first task is to recognize which objects are in the scene
and their poses.  This work
utilizes the perception pipeline in
Fig.~\ref{fig:perception_pipeline}. The workspace
$\mathcal{W}$ is assumed to contain some known obstacles
$\mathcal{O}_{st}$ (e.g., a table or a shelf), and can contain any of
up to $N$ objects from a set $\mathcal{O}_{obj} = \{O_1, \dots ,
O_N\}$, for which 3D models are available.  There is a target item $O_t$ in the scene, for which a model is also available.

\vspace{-0.03in}
\subsection{Learning the existence probability of objects}
\vspace{-0.02in}
Given an RGB image, a fully convolutional neural network ({\tt
  FCN}) \cite{shelhamer2016fully} is designed to detect the objects
in the scene and to compute their segmentation
masks. The neural network comprises a {\tt VGG16} feature encoder
\cite{simonyan2014very}, followed by {\it classification} (lower
branch in Fig. 2) and {\it segmentation} (top branch in Fig. 2). The
classification outputs confidence scores
corresponding to the probability $X_i$ of each object $O_i \in
\mathcal{O}_{obj}$ detected in the scene. The segmentation outputs $N$
probability masks, one corresponding to each object possibly
in the scene. Each pixel in an objects' probability mask indicates the
chance of the object being present at that pixel.

\vspace{-0.03in}
\subsection{Obtaining object pose hypotheses}
\vspace{-0.02in}
Given the probability maps from the segmentation, a geometric model matching process \cite{mitash2018robust} is initiated for all objects with $X_i$ greater than a threshold (0.3 in experiments). The process samples and evaluates a large number of pose hypotheses for each object. The poses are scored based on the point cloud matching between the observed point cloud and the object model placed at hypothesized poses. The poses are then sorted based on their matching scores and clustered. The clustering  iterates over the poses in order of their scores. If a  pose hypothesis is close to a higher-ranked pose (within 2.5cm and 15 degrees), it is clustered with and represented by the higher-ranked one. This ensures that similar poses are not selected and the representative is the one with highest alignment score. Finally, the top $K$ pose representatives for each object $O_i$ are returned with scores normalized to sum up to the existence probability, $X_i$. Denote $p_i^j$ as the $j$-th pose of object $O_i$ and $Pr(p^j_i)$ as the probability that object $O_i$ will appear at pose $p^j_i$. Then:

\vspace{-.1in}
\begin{equation}
    X_i = \sum_{j=1}^{K} Pr(p_i^j) \leq 1, \ \ \ \ \ \forall i \in [1,\dots,N].
\end{equation}
\vspace{-.05in}

The target item is assumed to be in the scene, i.e., $X_t = 1$. There is uncertainty, however, regarding its poses as well, i.e., poses $p_t^j$ with probabilities $Pr(p_t^j)$ are also detected for it. The number of hypotheses $K$ for each object can vary. For simplicity, the same value is used for all objects.

\section*{Appendix}
\label{Appendix}

\subsection{Reduction from {\tt MCR} to stochastic {\tt MCR}}
The hardness of stochastic {\tt MCR} can be deduced via a reduction from {\tt MCR},
the
 hardness of which has been shown by polynomial-time reduction from SET-COVER \cite{hauser2014minimum}.

For {\tt MCR}, the input
corresponds to an initial state $q_s$, the goal state $q_g$ and $N$
objects $\mathcal{O}_{obj} = \{O_1, \dots ,
O_N\}$.
For the
reduction, given any instance of {\tt MCR}, the input to a corresponding stochastic {\tt MCR} instance is generated according to the following polynomial-time process:

{\em (i)} the start $q_s$ and the goal $q_g$ remain the same as in {\tt MCR};

{\em (ii)} for each object $O_i$, the pose $P_i$ for object $O_i$
(deterministic) in {\tt MCR} defines a single pose
$p_i^1$ in stochastic {\tt MCR}. For the target, $p_t^1$ is the only target pose for stochastic {\tt MCR} and as a consequence, the target pose the goal configuration can pick is $J(q_g) = \mathcal{T}=[1]$. Here $q_g$ in {\tt MCR} is
equivalent to a single goal $g_g^1 \in \mathcal{G}$ in stochastic {\tt MCR};

{\em (iii)} all poses $p_i^1 (i=1, \cdots, N)$ are assigned the same
probability $\xi$, i.e., $Pr(p_i^1) = \xi \ (0 \leq \xi \leq 1)$.

Suppose the stochastic {\tt MCR} solver is able to find a solution path
$\pi^*$ of maximum $Succ(\pi^*)$ value (Eq. \ref{eq:max_success}) with $m$ poses intersected ($m \leq N$).
In this case, $\mathds{1}_{\pi^*}(1,i) = 1$ for those $m$ intersected poses and $\mathds{1}_{\pi^*}(1,i) = 0$ for the remaining $N-m$ poses (Eq. \ref{indicator random variable}).
Then according to Eq. \ref{survivability in labeled roadmap} where $j=1$, survivability $S_{\pi^*}$ is
\begin{equation}
    \label{survivability for pi_star}
    S_{\pi^*}
    = \prod_{i=1}^N
    (1 - w(l_i^1)\mathds{1}_{\pi^*}(1,i))
    = (1 - \xi)^m
\end{equation}
For the term $Pr(q_g|\pi^*)$, there are two cases
\begin{enumerate}
    \item The path $\pi^*$ intersects the target pose $p_t^1$.

    In this case, $\hat{J}_{\pi^*}(q_g) = J(q_g) \setminus {\overline{J}}_{\pi^*} = \emptyset$,
    which indicates that there are no remaining valid poses.
    According to Eq. \ref{conditional definition of Pr(q_{g})},
    $Pr(q_g|\pi^*) = 0$.
    Then
    $Succ(\pi^*) = S_{\pi^*} \cdot Pr(q_{g}|\pi^*) = 0$,
    which indicates that the stochastic {\tt MCR} instance is not solvable. This also indicates no solution in original {\tt MCR} problem as the robot cannot grasp the target object $O_t$ while colliding with it.

    \item The path $\pi^*$ does not intersect the target pose $p_t^1$.

    In this case, $\hat{J}_{\pi^*}(q_g)$ remains the same since $p_t^1$ is still available and $Pr(q_g|\pi^*) = Pr(p_t^1) = \xi$. Then
    $Succ(\pi^*) = S_{\pi^*} \cdot Pr(q_{g}|\pi^*) = (1-\xi)^m \xi$.
    To maximize the quantity $(1-\xi)^m \xi$, parameter $m$ needs to be
    minimized when $\xi$ is fixed, which corresponds to the objective of original {\tt MCR} problem (minimize the number of constraints violated).
\end{enumerate}

\begin{figure}[t]
    \centering \includegraphics[width = 0.48
      \textwidth]
      {figures/mcr_reduction.pdf}
    \vspace{-.1in}
\caption{\footnotesize
    \label{fig:reduction diagram}
    Diagram for the reduction from MCR to stochastic MCR}
\end{figure}

As a result, reconstructing the {\tt MCR}
solution from the stochastic {\tt MCR} one takes polynomial time.
Since the input/output transforms take polynomial time (Fig. \ref{fig:reduction diagram}),
if the stochastic {\tt MCR} solver can return a solution in polynomial time,
then {\tt MCR} is in P.
Nevertheless, {\tt MCR} is NP-hard
\cite{hauser2014minimum}.
Consequently, stochastic {\tt MCR} is an NP-hard problem.

\subsection{Roadmap generation}
The roadmap is generated as the input for the planning pipeline in this paper. Here the connectivity of the roadmap is defined similar to the ({\tt PRM}$^*$) variant, which achieves asymptotic
optimality \cite{Karaman:2011aa}, i.e., each node is connected to at
least $k^* = k_n \cdot log(n) = e(1+1/d)log(n)$ neighbors, where $e$
is the base of the natural logarithm, $d$ the dimension of the search
space (d=7) and $n$ the number of samples (n=5000).

\subsection{Accuracy of objects recognition}
As described in Section \ref{Perception pipeline}, one branch for the perception pipeline is to output the probability of each object detected in the scene. In the real-world experiment, the objects with probability $X_i$ larger than 0.3 are considered as existent in the scene. Table 1 shows the statistics of the object recognition process as a confusion matrix.

\vspace{0.04in}
\begin{table}[h!]
\centering
\begin{tabular}{|c|c|c|}
    \hline
     & Actually exist & Actually not exist \\
    \hline
     Predict as existent & 150 & 5 \\
     \hline
     Predict as not existent & 3 & 222 \\
     \hline
     \noalign{\vskip 1mm}
     \multicolumn{3}{c}{Table 1: Confusion matrix for object recognition.}
\end{tabular}
\label{table: confusion_matrix}
\end{table}

Based on Table 1, precision and recall are computed as
\begin{equation}
    \text{precision} = 150 / (150 + 5) = 96.8\%
\end{equation}
\begin{equation}
    \text{recall} = 150 / (150 + 3) = 98.0\%
\end{equation}

\vspace{0.06in}
The high precision ($96.8\%$) demonstrates the accuracy of excluding phantom objects (prevent extreme conservative plans) while the high recall ($98.0\%$) indicates the accuracy of detecting objects which are truly in the scene (critical for safe operation of the robot).

\subsection{Path cost and planning time}
The path cost (Euclidean distance between arm configurations along the path) and the planning time have also been computed for reference in Table 2, though they are not the main objectives considered in this paper.

\vspace{0.04in}
\begin{table}[h!]
\centering
\begin{tabular}{|c|c|c|c|c|c|c|}
    \hline
     & OSP & MCR-G & MCR-E & MLC & MSG & MSE \\
    \hline
    cost & 3.023 & 3.627 & 3.705 & 3.255 & 4.221 & 4.425 \\
    \hline
    time(s) & 0.030 & 0.031 & 0.033 & 0.031 & 0.045 & 0.046 \\
    \hline
    \noalign{\vskip 1mm}
    \multicolumn{7}{c}{Table 2: Path cost and planning time.}
\end{tabular}
\label{table: path cost and planning time}
\end{table}

redpajama_set_name: RedPajamaArXiv


Make your own Italian Chef to help you cook your favorite Italian dishes! An easy DIY for any age, an Italian Chef is a fun project for kids to make with the help of felt, chenille stems and a few other basic craft supplies.
Paint the front of the clothespins green and the 2 wood circles flesh tone. Let dry.
To create the head, glue the small circle to the large circle. Glue the large circle to the clothespin.
Referring to the photo, cut the pieces for the hat out of white felt. Glue the brim to the hat and then to the head.
Glue a 1" black chenille bump to the bottom of the small wood circle. Glue the wiggle eyes about the small wood circle.
Cut the bandana out of red felt and glue below the head.
For the apron, cut a 3" x 4.5" piece of white felt. Fold it over ½" on the narrow end and glue down. Glue the apron to the front of the clothespin.
Cut a 9" piece of chenille stem and slide it through the spring on the clothespin.


The benefits of cycling include but are not limited to: Not getting sat on by overly large people who want half of my bus seat, not sitting in all of Chicago's germs on public transit, fresh air, exercise, gorgeous lakefront bike paths, and thighs of steel.
I'd like to introduce my new signature scent, Freshly Minted Cyclist. This tantalizing parfum is made daily in small batches, so each bottle will be its own unique fragrance. However, we guarantee that your purchase will contain the essences of chain grease, sweat, rubber, and bruised ego. Your special variation may also include the delicate spice of automobile exhaust, the earthy fragrance of all-natural mud (good for the skin!), or strong and vibrant notes of abrasion antiseptic.
*Safety gear not included. Must be certifiably insane to attempt.


text:
source ~/.bashrc
PLANLOGGER_DIR=${HOME}/sr_experimental_data/
cd ${PLANLOGGER_DIR}
rm -Rf packaging
mkdir -p packaging

mongoexport -d roslog -c logged_designators -o packaging/logged_designators.json
mongoexport -d roslog -c tf -o packaging/tf.json

cp -r current-experiment/* packaging
./makedot.sh

DATE_STRING=`date +"%Y-%m-%d-%H-%M-%S"`
mkdir -p results
cd packaging
tar -czf ../results/log-packaged-${DATE_STRING}.tar.gz *
cd -

redpajama_set_name: RedPajamaGithub


text:
Q: MS-Access 2003 - Expression in a Text Box on a form just wondering when using an expression on a form in a text box, to return a value from a table, can the expression have multiple tables in the expression to return the value?
the tables are linked and I can return the value in a query, so I figured that Access would be able to do it with this method as well????
=DSum("[tblMain]![Revenue]","tblMain","[tblMain]![Quarter]=3 AND [tblMain]![Region]='NorthEast'" AND [tblOffice]![Location]='NewYork'")
this is the expression that I entered into my text box, without the reference to the 2nd table it works fine, but once I had it, I get the flickering error message in the text box (just as on a report)......
I know this method is probably used more in reports than forms, but I am novice, and trying to come up with a dashboard solution that returns lots of facts quickly per department. I am using this in the "Control Source" field of the data tab of the properties window, not VB. Mainly because I do not know how to get it to work with VB.
Thanks for the help as always!

A: How are these tables related?  Can you describe the relationship and any primary/foreign keys?
Also, referencing the table name is not necessary in the first parameter of this function (since it is already taken care of in the second one).
For example, your code could be:
=DSum("Revenue","tblMain","Quarter=3 AND Region='NorthEast'" AND [tblOffice]![Location]='NewYork'")
Just trying to save you some keystrokes and increase its readability. :)

A: As far as I know, you cannot refer to more than one table or query in a domain aggregate function. As grazird says, how are these tables related? Let us say it is on tblMain ID, you can build a query called, say, qryMainOffice, the SQL (SQL View, Query Design window) would look something like:
SELECT [tblMain].[Revenue],[tblMain]![Quarter],[tblMain]![Region],
       [tblOffice]![Location]
FROM tblMain
INNER JOIN tblOffice
ON tblMain.ID = tblOffice.MainID

DSum would then be (remove line break):
=NZ(DSum("[Revenue]","qryMainOffice",
 "[Quarter]=3 AND [Region]='NorthEast' AND [Location]='NewYork'"),"Not found")

You could also use a recordset or query in VBA to return the value.
EDIT re COMMENT
To use the above in VBA, you either need to add parameters or use a string:
''Reference: Microsoft DAO 3.x Object Library
Dim rs As DAO.Recordset
Dim db As Database
Dim strSQL as String

Set db= CurrentDB

strSQL = "SELECT Sum(t.[Revenue]) As TotalNY" _
       & "FROM tblMain t " _
       & "INNER JOIN tblOffice o " _
       & "ON t.ID = o.MainID " _
       & "WHERE t.[Quarter]=3 AND t.[Region]='NorthEast' " _
       & "AND o.[Location]='NewYork' " _

 '' I have use aliases for simplicity, t-tblMain, o-tblOffice
 '' If you wish to reference a control, use the value, like so:
 '' & " AND [Location]='" & Me.txtCity & "'"
 '' Dates should be formated to year, month, day
 '' For joins, see http://www.devshed.com/c/a/MySQL/Understanding-SQL-Joins/

 Set rs = db.OpenRecordset strSQL

 If Not rs.EOF Then
    Me.txtAnswer = rs!TotNY
 Else
    Me.txtAnswer = "N/A"
 End If

You can also use different queries to return several results that can be shown with a list box or a subform:
strSQL = "SELECT TOP 5 o.[Location]," _
       & "Sum(t.[Revenue]) AS TotRevenue" _
       & "FROM tblMain t " _
       & "INNER JOIN tblOffice o " _
       & "ON t.ID = o.MainID " _
       & "WHERE t.[Quarter]=3 AND t.[Region]='NorthEast' " _
       & "GROUP BY o.[Location]"

The above would return revenue for quarter 3 for all locations in NorthEast region. If you want the top values of each group, you are looking at a more complicated query, which I will leave for now.


In modern ATM the systems are adapted and developed to more current system design principles with a number of connected technologies.
These developments are raising concerns in the ATSEP community regarding the cybersecurity of the systems in this new role. Entry Point North explored the challenges and solutions regarding modern-day cybersecurity in ATM during this year's edition of our annual ATSEP Workshop.