Have you watched the "Extreme Shepherding" video that has become so popular in the past few days? Take a look…..
Every time I watch that video I'm amazed. And, I can't help but think of the first "Extreme Shepherding" that occurred in the first-century. It didn't involve LED lights, video cameras or any other technology, but I can imagine the sight was even more impressive. Read what Luke recorded in his gospel about the experience.
There are so many great take-aways from the shepherds' story. Lessons of openness to unexpected messages, of responding with immediate obedience, of excitedly sharing truth, and of worshiping unashamedly. One also cannot overlook the improbability of Jesus' birth announcement being first delivered to some of the lowest, poorest individuals in society or the significance of a large, singing choir of angels, or their proclamation of peace.
But more than anything the simple statement, "Seeing was believing" stands out to me. At first glance the statement appears exclusionary because after all, we weren't there, we didn't see, so however can we believe? But I think we're intended to think about it quite differently. While we weren't present at the manger on that first Christmas morning, we are continually offered glimpses of "God sightings" that can move us to belief.
* Brilliant colors painted across the horizon as the sun sets in the west.
* A child who spends his own allowance to buy a blanket for the man standing on the corner with a cardboard sign.
* Hoarfrost shimmering on a tree branch in the early dawn's light.
* The encouragement of an unexpected phone call "just to say Hi" on a day when it's most needed.
* Dancing lights in the northern night sky.
* True tales of selfless heroes and guardians of justice and hope.
Perhaps you judge these things as insignificant, especially compared to seeing the King of Kings and Lord of Lords majestically lying atop a mound of hay in a manger. But really the scene the shepherds saw was hardly majestic. They rejoiced and believed simply because they found what they had been told to look for.
Like the disciples who saw and believed, we too can believe when we see what we've been told to look for – beauty, purity, wisdom, and self-giving love. Now that's "Extreme Shepherding"!
Where have you seen and believed this Christmas season? How do you plan on doing your own "Extreme Shepherding" this season?


His new album 'A Family Like Yours' will be released next Monday, but while you wait for the new songs, watch Lucky Fonz III play old songs. Songs by artists who've influenced him heavily, like Bob Dylan, The Beatles, but also his friend Robin Block. He recites a poem by Block, and Block himself sings along on some of the songs, together with neighbour Cor.
The session, filmed in January 2009, was one of the funniest evenings so far on Onder Invloed. After eating only one sandwich on the train station in Utrecht, after working all day, the evening in Amsterdam was one of jokes; singing' tea, coffee, no, tea, no, coffee, oh and tea; spontaneous collaborations with fellow singersongwriter Robin Block and neighbour Cor – who brought some beer with him.
There's a Bob Dylan cover called 'Seven Curses', a Beatles song called 'Eleanor Rigby', a Chinup cover called 'Set On Sin' and 'Jij en Ik', a Dutch poem written by Robin Block.


Being a good employer sometimes means making difficult choices. Decisions aimed at improving profitability and efficiency can come at the cost of someone's job. Good communication and transparency from a company is important if you're to avoid employment disputes and litigation headaches.
When an employee brings a personal grievance for unjustified dismissal an employer will be called upon to justify that dismissal. The employer's decision and actions will have to be shown to be "what a fair and reasonable employer could have done in all the circumstances at the time of the dismissal".
The recent case of Ledger v Delmaine Fine Foods Limited, is an example of redundancy process gone wrong. In this case the employee was told that there was no longer a job for her due to the "economic downturn" and financial pressures upon the company. The Employment Relations Authority criticised the employer for not providing detailed supporting financial information or projected costs savings to show the reasoning behind her redundancy. Reliance on "economic downturn" and rumours of mergers in the industry lacked substance and therefore were no justification for the dismissal. The employer had to pay the employee approximately $36,000 plus costs.
A reading of that case suggests that this may well have been a good justifiable business decision on the part of the employer for reasons more specific than "economic downturn". However, there had been no objective analysis by the employer of the financial health of its business and how making Ms Ledger redundant would improve that situation - or at least not in a form that could be presented to the authority.
A decision to make redundancies cannot be made in a vacuum. It must be supported by analysis and information. That analysis must then feed in to the consultation process.
Contact us for information in relation to redundancy and restructuring processes.


The open positions posted currently on the website Kariyer.net are available for application. Click here for open positions.
Candidates can make their applications by sending their resumes to ik@tunelmak.com.tr.
Trainee applications received by Tunelmak are evaluated depending on related needs at head office or branch offices. The candidate's branch of education must conform to the subject of activity at the department and the company. Applications for training must be sent to ik@tunelmak.com.tr.


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Colombian Navy launches first domestically manufactured vessel
Other Navy ships built in Colombia "What we have today with this ship, which is 100 percent designed, manufactured and built in Colombia, is the dream of many people who put their hearts, hands, minds and efforts to transform steel into monuments for the homeland, peace, development and security," said Pinzon. Thanks to the construction of these and other vessels, the Colombian naval industry is respected throughout the world by countries which purchase vessels manufactured in the country. The main mission of the Punta Espada will be to carry out maritime interdiction, patrol and surveillance operations in Colombian waters. Security forces will use it to detect, intercept, and inspect suspicious vessels. . "At the tactical and operational level, Colombia has responded to a number of needs that conflict and drug trafficking have been creating," said Néstor Alfonso Rosania, a security analyst at the Center for Studies in Security, Defense and International Affairs of Colombia. The Armed Forces of Colombia will continue to receive the best available equipment and technological tools "because they are the ones who have put Colombia on a path towards peace," the defense minister said. Defense Minister Juan Carlos Pinzón, and the commander of the National Navy, Admiral Hernando Wills, presided over the launching ceremony of the Punta Espada in Cartagena. "Colombia has entered a select group of countries that have the technology and knowledge to build these kind of vessels," said Rear Adm. Roberto Sáchica, the president of Cotecmar. The ARC Punta Espada – the first CPV produced entirely in Colombia – touched water for the first time October 31. It was produced by the Science and Technology Corporation of Naval, Maritime and Riverine Industry Development (Cotecmar) in conjunction with the Social and Enterprise Defense Group (GSED), which is part of the Defense Ministry. By Dialogo November 28, 2014 "The coastal patrol boat responds to needs from armed conflict and transnational drug trafficking It will provide the Navy with more mobility and achievements in operations against threats facing the country. This boat is not only fundamental to Colombia's Navy, but it is also important to the Colombian military industry at the international level." "It is a great start that this patrol boat is already sailing," Rosania said. "This boat is the result of scientific and technological development that the Colombian government has been implementing in recent years. The Navy understands the need to build vessels to monitor both oceans and prevent drug trafficking from continuing in these areas. Authorities are concentrating their efforts on developing new technologies to combat threats of transnational crime and various related offenses." "What we have today with this ship, which is 100 percent designed, manufactured and built in Colombia, is the dream of many people who put their hearts, hands, minds and efforts to transform steel into monuments for the homeland, peace, development and security," said Pinzon. The Colombian military industry has built other Navy vessels. For example, in February the Colombian Navy launched the ARC 20 de Julio, the largest ship built in the country. It was designed and built by Cotecmar. For example, in September 2012, Brazil bought four LPR-40 patrol boats which were manufactured in Cartagena. It is important and interesting that countries like Peru and Colombia are becoming more technical with respect to the Navy. I read about ESMERALDA, a Chilean sailing vessel in AGORA, which until now was the largest, but according to what I read now it will be the UNION. Congratulations to both governments for their interest in becoming one of the big players in this area. Your information is very timely. I work in the National Port Security Commission in Honduras as head of Port Security Audits (APIP in Spanish)… I hope you continue to contribute with more information. "I congratulate everyone who has contributed to these projects, which were no simple feat," Pinzon said. "These are projects that carry the vision of great people of this country, officers, non-commissioned officers, engineers, sailors and good Colombians, who have visualized Colombia's real and strategic capacity in naval and maritime matters for several years." "It is a great start that this patrol boat is already sailing," Rosania said. "This boat is the result of scientific and technological development that the Colombian government has been implementing in recent years. The Navy understands the need to build vessels to monitor both oceans and prevent drug trafficking from continuing in these areas. Authorities are concentrating their efforts on developing new technologies to combat threats of transnational crime and various related offenses." The main mission of the Punta Espada will be to carry out maritime interdiction, patrol and surveillance operations in Colombian waters. Security forces will use it to detect, intercept, and inspect suspicious vessels. . The ARC Punta Espada – the first CPV produced entirely in Colombia – touched water for the first time October 31. It was produced by the Science and Technology Corporation of Naval, Maritime and Riverine Industry Development (Cotecmar) in conjunction with the Social and Enterprise Defense Group (GSED), which is part of the Defense Ministry. Other Navy ships built in Colombia Thanks to the construction of these and other vessels, the Colombian naval industry is respected throughout the world by countries which purchase vessels manufactured in the country. "At the tactical and operational level, Colombia has responded to a number of needs that conflict and drug trafficking have been creating," said Néstor Alfonso Rosania, a security analyst at the Center for Studies in Security, Defense and International Affairs of Colombia. "The coastal patrol boat responds to needs from armed conflict and transnational drug trafficking It will provide the Navy with more mobility and achievements in operations against threats facing the country. This boat is not only fundamental to Colombia's Navy, but it is also important to the Colombian military industry at the international level." Improving Colombia's strategic capacity The Punta Espada will help the Armed Forces continue on that path. Military officials appointed Naval Lt. Cmdr. Henry Mauricio Barón Franco as the patrol boat's commander. He will take command of a vessel that measures 45.25 meters in length, 7.1 meters in beam and 1.84 meters in draught. It can accommodate a crew of 23 people, and is powered by two diesel engines which drive a fixed pitched propeller. It's also outfitted with a 25-mm caliber cannon and two 60-mm caliber machine guns. Colombia's security forces recently obtained an important tool in their fight against international drug trafficking – a coastal patrol vessel (CPV). Improving Colombia's strategic capacity Colombian manufacturers used global technology to build the patrol boat, which has the capability of refueling rapid response boats. The Punta Espada will help the Armed Forces continue on that path. Military officials appointed Naval Lt. Cmdr. Henry Mauricio Barón Franco as the patrol boat's commander. He will take command of a vessel that measures 45.25 meters in length, 7.1 meters in beam and 1.84 meters in draught. It can accommodate a crew of 23 people, and is powered by two diesel engines which drive a fixed pitched propeller. It's also outfitted with a 25-mm caliber cannon and two 60-mm caliber machine guns. "Colombia has entered a select group of countries that have the technology and knowledge to build these kind of vessels," said Rear Adm. Roberto Sáchica, the president of Cotecmar. The Armed Forces of Colombia will continue to receive the best available equipment and technological tools "because they are the ones who have put Colombia on a path towards peace," the defense minister said. Defense Minister Juan Carlos Pinzón, and the commander of the National Navy, Admiral Hernando Wills, presided over the launching ceremony of the Punta Espada in Cartagena. The Colombian military industry has built other Navy vessels. For example, in February the Colombian Navy launched the ARC 20 de Julio, the largest ship built in the country. It was designed and built by Cotecmar. Colombia's security forces recently obtained an important tool in their fight against international drug trafficking – a coastal patrol vessel (CPV). "I congratulate everyone who has contributed to these projects, which were no simple feat," Pinzon said. "These are projects that carry the vision of great people of this country, officers, non-commissioned officers, engineers, sailors and good Colombians, who have visualized Colombia's real and strategic capacity in naval and maritime matters for several years." For example, in September 2012, Brazil bought four LPR-40 patrol boats which were manufactured in Cartagena. Colombian manufacturers used global technology to build the patrol boat, which has the capability of refueling rapid response boats. read more
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Semi-Finals here we come! Kwakwani, LTI and NAMS continue to NSBF semis
THE Youth Basketball Guyana (YBG) National Schools Basketball Festival (NSBF) U-19 quarterfinals showcased the best of the U-19 talent on the local circuit.There were three games played on the night, one blowout, one close encounter and one nail-biter that proved to be the game everyone was waiting to witness the entire tournament.In the first game of the night, Kwakwani Secondary made light work of Mackenzie High blowing them out of the water to show why they were defending champions winning 61-28. Led by the triple threat of national guards in Troy David, Stanton Rose and Damair Gladstone who had 10, 12 and 11 points respectively, the team cruised to victory. Kemmol Benjamin, Dillon Wallace and Jamal Gilkes registered 9, 7 and 6 points in the win also. For the outmatched Mackenzie side, Tim Veshon scored 8 points with Daniel Anthony supporting him with 7 points.The second encounter saw Linden Technical Institute spoiling the coming-out party for Jaleel Duke and his President's College side in a game that finished 47-33. Led by Akinni Wilson's 13, LTI continued their tradition of advancing to the final rounds to compete for a title. From the outset, President's College, pushing the tempo and looking very threatening, while doing so behind Duke's quick scoring.However, the tide soon changed as the Linden side started to lock down on defence and convert on offence. For Akinni, it was balanced scoring with an inside-out approach – whatever the defence gave him he took. He was supported by Tahquille Johnson's 9. On the President's College side, Jaleel Duke posted 14 points in the losing effort with Anton Fileen contributing 11. Sherland Gillis at line to close out the win for NAMS (Daniel Haynes photos)The final game of the night was definitely the one fans paid their money to see. New Amsterdam Multilateral Secondary (NAMS) took on St Rose's High and won in a game that went into overtime and finished 36-29.From the tip, both teams seemed evenly matched, trading baskets after the initial feel-out process was over. It was not just a battle of big men and point guards, but a battle of coaches, with Rose's Courtenay Taylor and NAMS Willon Cameron having both coached alongside each other at the National level.The battle of the 'bigs' that was expected turned out to be the mitigating factor with NAMS' Neil Wills, and Sherland Gillis contributing 10 points each for their side, with points coming at crucial moments. For Rose's it was the duo of Akil Vaughn and Leon Ross who held the offensive giant Wills to such a low total.Gillis was the X Factor for the NAMS side, and he seemed to find himself making the right basketball plays at the right moments. The first being a steal with seconds to go in the game leading to him being fouled and able to put away the game at the free throw line after Rose's took the lead with a minute to go.For Rose's it was Shamar Huntley whose 15 points stood out in the losing effort. There was much to be taken away from the game as in the overtime period the three-point shooting of Rose's went awry. There were missed calls on both ends and the foul game ultimately contributed to the game's outcome. Akinni Vaugn making a move for two of his points.Gillis was once again put at the line and made them count for the win. Coach Willon Cameron on how the win came to be stated "It was wanting it at all times, we fight and that's what we're about."AN emotional coach Taylor also gave his input stating, "It was always going to be a competitive game given the fact both teams are similar in their make-up and how they play.""The teams know each other as well through the friendship developed over the years but what played the separator in the teams was the officiating," continued Taylor.The semi-final rounds tip off today and promise much more action. The tournament is sponsored by Digicel, Banks DIH Limited and Beharry Group of Companies. read more
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Moorpark College hosts multiethnic celebration
160Want local news?Sign up for the Localist and stay informed Something went wrong. Please try again.subscribeCongratulations! You're all set! Among dozens of attractions, the events included lectures on Chumash culture, a film about a Japanese-internment camp, a lecture on the Harry Potter books, demonstrations by drummers and martial artists, along with flamenco dancing and Cajun music. MOORPARK – The 16th annual Multicultural Day at Moorpark College included everything from what the Bible teaches us about nutrition to the history of the boomerang. The event focusing on diversity was held Wednesday to promote global understanding through presentations and performances about various cultures and arts. Vendors offered ethnic foods. Some faculty members allowed students to attend several of the events in lieu of going to class. Local kindergarten-through-12th-grade schools, as well as nearby colleges, were invited to bring their students to see and hear music, dance, drama and lectures. read more
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Hackett , Future Planning Associates merge
Exchanges that will be 100 percent covered by FairPoint by 2010
Remarks of Senator Patrick Leahy at the Economic Recovery Conference at Champlain College
EPA sends $2 million in brownfield clean-up funds to Vermont
Legislation would bolster successful SBA loan program
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Workmen begin work on the project to replace the water mains on Bantry's main streets.
Traffic in Bantry will be disrupted over the next two months as Irish Water work to replace 395 metres of pipes in the town centre.
However, in order to minimise any disruption to residents and businesses in the area, the company carrying out the work, Coffey Northumbrian Ltd, has issued a specific schedule of work, which they say will last until May 8th.
Irish Water confirmed: 'Customers will be given a minimum of 48 hours-notice prior to any planned water shut offs' while local and emergency traffic will be maintained at all times.
Customers in the affected areas have also been given a callsave number – 1850 278278 – if they have any questions about the project.
Steven Blennerhassett of Irish Water's leakage reduction programme, said further mains replacement works in Bantry – which are at the design and planning stage – are expected to commence later this year.
A further 2km of mains at The Rope Walk, plus an additional 480m on the N71, is to be replaced in order to improve the security of water supply in the Bantry area.
As part of the first phase of the project, 395m of water mains in Main Street, Barrack Street and Market Street will be replaced with modern, high density polyethylene pipes.
New water service connections from the public water main to the customers' water supply will also be provided.
The chairman also made the point the €120,000 secured for public realm works at Main Street 'will now be put to very good use once the underground works are completed.


New designer In the House!
At least most of Second Life will find her new, but I've heard from a little birdie that she worked for a few big Fashion Houses before she struck out on her own. This fetching little number is called Debut- Michelle Dress in Teal. I was somewhat skeptical of mesh until I found NYU – Minimalism High Fashion Couture. But these clothes fit like a dream. You will be seeing a lot more of NyuNyu Kimono's sleek and sharp designs here in the future. BTW boys! She has stuff for you too! I teamed this up with Dura's Girl 36 in black and Face Paint night life Aqua makeup. Simple, Striking and Fab.
Next Post Vero Modero Goodness and more………..


Dense and often dry shade can be one of the most challenging situations in which to establish new plants and hedging. Take a look at our list of tough shade tolerant plants that will grow in these situations.
Growing a hedge in dense shade sounds like a challenge but in reality it isn't difficult. Success comes from choosing the correct hedging species, looking after them well after planting until established - and patience as they will certainly take longer to grow in these conditions.
Hedges For Dense Shade – Shady areas, often under the canopy of other much larger plants may also be particularly dry and are often considered difficult areas in which to have colour and interest with shrubs, hedges and ground cover plants.
There are in fact many hedges for dense shade that will tolerate, or even thrive in these conditions. All of the plants below are suitable but do remember that even the most drought resistant species will need regular watering during the early stages to get established. Dry shade areas that are sheltered by walls miss out on natural rainfall whilst areas shaded by mature trees with shallow roots are constantly having any rainfall or naturel moisture absorbed by the root system of the established trees.
Most hedges for dense shade will grow more slowly in these harsher conditions, growth rates given on our website are based on a 'good average', in dense shade they may only grow half as fast, or even slower. With patience and given sufficient watering and mulching to get the new hedge started, good results can be achieved.
However many plants can cope with these conditions in fact will often thrive if a little forward planning is applied. Ground preparation will help new shade loving plants get established quickly adding copious quantities of well rotted manure or compost digging well into the existing soil will help as will a good layer of mulch around your plants after planting.
Adding Rootgrow mycorrhizal fungi when planting can be a very helpful aid to establishment, particularly in harsh conditions.
The most popular hedges for dense shade include all of our Berberis hedging varieties, Box, Cotoneaster Hedges and Euonymus which is available in a variety of types for shade hedges of differing sizes.
Many of our best selling evergreens are suitable including all varieties of Laurels (except the Bay Laurel), Lonicera and Vibunum tinus, a super plant for brightening dark corners producing white flowerheads during the winter months.
Our sales team are always available to answer any questions you may have about hedges for dense shade, or any of our other hedge plants, please do call our office on 01580 765600.


text:
Dynamics and control of separable coupled rigid body systems
Kinda Khalaf1,
Dongming Gan ORCID: orcid.org/0000-0001-5327-19022 &
Hooshang Hemami3
Robotics and Biomimetics volume 4, Article number: 14 (2017) Cite this article
This paper explores the dynamics of separable coupled rigid body systems, a special class of constrained rigid body systems. These are defined as two systems that interact with each other by forces of contact, resulting in a reduction in dimensionality and complexity. The mechanics and consequences of this reduction are investigated here. The basic hypothesis and an example of the reduction in two successive steps are formulated. A simple mechanical biped model is developed and analyzed in some details by both system theoretical concepts and simulations. The main contribution of this work is the novel extension to the known dynamics of constrained rigid bodies. The modular, versatile and systematic formulation presented here is computationally efficient and has many applications in the studies of the human neuro-musculoskeletal system, robotic systems and humanoids, as well as clinical and sports biomechanics applications. Computer simulations are provided to demonstrate the feasibility and effectiveness of the methodology.
Numerous works on constrained rigid bodies and multibody dynamics (MBD) have been done over the last few decades, including several well-known textbooks [1, 2]. Various algorithms were also developed in a wide variety of fields and application areas [3,4,5,6,7]. Technological advancement warranted the advent of improved formulations with better computational efficiency [8]. Recent approaches such as the "divide-and-conquer" algorithm (DCA) were used to reduce the computational burden associated with many aspects of modeling, designing and simulating articulated multibody systems [7].
On the other hand, much less attention has been given to separable coupled rigid body mechanics, a particular class of constrained rigid bodies, as evidenced by the paucity of the literature in this area. Defined as systems where the physical coupling or interaction takes place primarily through the forces of contact [9], no gripping or holding occurs in such systems. In general, the two systems get separated when the forces of contact go to zero. It is well known that some human contact with certain machines or inanimate objects fall in this category. Specific examples include medical and sport-related interactions, such as rotating medical platforms with a human on the platform and humans on diving, skating or surfboards. This work extends the current body of the literature on constrained rigid body dynamics by proposing a computationally efficient formulation for separable coupled systems. We address the rigid body dynamics, stability and control of separable rigid bodies within the scope of human or robot interaction with a subset of the above three classes of objects: medical platform, human on skateboard and human on surfboard.
While the dynamics of the three situations are somewhat similar and can be formulated along the lines discussed in this paper, the control problem and objectives are, however, different. For example, in the medical platform case, the platform is independently moved, and the objective of the human or patient on the platform is to achieve postural stability, even though the exact mechanisms of such control by the central nervous system (CNS) are not well understood. In the skatingboard situation, the human controls both subsystems—the human's and the board's. The board does not exert any control of its own. In the surfboard scenario, the control is distributed between natural random forces that propel the board's translational and attitudinal motion, and the partial control the rider exerts to maintain stability, hold attitude relative to the waves for some not well-defined performance index and proceed with smooth transnational motion or achieve some acceptable mixture of all these objectives. When the two subsystems are humans, the dynamics and the control problem become more involved and complicated, and this case will not be pursued here.
Systems of connected rigid bodies with holonomic, non-holonomic and soft constraints can be adequately utilized to model robotic [10], humanoid [11] and locomotion systems [12]. The interaction of a robot with a moving platform or stable base can be represented in the equations of motion. This paper extends the previous body of work to theoretically formulate the dynamics and control of a multilink mechanical system in contact with a stationary or moving base of support. We will first formulate the general two rigid body system dynamics and apply it to simple models of platform rotation and skateboarding. We will discuss the control for some simple and specific maneuvers.
A certain amount of dimensionality and complexity reduction is achieved by replacing the dynamics of one subsystem with kinematics [13]. The equations of motion and procedures for their reduction are outlined. Stability is achieved by standard feedback technique to counteract the base movement. The biped is to maintain stance and postural stability under support platform disturbance [14]. The formulation here also allows computational studies and further quantitative assessment of sensory and processing deficits in stability and balance for both healthy and injured humans [14, 15]. With regard to postural adjustments, it is hypothesized that humans use ankle strategy, hip strategy and combinations of the two in order to maintain balance [16]. The formulation allows quantitative studies of such hypotheses and the role of certain variables such as center of gravity, center of pressure, shear and normal support forces [17, 18]. It may also be relevant to studies of vestibular deficit [19, 20].
This paper is structured as follows: The dynamics of the two-coupled separable systems is formulated in second section. Two examples, a biped model under rotational platform disturbances and a simple skateboard model, are formulated in third section. Stability and control are discussed in subsection. Simulations and comparisons are presented in fourth section. Discussions and conclusions are in fifth section followed by References and Appendices.
Coupled separable systems
For ease of comparison and reference we adopt the same notation and variable names as in Ref. [12]. The subsystems are assumed to be planar and given in the Lagrangian formulation:
$$I_{1} (\varTheta )\ddot{\varTheta } + B_{1} (\varTheta ,\dot{\varTheta })\dot{\varTheta } - gG_{1} (\varTheta ) = W_{1} U_{1} + [\partial C_{1} /\partial \varTheta ]\varGamma_{1}$$
$$I_{2} (\varPhi )\ddot{\varPhi } + B_{2} (\varPhi ,\dot{\varPhi })\dot{\varPhi } - gG_{2} (\varPhi ) = W_{2} U_{2} + [\partial C_{2}^{'} /\partial \varPhi ]\varGamma_{2}$$
The forces Γ1 and Γ2 are the forces that couple the above two subsystems. It is assumed that these are the only constraint forces that appear in the equations above with
$$\varGamma_{1} = - \varGamma_{2}$$
The algebraic constraint equations are, in general, functions of all the degrees of freedom.
$$\begin{aligned} C_{1} (\varTheta ,\varPhi ) = 0 \hfill \\ C_{2} (\varTheta ,\varPhi ) = 0 \hfill \\ \end{aligned}$$
A block diagram of the system is shown in Fig. 1 which is described in more detail later. The system could also have been described by combining constraints and forces of constraint
$$\begin{aligned} & CC = \left[ {C_{1}^{\prime } ,\; - C_{2}^{\prime } } \right]^{'} \\ & \varGamma = \varGamma_{1} \\ \end{aligned}$$
The planar one-segment biped and a particular planar platform subsystem
The matrices I and B of the combined system are block diagonal. This latter representation is useful when one subsystem controls both subsystems. For the time being, the objective is to consider the subsystem that is being controlled, i.e., the first subsystem. This subsystem is being controlled through the forces Γ exerted by the second subsystem. Further, it is assumed that the constraints C 1 can be separated into two parts as shown in Eq. (5):
$$C_{1} = C(\varTheta ) + D(\varPhi )$$
For the computation of the forces of constraint Γ1, it is necessary to differentiate equation (5) twice with respect to time. For ease of reference, the second derivative is symbolically reproduced here.
$$(\partial C^{\prime } /\partial \varTheta )(\ddot{\varTheta }) + \partial [(\partial C^{\prime } /\partial \varTheta )(\dot{\varTheta })]/\partial \varTheta [\dot{\varTheta }] + (\partial D^{\prime } /\partial \varPhi )(\ddot{\varPhi }) + \partial [(\partial D^{\prime } /\partial \varPhi )(\dot{\varPhi })]/\partial \varPhi [\dot{\varPhi }] = 0$$
The main point of the above equation is that the influence of the controlling subsystem on the controlled dynamics of the controlled subsystem is through Φ, \(\dot{\varPhi }\) and \(\ddot{\varPhi }\). In practical terms, this means that the controlled subsystem must, through its sensory apparatus, measure the forces of constraint Γ and, from these measurements and possibly its actuators dynamics that may be sensitive to the platform motion, extract the controlling subsystem's positions, velocities and acceleration variables. This issue is further elaborated in the examples and in the control. Consider a mechanical multilinkage system with Z as an n-vector of the degrees of freedom, U as the input vector of ideal moment of force generators, Γ as the vector of constraint forces and
$$C = 0$$
as a set of holonomic constraints governing the system. The equations of motion in the Z space are:
$$I(Z)\ddot{Z} + B(Z,\dot{Z})\dot{Z} - gG(Z) = WU + [\partial C/\partial Z]\varGamma$$
It is well known that when the constraints are maintained, the following equations describe the behavior of the system: When the constraints are satisfied, the forces of constraint are functions of the state Z and \(\dot{Z}\) and the inputs:
$$\begin{aligned} & C(Z) = 0 \\ & (\partial C^{{\prime }} /\partial Z)((I^{ - 1} )I\partial C/\partial Z)\varGamma = (\partial C^{{\prime }} /\partial Z)((I)^{ - 1} )( - B - gG + WU) - \partial [\partial C/\partial Z(\dot{Z})]/\partial Z(\dot{Z}) \\ \end{aligned}$$
When the constraints are not in effect,
$$\varGamma = 0$$
$$C \ne 0$$
Suppose the above system can be dichotomized into a dominant subspace p d or simply d and an influenced subspace p i or simply i. The motion of the dominant part is influenced only minimally by the motion of the influenced part. Physical examples of this situation arise, for example, when a human is on a ship, in a vehicle, on a surfingboard in water or on a moving platform. Let the lower r degrees of freedom of Z be the dominant subspace represented by vector Y, and an input set U d . Let the remaining vector X of n − r degrees of freedom be that of p i . The influence of the subspace d on subspace i is through the constraint forces that are active between the two subsystems Γ id and the known motion β of the subspace d. The subspace i has its own control inputs U d as part of the input vector U. The objective here is to arrive at the (reduced) dynamics of the subspace i with inputs U m , β and Γ id .
Suppose the dynamics of the subspace d be described by a very large moment of inertia matrix I r and inputs U d that are very large in magnitude. This assumption allows reduction in the dynamics of the subspace d to the following
$$I_{r} \ddot{Y} = W_{r} U_{r}$$
From the known motion β of the subspace d, the velocities \(\dot{\beta }\) and the accelerations \(\ddot{\beta }\) can be computed. Therefore, Eq. (9) can be replaced by
$$\ddot{Y} = \ddot{\beta }$$
Without loss of generality, we can assume I r is a diagonal matrix of dimension r, and the known accelerations are a vector of dimension r. The dynamics of the original system of Eq. (7) can be written as that of two disjoint subspaces except that the forces of support between the two subspaces Γ id must be computed.
The equations of motion for this combined system of dynamic subspace i and the kinematic subspace d are formulated here. Let Z 1 be the vector of [X, β]. Let I 1 be the two-block diagonal matrix. The upper block diagonal is the restriction of I to dimension n − r. The second block diagonal is the identity rxr matrix. The B 1 matrix is the same as B with Z 1. The same is true for G. The matrix W is the same except that all the elements in the last r rows are zero. Similarly, all the last r rows of ӘC′/ӘZ in Eq. (7) are set to zero. Let the latter matrix be called V.
However, vector C has remained intact and when it is differentiated with respect to time, the variables β remain in its last r columns. These last r columns of C′/Z do not affect the equations of motion for the combined system because the I 1 matrix is block diagonal. Let us assume, for simplicity and ease of notation, that the only forces of constraint remaining in the system are Γ id . The latter restriction is not major and can easily be lifted. Let V 1 be a vector comprising of all the remaining kinematic variables that have been moved to the left side of the equation from I, etc., namely, the kinematic degrees of freedom β, and their first and second derivatives with respect to time.
With these clarifications, the equations for the combined system are:
$$I_{1} (Z_{1} )\ddot{Z}_{1} + B(Z_{1} ,\dot{Z}_{1} )\dot{Z}_{1} - gG(Z_{1} ) = W_{1} U_{i} + V\varGamma_{id} + V_{1} (\beta ,\dot{\beta },\ddot{\beta })$$
From Eq. (11), one can derive the required forces of constraint Γ id similar to Eq. (8). Once this last step is carried out, the original system is effectively reduced to dimension n − r.
A major step in the above development is that the computation of forces of constraint has been extended to systems described by a combined system of kinematics and dynamics. The main difference between the all dynamic and the combined kinematic–dynamic systems is that, for the latter system, the forces of constraint are functions of the kinematic accelerations, velocity and positions in addition to being functions of the state and the remaining inputs.
A more precise description of the system as described is given in Fig. 1. The upper part of the figure shows the dynamics of the biped, i.e., the i subsystem. The lower part of the figure shows the dynamics of a special version of a d subsystem. The two subsystems are primarily coupled through the four forces of constraint Γ. These forces are, in general, functions of the states and inputs of both subsystems. B.C. or U i refers to biped controls. B.S. describes the biped dynamics. Integrators with respect to time are shown as 1/s. The variables W and dW/dt are, respectively, the position and velocity states of the biped. Γ is the vector of the forces of interaction between the platform and the biped. The inputs to the platform are U i . P.S. describes the platform dynamics. The angle of rotation of the platform is Φ. The compensator is of the PID type. The large gain is K and v 1 describes the dynamic effect of the forces of constraint on the platform support forces acting on the system.
Biped on a rotating platform
As an example, consider a planar biped with a two-segment feet on a platform as shown in Fig. 2. This biped is an example of the i subspace. The system angles, the inertial coordinate system and the platform rotation angle: β—positive clockwise are shown.
The one-segment biped with a two-segment foot and the platform support forces
The objective is to control the biped when it is disturbed by a platform rotation. The biped has five degrees of freedom: the translation of the center of gravity of the body, and the three angles of the body and the two segments of the foot relative to the vertical gravity axis. Let the angle of rotation β of the platform be positive in the clockwise direction—measured from the horizontal axis. Let Γ be the four forces of contact with the platform—two support forces and two shear forces
$$\varGamma = \left[ {F_{2v} ,G_{2v} ,F_{3v} ,G_{3v} } \right]^{{\prime }}$$
where the superscript means transpose.
Biped dynamics
The equations of motion in the W space are
$$J(W)\ddot{W} + B(W,\dot{W})\dot{W} - gG(W) = EU + [\partial C/\partial W]\varGamma$$
The matrices and vectors appearing in Eq. (12) are given below.
$$\begin{aligned} J(\omega ) = \hfill \\ \left[ {\begin{array}{*{20}c} {m_{1} + m_{2} + m_{3} } & 0 & { - (m_{2} + m_{3} )k_{1} \text{cos}(\omega_{3} )} & {m_{2} k_{2} \text{cos}(\omega_{4} )} & {m_{3} k_{\text{3}} \text{cos}(\omega_{5} )} \\ 0 & {m_{1} + m_{2} + m_{3} } & {(m_{2} + m_{3} )k_{1} \text{sin}(\omega_{3} )} & { - m_{2} k_{2} \text{sin}(\omega_{4} )} & { - m_{3} k_{3} \text{sin}(\omega_{5} )} \\ { - (m_{2} + m_{3} )k_{1} \text{cos}(\omega_{3} )} & {(m_{2} + m_{3} )k_{1} \text{sin}(\omega_{3} )} & {I_{1} + (m_{2} + m_{3} )k_{1}^{2} } & { - m_{2} k_{1} k_{2} \text{cos}(\omega_{3} - \omega_{4} )} & { - m_{3} k_{1} k_{3} \text{cos}(\omega_{3} - \omega_{5} )} \\ {m_{2} k_{2} \text{cos}(\omega_{4} )} & { - m_{2} k_{2} \text{sin}(\omega_{4} )} & { - m_{2} k_{1} k_{2} \text{cos}(\omega_{3} - \omega_{4} )} & {I_{2} + m_{2} k_{2}^{2} } & 0 \\ {m_{3} k_{3} \text{cos}(\omega_{5} )} & { - m_{3} k_{3} \text{sin}(\omega_{5} )} & { - m_{3} k_{1} k_{3} \text{cos}(\omega_{3} - \omega_{5} )} & 0 & {I_{3} + m_{3} k_{3}^{2} } \\ \end{array} } \right] \hfill \\ \end{aligned}$$
The equation for B is
$$B(W,\dot{W}) = \left[ {\begin{array}{*{20}c} 0 & 0 & {(m_{2} + m_{3} )k_{1} \dot{\omega }_{3} \text{sin}\omega_{3} } & { - m_{2} k_{2} \dot{\omega }_{4} \text{sin}\omega_{4} } & { - m_{3} k_{3} \dot{\omega }_{5} \text{sin}\omega_{5} } \\ 0 & 0 & {(m_{2} + m_{3} )k_{1} \dot{\omega }_{3} \text{cos}\omega_{3} } & { - m_{2} k_{2} \dot{\omega }_{4} \text{cos}\omega_{4} } & { - m_{3} k_{3} \dot{\omega }_{5} \text{cos}\omega_{5} } \\ 0 & 0 & 0 & {m_{2} k_{1} k_{2} \dot{\omega }_{4} \text{sin}(\omega_{4} - \omega_{3} )} & {m_{3} k_{1} k_{3} \dot{\omega }_{3} \text{sin}(\omega_{5} - \omega_{3} )} \\ 0 & 0 & {m_{2} k_{1} k_{2} \dot{\omega }_{3} \text{sin}(\omega_{3} - \omega_{4} )} & 0 & 0 \\ 0 & 0 & {m_{3} k_{1} k_{3} \dot{\omega }_{3} \text{sin}(\omega_{3} - \omega_{5} )} & 0 & 0 \\ \end{array} } \right]$$
The equation for the gravity vector is:
$$G(W) = \left[ {\begin{array}{*{20}c} 0 \\ { - m_{1} } \\ { - (m_{2} + m_{3} )k_{1} \text{sin}\omega_{3} } \\ { - m_{2} k_{2} \text{sin}\omega_{4} } \\ {m_{3} k_{3} \text{sin}\omega_{5} } \\ \end{array} } \right]$$
The coefficient matrix for the support force vector Γ is
$$\partial C/\partial W = \left[ {\begin{array}{*{20}c} 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ { - k_{1} \text{cos}\omega_{3} } & {k_{1} \text{sin}\omega_{3} } & { - k_{1} \text{cos}\omega_{3} } & {k_{1} \text{sin}\omega_{3} } \\ {l_{2} \text{cos}\omega_{4} } & { - l_{2} \text{sin}\omega_{4} } & 0 & 0 \\ 0 & 0 & {l_{3} \text{cos}\omega_{5} } & { - l_{3} \text{sin}\omega_{5} } \\ \end{array} } \right]$$
The biped has three actuators:
$$U = \left[ {u_{12} ,u_{13} ,u_{23} } \right]$$
The matrix E is:
$$E = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & { - 1} & 0 \\ { - 1} & 0 & 1 \\ 0 & 1 & { - 1} \\ \end{array} } \right]$$
referring to Fig. 1; the box B.S. represents Eq. (12). The outputs of this box are the acceleration and velocities to be integrated with respect to time.
Platform dynamics
The equations of the above system must be augmented with the dynamics of the platform. We assume the platform rotates about its center of gravity and is large enough and the actuators that implements its rotation are large. For simplicity, the equation of motion for the platform is taken to be a second-order system with one actuator.
$$I_{p} \ddot{\beta } + L_{p} \dot{\beta } + K_{p} \beta = v_{1} + v_{2}$$
The box labeled P.S. in Fig. 1 represents the scalar transfer function
$$\frac{Phi}{{U_{d} }} = \frac{1}{{(I_{p} s^{2} + L_{p} - ps + K_{p} )}}$$
The variable v 1 represents the moment of the forces of constraint
$$v_{1} = R_{p} \varGamma$$
The variable v 2 is the output of the controller: large gain proceeded by a PID controller. It is assumed that the output of the platform subsystem is the angle of rotation of the platform, and the input to the platform subsystem is the desired angle of rotation β, i.e.,
$$U_{d} = \beta$$
Standard control techniques can be applied to make the transfer function Φ/v 1 small and the transfer function Φ/U d close to identity. Our objective is to concentrate on the sensory and control aspects of the biped and, specifically, its postural stability in reaction to the platform disturbance. We further assume that
$$\varPhi = \beta$$
and would like to reduce the dynamics of the system to that of the biped alone and with the known kinematics of the platform motion. Contrast with a person on a skatingboard where the forces of contact and support are used to control the board.
Platform kinematics plus biped dynamics
It is assumed that the platform actuator and moment of inertia are large enough such that influence of the forces of support on the platform dynamics is minimal and hence negligible. This assumption allows the motion analysis to be restricted to the kinematics of the platform motion of specific known trajectories.
The augmented system is characterized by six degrees of freedom:
$$W_{a} = \left[ {W,\beta } \right]$$
The coefficient matrices in Eq. (7) must in turn be augmented:
$$J_{a} ,B_{a} ,Gr_{a} ,\partial C/\partial W_{a} ,\;{\text{and}}\;E_{a}$$
The structure of each of these matrices is briefly described. The two-block diagonal matrix of inertia J a is made up of J and J p . The matrix B a is the two-block diagonal matrix of B and a zero. The column vector of gravity Gr is augmented by a zero, because we assume the platform is rotated about its center of gravity. The matrix E a is extended by a sixth row of three zeros and one and by a fourth column of zeros except for the last element. This is to account for the platform acceleration as an input. The coefficient of Γ matrix will be augmented by a row of four zeros at the bottom. This merits some explanation. We are justified in taking this step since the dynamic equation of the platform does not depend on the forces of support. On the other hand when we differentiate the constraints with respect to β one gets a last row for ӘC a /ӘW a that is not zero. The importance of this last matrix is in the calculation of the support forces. Because J a is a block diagonal matrix with zeros in the last row and last column, the denominator of the computation of Γ will not depend on β as discussed earlier. The dependence of the forces of support on β, the angle of rotation, and its derivative and second derivative will be through the twice differentiation of the constraints with respect to time which leads to the direct dependence of the forces of support on the rotation angle, and its angular velocity and acceleration.
Stability can be achieved by control of the stiffness of agonist–antagonist pairs at joints and across the segments [21]. The simultaneous co-activation of agonist–antagonist pairs of muscles at least by a pair at every joint achieves the same end. The co-activation produces sufficient position and velocity feedback to bring about stability in some vicinity of the equilibrium position. Lyapunov stability can be utilized to establish the domain of attraction, and the platform disturbances are modeled as a perturbation.
Let K d be a diagonal 5 × 5 matrix whose diagonal elements are, respectively, the stiffnesses at the joints and across the joints. Similarly, let K p be a diagonal matrix of joint and across joint viscosities. Let \(\Delta \varTheta\) be defined as follows:
$$\Delta \varTheta = [\Delta \theta_{1} ,\Delta \theta_{2} ,\Delta \theta_{3} ]^{\prime}$$
The incremental work, ∆W, of the torques U = [u 12, u 13, u 23] on the system is
$$\Delta W = - (\Delta \varTheta )E^{\prime}U^{\prime}$$
Thus, the input to the system will be
$$T = - E^{\prime}U^{\prime}$$
For the input torques, it is designed using the PD control as
$$U = K_{p} E\varTheta + K_{d} E\dot{\varTheta }$$
Therefore, the effect of co-activation of the three torque pairs can be represented as
$$T = - E^{{\prime }} K_{p} E\varTheta - E^{{\prime }} K_{d} E\dot{\varTheta } = - K_{kP} \varTheta - K_{kd} \dot{\varTheta }$$
$$K_{kp} = \left[ {\begin{array}{*{20}c} {k_{p1} + k_{p2} } & { - k_{p1} } & { - k_{p2} } \\ { - k_{p1} } & {k_{p1} + k_{p3} } & { - k_{p3} } \\ { - k_{p2} } & { - k_{p3} } & {k_{p2} + k_{p3} } \\ \end{array} } \right]$$
This matrix allows one to do quantitative analysis by selecting the joint and biarticular stiffnesses. The velocity feedback matrix K kd is constructed by assuming as a diagonal matrix and is a fraction of the diagonal matrix K kp .
The above analytically shows that the co-activation of a pair of agonist–antagonist actuators results in negative angular position and angular velocity feedback. The stiffness and viscosity, i.e., the position and the velocity feedback gains, can be programmed. Thus, the system is activated by three quantities: stiffness and viscosity at the three joints among the three segments of the biped in Fig. 1. We consider the stability of the system about the vertical stance.
Simulations and comparison
When the planar biped is on a rotating platform as in Fig. 1, the effect from the platform to the biped is the centrifugal force. In this case we only consider the balance in the biped plane and assume that the motion perpendicular to the biped plane is fixed. Thus, the system can be described as
$$\left[ {\begin{array}{*{20}c} {{\text{eq}}1} \\ {{\text{eq}}2} \\ {{\text{eq}}3} \\ {{\text{eq}}4} \\ {{\text{eq}}5} \\ \end{array} } \right] = J(W)_{5 \times 5} \left[ {\begin{array}{*{20}c} {\ddot{x}} \\ {\ddot{y}} \\ {\ddot{\theta }_{1} } \\ {\ddot{\theta }_{2} } \\ {\ddot{\theta }_{3} } \\ \end{array} } \right] - \left[ {\frac{\partial C}{\partial W}} \right]_{5 \times 4} \left[ {\begin{array}{*{20}c} {F_{2v} } \\ {G_{2v} } \\ {F_{3v} } \\ {G_{3v} } \\ \end{array} } \right] + B(W,\dot{W})\dot{W} - gG(W) - E\left[ {\begin{array}{*{20}c} {u_{12} } \\ {u_{13} } \\ {u_{23} } \\ \end{array} } \right] + \dot{\beta }^{2} {\text{Cen}} = 0$$
where Cen is the centrifugal force as
$${\text{Cen}} = \left[ {\begin{array}{*{20}c} {(m_{1} + m_{2} + m_{3} )r} \\ 0 \\ { - (m_{2} + m_{3} )(r + k_{1} \text{sin}\omega_{3} )k_{1} \text{cos}\omega_{3} } \\ { - m_{2} (r + k_{1} \text{sin}\omega_{4} )k_{2} \text{cos}\omega_{4} } \\ { - m_{3} (r + k_{1} \text{sin}\omega_{5} )k_{3} \text{cos}\omega_{5} } \\ \end{array} } \right]$$
where r is the distance from the center of mass of the biped to the platform rotation axis.
For two-feet support, the geometric constraints of the biped are
$$C = \left\{ {\begin{array}{*{20}l} {l_{2} \text{cos}\theta_{2} = l_{3} \text{cos}\theta_{3} } \\ {l_{2} \text{sin}\theta_{2} - l_{3} \text{sin}\theta_{3} = d} \\ \end{array} } \right.$$
From the rotating system, there is no translation resulting in \(\ddot{x} = \ddot{y} = 0\). By taking double derivative of geometric constraint in Eq. [16], \(\ddot{\theta }_{2} ,\ddot{\theta }_{3}\) will be obtained. Substitute these into Eq. (15), five equations with five unknowns (\(\ddot{\theta }_{1} ,F_{2v} ,G_{2v} ,F_{3v} ,G_{3v}\)) can be solved.
For single-foot support, (16) does not exist resulting in \(\ddot{\theta }_{2} ,\ddot{\theta }_{3}\) as unknowns. At the same time, two of the four ground forces disappear when considering left or right foot supports the body. In this case, there are still five unknowns (\(\ddot{\theta }_{1} ,\ddot{\theta }_{2} ,\ddot{\theta }_{3} ,F_{2v} ,G_{2v}\)) (left foot support, for right foot support it is (\(\ddot{\theta }_{1} ,\ddot{\theta }_{2} ,\ddot{\theta }_{3} ,F_{3v} ,G_{3v}\))) which can be solved from the five equations in (15).
The above analysis will be used in the following simulations covering both single-foot support and double-feet support balance with the platform rotation as disturbance. Parameter I refers to the moment of inertia in Kgm 2 about the center of gravity of the link. Parameter m refers to the mass of the link in Kg. Parameter l refers to the length of the link in m. Parameter k refers to the distance of the center of mass of the link from the lower joint. The system parameters are given as:
$$r = 3,l_{2} = 1,l_{3} = 1,k_{1} = 0.28,k_{2} = 0.46,k_{3} = 0.46,I_{1} = 3.25,I_{2} = 1.4,I_{3} = 1.4,m_{1} = 50,m_{2} = 12,m_{3} = 12,g = 10.$$
Two feet are on the platform and not moving, while the platform has a fixed angular velocity as 1 rad/s. The torso is the main moving part with u 12 = −400 * θ 1 − 40 \(\dot{\theta }_{1}\), u 13 = −400 * θ 1 − 40 \(\dot{\theta }_{1}\), u 23 = 0 as the input using the negative position and velocity feedback [22]. The initial position is θ 1 = 0, θ 2 = 3π/4, θ 3 = 5π/4. The simulation results show that the torso comes to the equilibrium position within 0.6 s as in Fig. 3a and the ground forces on the two feet also stabilize fast as shown in Fig. 3b. The ground forces [23] on the right foot increase to the equilibrium point, while those on the left foot decrease due to the double-feet support position and the centrifugal force of the platform pointing from left foot to the right. The simulation results conform to the human hip control strategies in disturbed standing [24, 25] by moving the center of mass anteriorly as seen from the θ1 value in Fig. 3a. A bigger right foot vertical force G2v than the left foot G3v also proves that the center of mass moves to the right. This is also in line with the analysis in [21] that the effect of a horizontal disturbance can be reduced when the torso bends to be parallel to the horizontal plane.
Simulation results for case 1. a Torso motion. b Ground forces
In this case, the platform angular velocity is set as sinusoidal function sin((2 * π/2) * t). The simulation result is shown in Fig. 4 which illustrates the stabilization with the input and initial position the same as in case 1. The torso can follow the platform disturbance after about 0.6 s, and the ground forces also balance with the process as in Fig. 4b. Since the centrifugal force constantly points from the left foot to the right foot, the hip adjusts the torso following the speed change of the platform to move the center of mass to the balanced point [24, 25] which is in the anterior side as seen from the sinusoidal wave of θ 1 upon zero line in Fig. 3a. This can be also seen from the bigger right foot vertical force G2v varying between 380 and 540 N, and the combined horizontal force F2v and F3v keeps negative in the process due to the positive centrifugal force direction.
In this case only the right foot stands on the rotational platform to support the body, while the platform has a fixed angular velocity as 1 rad/s. The right leg is left free, and the body starts from the position θ 1 = 0, θ 2 = π, θ 3 = π. The negative position and velocity feedback are chosen as K = [300, 300, 200] and L = [50, 50, 50]. The system stabilizes in about 0.8 s as shown in Fig. 5. The ground forces on the right foot also balance along the process, while the input torques for the three joints are illustrated in Fig. 5b. The horizontal platform disturbance is fully balanced by the horizontal ground force F2v, while the vertical ground force G2v mainly supports the body weight after the balance. The joint angles show that the torso moves the negative side (θ 1 < 0) and both the legs move to the right (θ 2, θ 3 < π) of the vertical line. This conforms to the human ankle and hip strategy [26, 27] in disturbance standing in sagittal plane in which a double-segment inverted pendulum control strategy is used for the balance. When the body is balanced with the constant centrifugal force, the center of mass is moved to the opposite side of the centrifugal force direction as there is only one leg support and this is different to case 1 with two-foot support.
Simulation results for case 3. a Torso motion. b Ground forces and input torques
Following case 3, this case changes the platform angular velocity to sin((2 * π/2) * t). The simulation result is shown in Fig. 6 which illustrates the stabilization process in which the body follows the platform disturbance in less than 1 s. Similar to case 3, the horizontal ground force F2v resists the platform rotation force, while the vertical ground force G2v supports the body weight. It can be seen from the vertical ground force change that between two big peak changes a small peak exists due to the free left leg balancing. Input torques between − 22 and 18 N m are needed in the whole process. The results show similar strategy in the body balance with case 3 but with a sinusoidal process due to the sinusoidal balance. The body balances the center of mass between the left side of the vertical line and the right vertical position as seen from the joint angles in Fig. 6a.
The work presented here explores the dynamics of separable coupled rigid body systems, a special class of constrained rigid body systems. Specifically, the dynamics of the two-coupled separable systems is formulated, and two examples, a biped model under rotational platform disturbances and a simple skateboard model, are analyzed for illustration and computationally simulated. The results of the simulations adequately validate the proposed theoretical models. The inertia forces, which resulted from the moving platform, can be decoupled and integrated into the body system as a disturbance, and the balance and stability of the body can be guaranteed with the stiffness and viscosity feedback control.
The main contribution of this work is the novel extension to the known dynamics of constrained rigid bodies. The modular, versatile and systematic formulation presented here is computationally efficient and has many applications in the studies of the human neuro-musculoskeletal system, robotic systems and humanoids [28], as well as clinical and sports biomechanics applications. Examples include clinical settings of patients interfacing with a rotating medical platform or machine, as well as the dynamics, stability and control of athletes on surf or diving boards. Further potential applications include quantitative studies on the balance and postural strategies as related to balance and vestibular dysfunction and deficits. Simulation and animation studies of human motion in interface with stationary or moving bases of support could also benefit from the work presented here. Examples include some of today's extreme sports, such as skateboarding and surfboarding, where balancing and control are critical for safety.
The current simulation used a simplified three-rigid body link model, where only hip joint control strategies were included. Since the ankle strategy is typically adopted in human balance control modeling [21], a more complex musculoskeletal model that also includes the knee and ankle joints would allow for better biofidelic representation of human motion. Future work should also study the effect of the inertial forces of the moving base on the control strategies, as these forces are integral to physiological movement and human interaction with the environment. The motion of the moving base in this work was assumed as a simple rotation with constant velocity. Future work should consider more complex motions of the base, including translation, and a variety of speeds in order to simulate various real-life scenarios such as the interaction with an accelerating or turning vehicle. Future work would also benefit by including experiments with human participants for validating the simulation results and to extract more realistic motion control strategies.
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Hemami H, Wyman B. Modeling and control of constrained dynamic systems with application to biped locomotion in the frontal plane. IEEE Trans. Autom Control. 1979;4:526–35.
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Shupert F, Horak CL, Black F. Hip sway associated with vestibulopathy. J Vestib Res. 1994;4(3):231–44.
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Hemami H, Barin K, Pai Y-C. Quantitative analysis of the ankle strategy under translational platform disturbance. IEEE Trans Neural Syst Rehabil Eng. 2006;14(3):2–12.
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Chung SY, Khatib O. Contact-consistent elastic strips for multi-contact locomotion planning of humanoid robots. In: 2015 IEEE international conference on robotics and automation (ICRA), Washington State Convention Center Seattle, Washington, 26–30 May 2015.
KF initiated the research idea, proposed the decoupled dynamic modeling method, developed the biped dynamic model and contributed to the main part of the writing. DM developed the simulation and decoupled dynamics model of the biped model and contributed to the simulation result analysis. HH was overseeing the whole research concept and technical insights. All authors read and approved the final manuscript.
The authors gratefully acknowledge the assistance of the Computer Facilities personnel of the Department of Electrical Engineering at the Ohio State University, specifically Vincent Juodvalkis, Donald S. Gibb and Aaron Aufderheide.
This research was supported by the internal research fund from Khalifa University of Science and Technology. This work was also partially supported by the Natural Science Foundation of China (Project No. 51475332), the Program of Introducing Talents of Discipline to Universities ("111 Program") under Grant No. B16034 and the Beijing Natural Science Foundation (Project No. 3172010).
Department of Biomedical Engineering, Khalifa University of Science and Technology, Abu Dhabi, UAE
Kinda Khalaf
Robotics Institute/Mechanical Engineering Department, Khalifa University of Science and Technology, Abu Dhabi, UAE
Dongming Gan
Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, 43210, USA
Hooshang Hemami
Correspondence to Dongming Gan.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Khalaf, K., Gan, D. & Hemami, H. Dynamics and control of separable coupled rigid body systems. Robot. Biomim. 4, 14 (2017). https://doi.org/10.1186/s40638-017-0068-0
Coupled mechanical systems
Constrained dynamics
Dimensionality reduction


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March 1, 1994 Journal article Open Access
Ford revisited: A critical review of the chronology and relationships of the earliest ceramic complexes in the New World, 6000-1500 B.C.
Hoopes, John W.
Citation Style Language JSON Export
"DOI": "10.1007/bf02221836",
"author": [
"family": "Hoopes, John W."
"issued": {
"date-parts": [
"abstract": "In 1969, Ford offered a comprehensive model for the diffusion of ceramic production and Formative lifeways in the New World. Although criticized as simplistic, it was echoed by other \"unitary\" models, such as Lathrap's spread of Tropical Forest culture outward from a lowland South American hearth. Radiocarbon dates suggest that the earliest American pottery appears in the Amazon basin as early as 6000 B.C. However, there is little support for an \"ex Amazonas lux\" spread of pottery technology.  Diffu\u00acsionary models predict early complexes will resemble one another at first and then diverge over time, but comparative analysis reveals substantial variability even at the earliest time level. Heterogeneity among the earliest complexes indicates several likely hearths for the independent evolution of ceramic production, including: 1) lowland Brazil, 2) northern Colombia; 3) coastal Ecuador, 4) coastal Peru, 5) central Panama, 6) southern Mesoamerica, 7) the southeastern U.S., and 8) the central U.S.",
"title": "Ford revisited: A critical review of the chronology and relationships of the earliest ceramic complexes in the New World, 6000-1500 B.C.",
"type": "article-journal",
"id": "848786"
Data volume 1.3 GB
Unique views 1,242
Unique downloads 1,486


text:
Q: DataTables - scrollX wont Go Away when scrollY enabled Below is the code I am using, and here is a working example with dummy data.  When I enable scrollY and set scrollX: false, scrollX is not disabled!  What am I doing incorrectly?
$(document).ready( function () {
  var table = $('#example').DataTable({
    scrollY: 300,
    scrollX: false
  });
} );

A: You need set table width
table {

       table-layout:fixed;
       width: 98% !important;
}

And change your div table instead nowrap class apply wrap class
So you table div should be like this:
<table id="example" class="display wrap" width="100%">

Hope this help you Thanks !

A: I suppose that you've had this problem for the same reason i did:
When scrollY is active but scrollX isn't, the scrollX bar is visible, but only move the tbody.
If that is indeed why, then the solution to the problem is simply to set scollX: true. Then the header and footer scolls along with the body.

redpajama_set_name: RedPajamaStackExchange


text:
Last edited by Togis
5 edition of German immigrants in America found in the catalog.
German immigrants in America
Elizabeth Raum
an interactive history adventure
by Elizabeth Raum
Published 2008 by Capstone Press in Mankato, Minn .
German Americans -- History -- Juvenile literature.,
Immigrants -- United States -- History -- Juvenile literature.,
German Americans -- Texas -- History -- 19th century -- Juvenile literature.,
German Americans -- Dakota Territory -- History -- Juvenile literature.,
German Americans -- Wisconsin -- Milwaukee -- History -- 20th century -- Juvenile literature.,
United States -- Emigration and immigration -- History -- Juvenile literature.,
Germany -- Emigration and immigration -- History -- Juvenile literature.
Statement by Elizabeth Raum.
Genre Juvenile literature.
Series You choose books
LC Classifications E184.G3 R33 2008
ISBN 10 9781429613569, 9781429617635
This book is written for children to get a glimpse of German immigrants from Germany and from Russia. Although there were Germans in North America as early as the 's, this book deals with those coming here in the 19th century, and it covers especially well the trials and tribulations of early German settlers in Texas, mid-America, the Dakotas, and even Milwaukee. The German Immigration to America in the 's constituted the largest single immigrant group during the colonial era. German Immigration to America continued into the late 's but conflict began to grow between Britain and the colonies and the American War of Independence ( - ) erupted.
Even though large bookstores have for the most part shut down in America there are still many independent bookstores. Many of them cater to specific genres or types of books. If learning languages and foreign translations are your things then these bookstores are a must see. The following is a listing of German bookstores and distributors both online and via telephone in the United States an Author: Ingrid Bauer. This immigration database includes more than 4 million Germans who arrived in the United States between and through the ports of Baltimore, Boston, New Orleans, New York, and Philadelphia. German Immigration records may include: • First name (s) • Year of Arrival. • country of origin. • city or town of last residence.
In the second part of the book (Chapters 9 through 18) Grubb focuses on German immigrants to discuss a myriad of issues involving the institution of servitude. A large proportion of immigrants to the American colonies worked as indentured servants in their first years to pay off passage costs. "America Is Immigrants" is a wonderful collection of short biographies on famous immigrants in the United States. The book features everyone from athletes to diplomats to scientists. It shows how valuable immigration is to our country and the contribution immigrants have made to our country.4/5(33).
Builders of the Quaker road
Patterns of self-destruction
The destroyer
Fun Without Vulgarity
What are Americas social values?
Focus on New Zealand.
The Present Status of the Quantum Theory of Light
Haunted Cincinnati and Southwest Ohio
Health promotion clinics in general practice
The Best of Super Ford How to Hop Up Your 5.0 Mustang
Drawing: ideas, materials, and techniques
Psychological Evaluations for the Courts
Clash in the north
Military Functions, National Military Establishment Appropriation Bill for 1949.
German immigrants in America by Elizabeth Raum Download PDF EPUB FB2
No history per se about German immigrants. Read more. 3 people found this helpful. Helpful. Comment Report abuse. love2shop. out of 5 stars Five Stars. Reviewed in the United States on Verified Purchase.
My children thoroughly enjoy these interactive history books. Great book and keeps kids engaged. Read more/5(8). This is a wonderful and insightful book with 32 pages of good solid information about German immigrants to America. Wonderful photos, color and b&w. In the back it has a timeline, a page of 'words to know', a section called 'learn more', a list of places to 'write and visit', some internet sites, and an index/5(2).
Data files relating to the immigration of Germans to the United States for arrivals Created by the Balch Institute for Ethnic Studies, Center for Immigration Research.
In August ofthe National Archives replaced the ARC – Archival Research Catalog - with the OPA – Online Public Access. ARC identifiers will still work to access the collections in OPA.
"German Immigration to America: The First Wave," by Don Heinrich Tolzmann, Heritage Books, Bowie, MD, This page paperback is a reprint of two articles on the major German Palatine migration from This was the first major non-religious immigration of Germans to North America consisting of people in 10 s: 3.
Because Germany was one of America's adversaries in the war, many Anglo-Americans began to fear that German Americans were still loyal to the Kaiser, or German ly, German Americans Author: Becky Little. Germans to America is a series of books which index ship passenger arrival records of German immigrants for the years listed below.
Each volume contains a chronological listing of the passenger lists, followed by an alphabetical index of each passenger in that volume. There are approximat names in each volume. - About German-language journals were being printed in the United States, the greatest number ever.
A typical newspaper was the New York Staats Zeitung. - In this year, an estimated million German-born immigrants lived in the United States. With declining immigration and increasing assimilation, the number of German-language.
Describes the experiences of German immigrants upon arriving in America. The readers choices reveal historical details from the perspective of Germans who came to Texas in the s, the Dakota Territory in the s, and Wisconsin before the start of World War I/5.
Populous as German immigrants to America were by the end of the eighteenth century, the major waves of immigration came after the conclusion of the Napoleonic Wars in Germany's economy suffered in several ways.
Too many goods were imported, especially cloth from industrialized England. The German immigrant story is a long one—a story of early beginnings, continual growth, and steadily spreading influence. Germans were among the first Europeans to make their homes in the New World, and are among the United States' most recent arrivals.
They were aboard the first boats that came. Find many great new & used options and get the best deals for Three Hundred Years of German Immigrants in North America, Their Contributions to the Evolution of the New World: a Pictorial History with Illustrations by Klaus German Wust and Heinz Moos (, Book, Illustrated) at the best online prices at eBay.
Free shipping for many products. German Immigrant Arrivals: Resources in the Library of Con gress Compiled and Annotated by Barbara B.
Walsh The purpose of this bibliography is to identify lists of German immigrants in the Library of Congress (published, manuscript, and electronic). A discussion of Germans in colonial America. German and American Sources for German. Are you researching German immigrants to America during the 19th century.
"Germans to America," compiled and edited by Ira A. Glazier and P. William Filby, is a series of books which indexes passenger arrival records of ships carrying Germans to the U.S.
ports of Baltimore, Boston, New Orleans, New York, and presently covers the records of over 4 million passengers during the. Trumbauer, L. German Immigration.
New York: Facts On File, Details personal stories of German immigrants to the United States and the key players in the formation of the country. Wittke, Carl. Refugees of Revolution: The German Forty-eighters in America. Philadelphia: University of.
Primary Sources German Immigration. Francis Daniel Pastorius was a lawyer in Krefeld but because of his religious beliefs was forced to leave the country in Pastorius arranged for twelve other Quaker families from Krefeld to sail to America on a ship called the ius and his followers established Germantown, the first permanent settlement of German immigrants in America.
Discusses reasons German people left their homeland to come to America, the experiences immigrants had in the new country, and the contributions this cultural group made to American society.
Includes activities. German Immigrants, The book below describes the history and process of migrating from Germany to the United States: Wellauer, Maralyn Ann. German Immigration to America in the Nineteenth Century: A Genealogist's Guide. Milwaukee, Wisconsin, USA: Roots International, (FHL book W2we.
To trace German origins in Pennsylvania can be a daunting task. Before the war broke out, America had welcomed German immigrants and regarded them highly.
German was the second most widely spoken language in the. Q: Where were German immigrants allowed to work in America. When. My 7th great-grandfather, Johann Michael Hennescheid (–), was born in the Palatinate at a place called Naumburger Hof.
It was a farm that still exists today. In the early Whatever vestige of German America remained after the s was wiped out by similar pressures during World War II, not to mention the shame that came with German identity after it.
German Immigrants, at Ancestry/free with registration; includes searchable, digitized emigration lists from these six books by Clifford Neal Smith: Emigrants from the Former Amt Damme, Oldenburg (Now Niedersachsen), Germany, Mainly to the United States, Describes the experiences of German immigrants upon arriving in America.
The readers choices reveal historical details from the perspective of Germans who came to Texas in the s, the Dakota Territory in the s, and Wisconsin before the start of World War I.Get this from a library! Why German immigrants came to America.
[Lewis K Parker] -- Explores German immigration to the United States from colonial days to the present, and looks at the contributions of German Americans to the culture of the United States.
forabetterchicago.com - German immigrants in America book © 2020


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text:
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You are at:Home » Tumour Stream » GI Cancers » Genetic test for anal cancer could identify those at high risk
Genetic test for anal cancer could identify those at high risk
By ONA Editor	 May 31, 2017 No Comments
A new test, based on a patient's epigenetics, could be an accurate and inexpensive way to find and treat those at highest risk of anal cancer – a disease with growing incidence in women, men who have sex with men (MSM) and people with HIV.
The early research by Queen Mary University of London (QMUL), which was funded by Cancer Research UK, finds that the test could lead to a reduction in painful procedures and minimise the over-treatment of people at low risk.
Anal cancer is mostly caused by human papillomavirus (HPV) – the same virus that causes cervical cancer.
In 2014, the UK had around 1,300 new cases of anal cancer and 360 deaths.
In addition to rising levels in women and MSM, anal cancer is more common in HIV-positive MSM with around 100 cases per 100,000, compared to 25 in HIV-negative MSM, and only 1.5 in men in general.
Diagnosis presents many challenges.
Full biopsies are painful, and taking a small sample of cells ('cytology') is problematic because lesions can be hidden and clinicians give varying interpretations of results.
High-resolution anoscopy, where the anal canal is examined with a high resolution magnifying instrument, is often used as the primary screening tool for high-risk populations but is uncomfortable for the patient, expensive, complex and generates subjective results.
Lead researcher Professor Attila Lorincz from QMUL said: "The widespread over-treatment of anal precancerous lesions is necessary today because we don't know which ones will progress to cancer. But this creates a large burden on anoscopy clinics in the UK and the procedures can be detrimental to people's quality of life. Many people are undergoing these procedures unnecessarily, so what we really need is precision medicine to identify those who do need treatment."
The research, published in the journal Oncotarget, involved studying anal biopsy specimens from 148 patients in London, including 116 men (mostly MSM).
The specimens were analysed to look for genetic markers that may be associated with the presence of anal cancer.
The team specifically looked at the patients' epigenetics and found that all of the anal cancers showed the presence of specific epigenetic methylation markers on the patients' EPB41L3 gene (a tumour suppressor gene) and also on certain regions of their viral HPV genome.
The results suggests that epigenetic testing may be an accurate and thorough method to indicate whether a patient's lesions are destined to progress to anal cancer.
This could reduce the costs, pain and anxiety from other methods of diagnosis, and minimise over-treatment of low risk people.
Professor Lorincz added: "We thought this would require a complicated genomic signature involving hundreds of genes, so we were surprised that we could get such an accurate prediction from just two biomarker genes. That's important because the expected cost of the test will be fairly low.
"Now that we can identify those at risk, and conversely, those not at risk, we hope to see a big improvement, by making sure that anoscopies and laser or chemical surgery are only given to those who need it." Professor Lorincz
Once developed, the test would involve taking a small sample of cells from the anal canal via a swab and then sending the sample off to a laboratory for epigenetic analysis.
While a test could be developed within five years, the researchers caution that the results first need to be confirmed in a much larger study across the UK, and repeated using swab samples rather than the biopsies which were used in the current study.
Dr Rachel Orritt, Cancer Research UK's health information officer, said: "This study builds on what we already know about the link between changes to cell DNA and cervical cancer, and shows that similar changes to the DNA in anal cells could suggest anal cancer.
"If other studies confirm and build upon these findings, this promising research could be used to develop a less invasive method to help doctors identify people who are at a higher risk of anal cancer and avoid unnecessary procedures for those who are at a lower risk."
The researchers say that these types of biomarker – epigenetic methylation biomarkers – are important in a large number of other diseases, and could lead to a completely new approach to diagnostics and drug therapy.
Professor Lorincz explained: "These could be the early stages of a discovery of a universal set of biomarkers for any cancer. And there may be implications on therapies, as there are new techniques where the epigenetic pathway can be targeted by drugs. This is going to be the hot new area going forward in the next 15 years, so people need to be paying attention to this space."
Source: Queen Mary University of London
ONA Editor
The ONA Editor curates oncology news, views and reviews from Australia and around the world for our readers. In aggregated content, original sources will be acknowledged in the article footer.
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text:
Seventh-century workshop 'that built priceless Sutton Hoo treasures' is uncovered by archaeologists
Seventh-century workshop 'that built priceless Sutton Hoo treasures' is uncovered by archaeologists in Suffolk just three miles away from where Anglo-Saxon burial ship was unearthed in 1939
The community of craftsmen, which dates back at least 1,400 years, was discovered in Rendlesham, Suffolk.
The site is just three miles from Sutton Hoo, described as the UK's greatest archaeological discovery and portrayed in the hit Netflix film The Dig.
Melted metal fragments and slag found at the Rendlesham site indicate workers were involved in iron smithing and producing items out of copper alloy.
Artefacts made from copper alloy and iron were found in the 88ft burial ship – including an ornate helmet believed to have provided protection in battle while also used as a crown.
The items may have belonged to East Anglia's King Raedwald, who is widely thought to be the ruler buried in the ship in the 7th century AD.
A Suffolk County Council spokesman said those buried at Sutton Hoo would have 'probably lived at Rendlesham', adding: 'There is also evidence of craft working at Rendlesham, so it is possible they may have produced some of the objects discovered in the Sutton Hoo burial grounds.'
The unearthing of the ship in 1939 changed the narrative of British history as it showed the Anglo-Saxons were far more advanced than previously thought.
The Dig, released last year, starred Ralph Fiennes as archaeologist Basil Brown, who found the ship after being hired by landowner Edith Pretty, played by Carey Mulligan, to excavate burial mounds.
Other artefacts found at Rendlesham include spindle whorls and loomweights used in spinning and weaving, and dress items such as a copper alloy brooch and buckle.
There were also pottery vessels for cooking and storage, and bones from butchered cattle, sheep and pigs. The remains of what may have been a palace for King Raedwald and other Anglo-Saxon rulers was found nearby during excavations betwwen 2008 and 2014.
The latest dig took place this year as the first phase of a four-year project backed by a £517,000 National Lottery Heritage Fund grant. Its exact location is being kept a secret to deter treasure hunters and metal detectorists.
Much of the excavation was carried out by 150 volunteers – among them pupils of Rendlesham primary school and youngsters from the Suffolk Family Carers charity – under the guidance of Suffolk council's archaeological service and Cotswold Archaeology Ltd.
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Umami Burger's Parent Company to Open Food Hall in NYC This July
The design for C3's forthcoming food hall in New York aims to be "more reminiscent of an upscale restaurant than a traditional food hall." Rendering Courtesy of C3
Creating Culinary Communities (aka C3) is bringing its varied fast-casual brands, many of which have gained traction through shared kitchens, forward in another format: food halls.
C3's Citizens food halls, the first of which is set to open this July in New York City, will exclusively feature nine-plus vendors owned and operated by C3; its brands include Umami Burger, Krispy Rice, EllaMia, S Bar, Casa Dani, Katsuya and Sam's Crispy Chicken.
Further seeking to keep its operations in-house and offer seamless ordering across multiple brands, C3 will rely on its own online ordering and delivery app, Citizens Go, which it launched last month.
For those wanting to dine in-person, the food halls will offer sit-down and full-service as well as grab-and-go options, including hand-rolled sushi, pasta, sandwiches and pastries.
Citizens in NYC also will include a boutique wine shop with interactive classes.
The forthcoming NYC food hall was designed by award-winning architect and designer David Rockwell. It will feature geometric food counters, vibrant brand imagery and stone pillars, all of which seek to create an ambiance "more reminiscent of an upscale restaurant than a traditional food hall," according to a press release.
Grab-and-go options will be plentiful at the new food hall. Renderings Courtesy of C3
A second Citizens food hall is set to debut next year in Atlanta, and additional locations are planned in Seattle, Miami and California.
Sam Nazarian, founder and CEO of C3, called Atlanta and New York "dynamic, culinary-centric cities whose restaurant industries have significantly suffered this past year."
"With Citizens, we aim to bring fresh energy, variety and employment opportunities to these culinary spaces at a time when diners are beginning to look forward to immersive, in-person dining experiences again," Nazarian adds.
Also starting this year, C3 is launching delivery-focused food halls within Graduate Hotels; those, too, will exclusively feature C3's brands, with up to six per location.
As of February 2021, C3 operated 250 digital kitchens and 15 brands.
Despite not yet recovering all its in-store sales, periodic staffing challenges, menu price hikes and supply chain disruptions, Chipotle Mexican Grill had a record third quarter, bringing in $2 billion...
This week in Expansion Roundup, FER checks out growth plans for Bad Ass Coffee of Hawaii, The Peach Cobbler Factory, Jack in the Box, Chicken Salad Chick, Peter Piper Pizza...