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Complementarity Formulations and Existence of Solutions of Dynamic MultiRigidBody Contact Problems with Coulomb Friction
 Mathematical Programming
"... . In this paper, we study the problem of predicting the acceleration of a set of rigid, 3dimensional bodies in contact with Coulomb friction. The nonlinearity of Coulomb's law leads to a nonlinear complementarity formulation of the system model. This model is used in conjunction with the theory of ..."
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Cited by 42 (6 self)
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. In this paper, we study the problem of predicting the acceleration of a set of rigid, 3dimensional bodies in contact with Coulomb friction. The nonlinearity of Coulomb's law leads to a nonlinear complementarity formulation of the system model. This model is used in conjunction with the theory of quasivariational inequalities to prove for the first time that multirigidbody systems with all contacts rolling always has a solution under a feasibilitytype condition. The analysis of the more general problem with sliding and rolling contacts presents difficulties that motivate our consideration of a relaxed friction law. The corresponding complementarity formulations of the multirigidbody contact problem are derived and existence of solutions of these models is established. Key Words. Rigidbody contact problem, Coulomb friction, linear complementarity, quasivariational inequality, setvalued mappings. 1 Introduction One of the main goals of the robotics research community is to a...
Grasp Analysis as Linear Matrix Inequality Problems
"... Three important problems in the study of grasping and manipulation by multifingered robotic hands are: (a) Given a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure; (b) If the grasp does not have force closure, determine if th ..."
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Cited by 33 (2 self)
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Three important problems in the study of grasping and manipulation by multifingered robotic hands are: (a) Given a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure; (b) If the grasp does not have force closure, determine if the ngers are able to apply a specified resultant wrench on the object; and (c) Compute "optimal" contact forces if the answer to problem (b) is affirmative. In this paper, based on an early result by Buss, Hashimoto and Moore, which transforms the nonlinear friction cone constraints into positive definiteness of certain symmetric matrices, we further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate all three of the problems stated above as a set of convex optimization problems involving LMIs. The latter problems have been extensively studied in optimization and control community and highly efficient algorithms with polynomial time complexity are now available for their solutions. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.
The Linear Complementarity Problem as a Separable Bilinear Program
 Journal of Global Optimization
, 1995
"... . The nonmonotone linear complementarity problem (LCP) is formulated as a bilinear program with separable constraints and an objective function that minimizesa natural error residual for the LCP. A linearprogrammingbasedalgorithm applied to the bilinear program terminates in a finite number of ste ..."
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Cited by 18 (4 self)
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. The nonmonotone linear complementarity problem (LCP) is formulated as a bilinear program with separable constraints and an objective function that minimizesa natural error residual for the LCP. A linearprogrammingbasedalgorithm applied to the bilinear program terminates in a finite number of steps at a solution or stationary point of the problem. The bilinear algorithm solved 80 consecutive cases of the LCP formulation of the knapsack feasibility problem ranging in size between 10 and 3000, with almost constant average number of major iterations equal to four. Keywords: linear complementarity, bilinear programming, knapsack 1. Introduction It is well known that the linear complementarity problem [4], [16] 0 x ? Mx+ q 0; (1) for a given n \Theta n real matrix M and a given n \Theta 1 vector q, can be written as the bilinear program min x;w fx 0 wjw = Mx+ q; x 0; w 0g: (2) For the case of a general M , considered here, the objective function of (2) is nonconvex and the cons...
Anytime coordination using separable bilinear programs
 In AAAI
, 2007
"... Developing scalable coordination algorithms for multiagent systems is a hard computational challenge. One useful approach, demonstrated by the Coverage Set Algorithm (CSA), exploits structured interaction to produce significant computational gains. Empirically, CSA exhibits very good anytime perfor ..."
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Cited by 17 (9 self)
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Developing scalable coordination algorithms for multiagent systems is a hard computational challenge. One useful approach, demonstrated by the Coverage Set Algorithm (CSA), exploits structured interaction to produce significant computational gains. Empirically, CSA exhibits very good anytime performance, but an error bound on the results has not been established. We reformulate the algorithm and derive both online and offline error bounds for approximate solutions. Moreover, we propose an effective way to automatically reduce the complexity of the interaction. Our experiments show that this is a promising approach to solve a broad class of decentralized decision problems. The general formulation used by the algorithm makes it both easy to implement and widely applicable to a variety of other AI problems.
A Bilinear Programming Approach for Multiagent Planning
"... Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of twoagent problems can be formulated as bilinear programs. We present a successive approximation algorithm that significantly outperforms the coverage set algorithm, which is t ..."
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Cited by 9 (2 self)
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Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of twoagent problems can be formulated as bilinear programs. We present a successive approximation algorithm that significantly outperforms the coverage set algorithm, which is the stateoftheart method for this class of multiagent problems. Because the algorithm is formulated for bilinear programs, it is more general and simpler to implement. The new algorithm can be terminated at any time and–unlike the coverage set algorithm–it facilitates the derivation of a useful online performance bound. It is also much more efficient, on average reducing the computation time of the optimal solution by about four orders of magnitude. Finally, we introduce an automatic dimensionality reduction method that improves the effectiveness of the algorithm, extending its applicability to new domains and providing a new way to analyze a subclass of bilinear programs. 1.
A timestepping scheme for quasistatic multibody systems
 International Symposium of Assembly and Task Planning
, 2005
"... Two new instantaneoustime models for predicting the motion and contact forces of threedimensional, quasistatic multirigidbody systems are developed; one linear and one nonlinear. The nonlinear characteristic is the result of retaining the usual quadratic friction cone in the model. Discretetime ..."
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Cited by 6 (2 self)
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Two new instantaneoustime models for predicting the motion and contact forces of threedimensional, quasistatic multirigidbody systems are developed; one linear and one nonlinear. The nonlinear characteristic is the result of retaining the usual quadratic friction cone in the model. Discretetime versions of these models provide the first timestepping methods for such systems. As a first step to understanding their usefulness in simulation and manipulation planning, a theorem for solution uniqueness is presented along with simulation results for a simple example. 1
Anytime Coordination Using Separable Bilinear Programs
"... Developing scalable coordination algorithms for multiagent systems is a hard computational challenge. One useful approach, demonstrated by the Coverage Set Algorithm (CSA), exploits structured interaction to produce significant computational gains. Empirically, CSA exhibits very good anytime perfor ..."
Abstract
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Developing scalable coordination algorithms for multiagent systems is a hard computational challenge. One useful approach, demonstrated by the Coverage Set Algorithm (CSA), exploits structured interaction to produce significant computational gains. Empirically, CSA exhibits very good anytime performance, but an error bound on the results has not been established. We reformulate the algorithm and derive both online and offline error bounds for approximate solutions. Moreover, we propose an effective way to automatically reduce the complexity of the interaction. Our experiments show that this is a promising approach to solve a broad class of decentralized decision problems. The general formulation used by the algorithm makes it both easy to implement and widely applicable to a variety of other AI problems.
A Successive Approximation Algorithm for Coordination Problems ∗
"... Developing scalable coordination algorithms for multiagent systems is a hard computational challenge. One useful approach, demonstrated by the Coverage Set Algorithm (CSA), exploits structured interaction to produce significant computational gains. Empirically, CSA exhibits very good anytime perfor ..."
Abstract
 Add to MetaCart
Developing scalable coordination algorithms for multiagent systems is a hard computational challenge. One useful approach, demonstrated by the Coverage Set Algorithm (CSA), exploits structured interaction to produce significant computational gains. Empirically, CSA exhibits very good anytime performance, but an error bound on the results has not been established. We reformulate the algorithm and derive an online error bound for approximate solutions. Moreover, we propose an effective way to automatically reduce the complexity of the interaction. Our experiments show that this is a promising approach to solve a broad class of decentralized decision problems. The general formulation used by the algorithm makes it both easy to implement and widely applicable to a variety of other AI problems. 1