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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 theor ..."
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Cited by 54 (7 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
 IEEE Transactions on Robotics and Automation
, 2000
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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 20 (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 20 (10 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 16 (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
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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 ..."
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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 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
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 ..."
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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.
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.