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DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 167 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the semidefinite programming problem. We give an overview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interiorpoint method, with a simplified analysis of the worstcase complexity and numerical results that indicate that the method is very efficient, both in theory and in practice. Compared to existing specialized algorithms (where they are available), the interiorpoint method will generally be slower; the advantage is that it handles a much wider variety of problems.
GraspIt!  A Versatile Simulator for Robotic Grasping
, 2004
"... Research in robotic grasping has flourished in the last 25 years. A recent survey by Bicchi [1] covered over 140 papers, and many more than that have been published. Stemming from our desire to implement some of the work in grasp analysis for particular hand designs, we created an interactive graspi ..."
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Cited by 93 (15 self)
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Research in robotic grasping has flourished in the last 25 years. A recent survey by Bicchi [1] covered over 140 papers, and many more than that have been published. Stemming from our desire to implement some of the work in grasp analysis for particular hand designs, we created an interactive grasping simulator that can import a wide variety of hand and object models and can evaluate the grasps formed by these hands. This system, dubbed “GraspIt!,” has since expanded in scope to the point where we feel it could serve as a useful tool for other researchers in the field. To that end, we are making the system publicly available (GraspIt! is available for download for a variety of platforms from
Asymptotically Optimal WaterFilling in Vector MultipleAccess Channels
 IEEE Trans. Inform. Theory
, 2001
"... Dynamic resource allocation is an important means to increase the sum capacity of fading multipleaccess channels (MACs). In this paper, we consider vector multiaccess channels (channels where each user has multiple degrees of freedom) and study the effect of power allocation as a function of the ch ..."
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Cited by 62 (4 self)
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Dynamic resource allocation is an important means to increase the sum capacity of fading multipleaccess channels (MACs). In this paper, we consider vector multiaccess channels (channels where each user has multiple degrees of freedom) and study the effect of power allocation as a function of the channel state on the sum capacity (or spectral efficiency) defined as the maximum sum of rates of users per unit degree of freedom at which the users can jointly transmit reliably, in an information theoretic sense, assuming random directions of received signal. Directsequence codedivision multipleaccess (DSCDMA) channels and MACs with multiple antennas at the receiver are two systems that fall under the purview of our model. Our main result is the identification of a simple dynamic powerallocation scheme that is optimal in a large system, i.e., with a large number of users and a correspondingly large number of degrees of freedom. A key feature of this policy is that, for any user, it depends on the instantaneous amplitude of channel state of that user alone and the structure of the policy is "waterfilling." In the context of DSCDMA and in the special case of no fading, the asymptotically optimal power policy of waterfilling simplifies to constant power allocation over all realizations of signature sequences; this result verifies the conjecture made in [28]. We study the behavior of the asymptotically optimal waterfilling policy in various regimes of number of users per unit degree of freedom and signaltonoise ratio (SNR). We also generalize this result to multiple classes, i.e., the situation when users in different classes have different average power constraints.
sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure
 In Recent advances in LMI methods for control
, 1995
"... . A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization, computational geometry, circuit design, and other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet pr ..."
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Cited by 44 (18 self)
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. A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization, computational geometry, circuit design, and other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet problems). These problems often have matrix structure, i.e., some of the optimization variables are matrices. This matrix structure has two important practical ramifications: first, it makes the job of translating the problem into a standard SDP or maxdet format tedious, and, second, it opens the possibility of exploiting the structure to speed up the computation. In this paper we describe the design and implementation of sdpsol, a parser/solver for SDPs and maxdet problems. sdpsol allows problems with matrix structure to be described in a simple, natural, and convenient way. Although the current implementation of sdpsol does not exploit matrix structure in the solution algorithm, the languag...
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.
Distributed compressionestimation using wireless sensor networks  The design goals of performance, bandwidth efficiency, scalability, and robustness
 IEEE SIGNAL PROCESSING MAG
, 2006
"... A wireless sensor network (WSN) consists of a large number of spatially distributed signal processing devices (nodes), each with finite battery lifetime and thus limited computing and communication capabilities. When properly programmed and networked, nodes in a WSN can cooperate to perform advance ..."
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Cited by 32 (1 self)
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A wireless sensor network (WSN) consists of a large number of spatially distributed signal processing devices (nodes), each with finite battery lifetime and thus limited computing and communication capabilities. When properly programmed and networked, nodes in a WSN can cooperate to perform advanced signal processing tasks with unprecedented robustness and versatility, thus making WSN an attractive lowcost technology for a wide range of remote sensing and environmental monitoring applications [1], [32].
Taskoriented quality measures for dextrous grasping
 in Proc
, 2005
"... Abstract — We propose a new and efficient approach to compute task oriented quality measures for dextrous grasps. Tasks can be specified as a single wrench to be applied, as a rough direction in form of a wrench cone, or as a complex wrench polytope. Based on the linear matrix inequality formalism t ..."
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Cited by 10 (2 self)
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Abstract — We propose a new and efficient approach to compute task oriented quality measures for dextrous grasps. Tasks can be specified as a single wrench to be applied, as a rough direction in form of a wrench cone, or as a complex wrench polytope. Based on the linear matrix inequality formalism to treat the friction cone constraints we formulate respective convex optimization problems, whose solutions give the maximal applicable wrench in the task direction together with the needed contact forces. Numerical experiments show that application to complex grasps with many contacts is possible. Index Terms — grasp quality measure, force optimization I.
Output Feedback Robust Stabilization of Uncertain Linear Systems with Saturating Controls: An LMI Approach
 Proceedings of the Conference on Decision and Control, IEEE
, 1997
"... : The problem of robust controller design is addressed for an uncertain linear system subject to control saturation. No assumption is made concerning openloop stability and no a priori information is available regarding the domain of stability. A saturating linear output feedback law and a safe set ..."
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Cited by 5 (5 self)
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: The problem of robust controller design is addressed for an uncertain linear system subject to control saturation. No assumption is made concerning openloop stability and no a priori information is available regarding the domain of stability. A saturating linear output feedback law and a safe set of initial conditions are determined using a heuristic based on iterative LMI relaxation procedures. A readily implementable algorithm based on standard numerical techniques is described and illustrated on two numerical examples. 1 Introduction During the last two decades a considerable amount of time has been spent analyzing the question of whether some properties of a system (mainly asymptotic stability) are preserved under the presence of unknown perturbations. Several important findings have appeared in the open literature, leading to procedures for designing the socalled robust controllers, see [9, 17] and references therein. However these design procedures usually do not take direc...
Connections Between SemiInfinite and Semidefinite Programming
"... We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T ..."
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Cited by 5 (2 self)
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We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T
Algorithms and Software for LMI Problems in Control
 IEEE Control Systems Magazine
, 1997
"... this article is to provide an overview of the state of the art of ..."
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Cited by 4 (0 self)
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this article is to provide an overview of the state of the art of