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Hands for dexterous manipulation and robust grasping: A difficult road toward simplicity
 IEEE Tran. on Robotics and Automation
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Rolling Bodies with Regular Surface: Controllability Theory and Applications
, 2000
"... Pairs of bodies with regular rigid surfaces rolling onto each other in space form a nonholonomic system of a rather general type, posing several interesting control problems of which not much is known. The nonholonomy of such systems can be exploited in practical devices, which is very useful in rob ..."
Abstract

Cited by 38 (5 self)
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Pairs of bodies with regular rigid surfaces rolling onto each other in space form a nonholonomic system of a rather general type, posing several interesting control problems of which not much is known. The nonholonomy of such systems can be exploited in practical devices, which is very useful in robotic applications. In order to achieve all potential benefits, a deeper understanding of these types of systems and more practical algorithms for planning and controlling their motions are necessary. In this paper, we study the controllability aspect of this problem, giving a complete description of the reachable manifold for general pairs of bodies, and a constructive controllability algorithm for planning rolling motions for dexterous robot hands. Index TermsNonholonomic systems, nonlinear controllability theory, robotic manipulation. I. INTRODUCTION N ONHOLONOMIC systems have been attracting much attention in control literature recently, due to both their relevance to practical ap...
Reachability Analysis for a Class of Quantized Control Systems
, 2000
"... In this paper we study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, whichmay turn out to be either dense or discrete. We report on some recent results on the reachable set of linear quantized systems ..."
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Cited by 11 (2 self)
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In this paper we study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, whichmay turn out to be either dense or discrete. We report on some recent results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure.
Trajectory Planning Using ReachableState Density Functions
 IN PROC. IEEE INT. CONF. ON ROBOTICS AND AUTOMATION (ICRA
, 2002
"... This paper presents a trajectory planning algorithm for mobile robots which may be subject to kinodynamic constraints. Using computational methods from noncommutative harmonic analysis, the algorithm eciently constructs an approximation to the robot's reachablestate density function. Based on ..."
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Cited by 6 (0 self)
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This paper presents a trajectory planning algorithm for mobile robots which may be subject to kinodynamic constraints. Using computational methods from noncommutative harmonic analysis, the algorithm eciently constructs an approximation to the robot's reachablestate density function. Based on a multiscale approach, the density function is then used to plan a path. One variation of the algorithm exhibits time complexity that is logarithmic in the number of steps. Simulations illustrate the method.
Reachability and Steering of Rolling Polyhedra: A Case Study in Discrete Nonholonomy
, 2004
"... Rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks, and the problem is also well understood for any smooth deformation of the surfaces. For nonsmoothly deformed surfaces, however, much less is known. Although it may seem intuitive that nonholonomy is conserved ..."
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Cited by 3 (0 self)
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Rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks, and the problem is also well understood for any smooth deformation of the surfaces. For nonsmoothly deformed surfaces, however, much less is known. Although it may seem intuitive that nonholonomy is conserved (think e.g. to polyhedral approximations of smooth surfaces), current definitions of “nonholonomy ” are inherently referred to systems described by ordinary differential equations, and are thus inapplicable to such systems. In this paper, we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces. We provide a description of such reachable set, discuss conditions under which the set is dense, or discrete, or has a compound structure, and provide a method for steering the system to a desired reachable configuration, robustly with respect to model uncertainties. Based on ideas and concepts encountered in this case study, and in some other examples we provide, we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of (kinematic) nonholonomy to nonsmooth, discrete, and hybrid dynamical systems. To capture the essence of phenomena commonly regarded as “nonholonomic,” at least two irreducible concepts are to be defined, of “internal” and “external” nonholonomy, which may coexist in the same system. These definitions are instantiated by examples.