Softcover reprint of the original 1st ed. 1993, XV, 448 p.
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Nonholonomic Motion Planning grew out of the workshop that took place at the 1991 IEEE International Conference on Robotics and Automation. It consists of contributed chapters representing new developments in this area. Contributors to the book include robotics engineers, nonlinear control experts, differential geometers and applied mathematicians. Nonholonomic Motion Planning is arranged into three chapter groups: Controllability: one of the key mathematical tools needed to study nonholonomic motion. Motion Planning for Mobile Robots: in this section the papers are focused on problems with nonholonomic velocity constraints as well as constraints on the generalized coordinates. Falling Cats, Space Robots and Gauge Theory: there are numerous connections to be made between symplectic geometry techniques for the study of holonomies in mechanics, gauge theory and control. In this section these connections are discussed using the backdrop of examples drawn from space robots and falling cats reorienting themselves. Nonholonomic Motion Planning can be used either as a reference for researchers working in the areas of robotics, nonlinear control and differential geometry, or as a textbook for a graduate level robotics or nonlinear control course.
Introduction. Nonholonomic Kinematics and the Role of Elliptic Functions in Constructive Controllability; R.W. Brockett, Liyi Dai. Steering Nonholonomic Control Systems using Sinusoids; R.M. Murray, S.S. Sastry. Smooth Time-Periodic Feedback Solutions for Nonholonomic Motion Planning; L. Gurvits, Zexiang Li. Lie Bracket Extensions and Averaging: the Single-Bracket Case; H.J. Sussmann, Wensheng Liu. Singularities and Topological Aspects in Nonholonomic Motion Planning: J.-P. Laumond. Motion Planning for Nonholonomic Dynamic Systems; M. Reyhanoglu, N.H. McClamroch, A.M. Bloch. A Differential Geometric Approach to Motion Planning; G. Lafferriere, H.J. Sussmann. Planning Smooth Paths for Mobile Robots; P. Jacobs, J.F. Canny. Nonholonomic Control and Gauge Theory; R. Montgomery. Optimal Nonholonomic Motion Planning for a Falling Cat; C. Fernandes, L. Burvits, Zexiang Li. Nonholonomic Behavior in Free-Floating Space Manipulators and its Utilization; E.G. Papadopoulos. Index.