Essays on Mathematical Robotics
By: edited by John Baillieul, Shankar S. Sastry, Hector J. Sussmann
Contributors: Sastry, Shankar S.; Sussmann, Hector J.
Series: The IMA Volumes in Mathematics and its Applications -- 104; IMA volumes in mathematics and its applications -- 104.
Publisher: Springer New York
Published: 1998
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 384
ISBN-13: 9781461272519; 9781461217107
Subjects: Mathematics; Mathematical optimization; Systems theory
Description: The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "hyper-redundancy", highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops. The principal topics covered in the book are: adaptive control for a class of nonlinear systems, event-based motion planning, nonlinear control synthesis and path planning in robotics with special emphasis on nonholonomic and "hyper-redundant" robotic systems, control design and stabilization of driftless affine control systems (of the type arising in the kinematic control of nonholonomic robotic systems), control design methods for Hamiltonian systems and exterior differential systems. The chapter covering exterior differential systems contains a detailed introduction to the use of exterior differential methods, including the Goursat and extended Goursat normal forms and their application to path planning for nonholonomic systems.
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Table of contents: title: Foreword; title: Preface; title: The role of compliant fingerpads in grasping and manipulation: Identification and control; title: Event-based planning and control for robotic systems: Theory and implementation; title: The kinematics of hyper-redundant robots; title: Line-integral estimates and motion planning using the continuation method; title: Kinematic path planning for robots with holonomic and nonholonomic constraints; title: A general approach to path planning for systems without drift; title: Discontinuous stabilization of Brockett's canonical driftless system; title: On feedback linearization of robot manipulators and Riemannian curvature; title: Averaging and energy methods for robust open-loop control of mechanical systems; title: Exterior differential systems in control and robotics.