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Title:Geometric control and motion planning for three-dimensional bipedal locomotion
Author(s):Gregg, Robert D., IV
Director of Research:Spong, Mark W.
Doctoral Committee Chair(s):Spong, Mark W.
Doctoral Committee Member(s):Bretl, Timothy W.; Hutchinson, Seth A.; Mehta, Prashant G.
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Dynamic Walking
Geometric Control
Motion Planning
Three-Dimensional (3D)
Reduction-based Control
Controlled Reduction
Hybrid Limit Cycles
Abstract:This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the "divided" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive "funneling" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies.
Issue Date:2011-01-14
Rights Information:Copyright 2010 Robert D. Gregg IV Copyright 1999 SAGE Publications (Figures 1.4 and 7.1)
Date Available in IDEALS:2011-01-14
Date Deposited:December 2

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