Geometric control and motion planning for three-dimensional bipedal locomotion

"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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Gregg, Robert D., IV

Contributors dc:contributor

• Spong, Mark W.
• Bretl, Timothy W.
• Hutchinson, Seth A.
• Mehta, Prashant G.

• Robots
• Bipedal
• Walking
• Locomotion
• Dynamic Walking
• Geometric Control
• Motion Planning
• Three-Dimensional (3D)
• Reduction-based Control
• Controlled Reduction
• Hybrid Limit Cycles

Statement dc:rights

• Copyright 2010 Robert D. Gregg IV Copyright 1999 SAGE Publications (Figures 1.4 and 7.1)

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/18397

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/18397