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Spong, Mark W. Spong, Mark W. Bretl, Timothy W. Hutchinson, Seth A. Mehta, Prashant G. Gregg, Robert D., IV 2011-01-14T22:49:05Z 2011-01-14T22:49:05Z 2011-01-14T22:49:05Z "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." 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No. of bitstreams: 20 Gregg_Robert.pdf: 2695035 bytes, checksum: 47511aeea433f04b4cf44ab6d878ce21 (MD5) license.txt: 4060 bytes, checksum: ec76352010e357de0f8c258a3f76da01 (MD5) Dissertation.tex: 9962 bytes, checksum: dfaeb7988b9ba30acfa39f62fe08fe5a (MD5) intro.tex: 32933 bytes, checksum: 4545e8e256c46d7b6c068e78c30eea7f (MD5) aubio.tex: 1539 bytes, checksum: 8361c48f1eb3abf1878bccd9d62e750b (MD5) abs.tex: 2394 bytes, checksum: 56cabf359f6612e97f9b30eeaa3a5613 (MD5) Mechanical.tex: 26962 bytes, checksum: 87e4081d2789810a02cc70cdfc19cf4c (MD5) ControlledReduction.tex: 62144 bytes, checksum: f32538ad21a04ade3044af050e60848f (MD5) RBControl.tex: 37736 bytes, checksum: c1f25a165a9bbc0f5a5795e1e5938883 (MD5) GaitPrimitives.tex: 51684 bytes, checksum: ae4f243260e3b662ded7a21239e56f74 (MD5) Rehab.tex: 22761 bytes, checksum: eaca380efeeff7e23190ba79af1d9226 (MD5) concl.tex: 9121 bytes, checksum: 585ce4da44fc5668a2528e90ae439c27 (MD5) BipedWalking.tex: 74369 bytes, checksum: 47509ea40c3386a92a6bcc592af7b230 (MD5) ack.tex: 4867 bytes, checksum: 2dfc8deb26c0b5d7c16a525e84046017 (MD5) Appendix.tex: 32501 bytes, checksum: aadb8c8228e277f1251156ecb051d4bb (MD5) DissertationBib.bib: 51231 bytes, checksum: 6fb18d95907556618aa7f6b65fafab87 (MD5) Dissertation.sty: 9648 bytes, checksum: 23536680e54ee7c37c08beb8e357c2bc (MD5) IEEE_ECE.bst: 61786 bytes, checksum: e34f041873deb4165fc8d76725c453c4 (MD5) uiucecethesis09.cls: 21157 bytes, checksum: 8a2975a9bd857ec4f015bf1dcefcdf94 (MD5) figures.zip: 2273225 bytes, checksum: c79b3abd87a049ffa5f5c5607d475c25 (MD5) http://hdl.handle.net/2142/18397 en Copyright 2010 Robert D. Gregg IV Copyright 1999 SAGE Publications (Figures 1.4 and 7.1) Robots Bipedal Walking Locomotion Dynamic Walking Geometric Control Motion Planning Three-Dimensional (3D) Reduction-based Control Controlled Reduction Hybrid Limit Cycles Geometric control and motion planning for three-dimensional bipedal locomotion 2010-12 Electrical & Computer Eng 1933 Electrical & Computer Engr 1200 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Electr & Computer Eng-UIUC 10KS1200PHD