Journal
INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
Volume 29, Issue 8, Pages 1038-1052Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/0278364910369189
Keywords
randomized motion planning; Lyapunov verification; trajectory libraries
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Funding
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [0746194] Funding Source: National Science Foundation
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [0915148] Funding Source: National Science Foundation
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Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth non-linear systems. Here we present a feedback motion-planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQR-stabilized trajectories. The region of attraction of this non-linear feedback policy probabilistically covers the entire controllable subset of state space, verifying that all initial conditions that are capable of reaching the goal will reach the goal. We numerically investigate the properties of this systematic non-linear feedback design algorithm on simple non-linear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm.
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