LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

Authors:
Russ Tedrake;Ian R. Manchester;Mark Tobenkin;John W. Roberts
Affiliations:
Computer Science and Artificial Intelligence, Lab,MassachusettsInstitute of Technology, Cambridge, MA 02139, USA;Computer Science and Artificial Intelligence Lab, Lab,MassachusettsInstitute of Technology, Cambridge, MA 02139, USA;Computer Science and Artificial Intelligence Lab, Lab,MassachusettsInstitute of Technology, Cambridge, MA 02139, USA, mmt,@mit.edu;Computer Science and Artificial Intelligence Lab, Lab,MassachusettsInstitute of Technology, Cambridge, MA 02139, USA
Venue:
International Journal of Robotics Research
Year:
2010

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Abstract

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 â聙聹probabilistically coversâ聙聺 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.