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

Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear 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 nonlinear feedback policy "probabilistically covers" the entire controllable subset of the 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 nonlinear feedback design algorithm on simple nonlinear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm.

• Type: Journal
• Year: 2010
• Where: IJRR
• Authors: Russ Tedrake, Ian R. Manchester, Mark Tobenkin, John W. Roberts
• Keywords: IJRR 2010, Nonlinear Feedback, Nonlinear Systems, Smooth Nonlinear Systems