Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate local regions of stability for smooth nonlinear systems. These tools can be combined with randomized motion planning algorithms to obtain new feedback motion planning algorithms which probabilistically cover a bounded reachable state-space with verified regions of stability; efficiently constructing a global feedback controller out of many locally valid controllers. If successful, the proposed work will generate a class of algorithms capable of computing covering feedback policies for nonlinear systems with dimensionality beyond that of dynamic programming. In addition, the algorithms operate directly on the continuous state and action spaces, and thus are not subject to the pitfalls of discretization. By considering feedback during the planning process, the resulting plans are robust to disturbances and quite suitable for implementation on real robots.
Through both theoretical and experimental validation of these algorithms, this work aims to have broad impact on the experimental control of nonlinear and underactuated systems, including walking robots, aerial vehicles, and robots which grasp and manipulate the environment. The algorithms and robotic experiments will be integrated in the PI's graduate robotics curriculum and outreach activities, and the algorithms will be disseminated through a software distribution.
