with Reachable Sets

In this thesis we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environ-ment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, be-cause constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Previous work on feedback motion planning for nonlinear systems was limited to offline planning due to the computa-tional cost of safety verification. Here we augment the traditional trajectory library approach by designing locally stabilizing controllers for each nominal trajectory in the library and providing guarantees on the resulting closed loop systems. We leverage sums-of-squares programming to design these locally stabilizing controllers by explic-itly attempting to minimize the size of the worst case reachable set of the closed-loop system subjected to bounded disturbances and uncertainty. The reachable sets as-sociated with each trajectory in the library can be thought of as "funnels " that th