We present a framework for online generation of robust motion plans for robotic systems with
nonlinear dynamics subject to bounded disturbances, control constraints, and online state …

We study a family of gradient obstacle problems on a compact Riemannian manifold. We
prove that the solutions of these free boundary problems are uniformly semiconcave and, as …

Integrating autonomous robots into safety-critical settings requires reasoning about
uncertainty at all levels of the autonomy stack. This thesis presents novel algorithmic tools …

We study 1 k-geodesics, those closed geodesics that minimize on all subintervals of length L
k, where L is the length of the geodesic. We develop new techniques to study the minimizing …

This thesis is composed of two parts. In the first part, we study a generalization of the
variational problem of elastic-plastic torsion problem to manifolds. We show that in the case …

A geodesic in a metric space M is a locally length-minimizing curve. Some metric spaces
admit closed geodesics, WS 1! M, which can be viewed as maps from the circle S 1 D Œ0; 2 …