My Ph.D. work included a deep dive into dynamics, control, and motion planning for bouncing robots: mobile robots that have structured interactions with boundaries of their environment. Examples include robot vacuums that bump into walls to guarantee coverage of an entire room; micro-organisms and micro-robots; or a fixed-wing drone making straight passes over a forest and only turning when it reaches the edge.
My approach involves computing discrete representations of the geometry and dynamics of robot trajectories in a given environment. By establishing equivalence classes over the environment and control spaces, we allow for nondeterminism and uncertainty at the planning stage and still compute plans that have analytical guarantees on their stability and long-term dynamical behavior. This allows us to use the intrinsic, messy dynamics of the robot to engineer robust high-level behaviors such as navigating or patrolling a space, and even object manipulation.