SUMMARY

The proposed research philosophy is to expose the general mechanics of a particular class of bipedal walking robots and then construct controllers which manipulate these mechanics to achieve stable walking. The class of robots is characterized a lack of feet -- the robot's lower leg contacts the ground at a single, unactuated pivot point. Stabilizing this type of robot walking can be challenging: underactuation corresponds to nonlinear dynamics that are not affected by the robot's motors and thus not locally controllable. To date, successful methods of stabilizing these robots have leveraged mathematical properties of hybrid walking models to construct nonlinear optimization problems which search for stable walking gaits. This dissertation builds upon the hybrid control system approaches by illuminating useful properties of the hybrid mechanics of underactuated walking -- namely that the underactuated dynamics correspond to the angular momentum about the support pivot and that angular momentum is conserved about the points of impact between the robot and the ground -- which can be manipulated to produce stabilizing controllers without use of nonlinear optimization.