The Bow Leg Hopping Robot

The Bow Leg Hopper is a new type of running robot with an efficient, flexible leg. A one-legged planar prototype has been developed that passively stabilizes body attitude and is efficient enough to use on-board batteries. It is controlled by a real-time planner and has demonstrated crossing of simple artificial terrain including stepping stones and shallow stairs. The machine hops using a Bow Leg, a new type of resilient, flexible leg named for its similarity to an archery bow. The Bow Leg comprises a curved leaf spring, foot, freely pivoting hip, and the Bow String that holds the leg in compression. The Bow String is used to control the leg potential energy: it may be retracted to store energy by bending the leg, held in place, and released to perform useful work. The leg is positioned using a hobby servomotor coupled to the foot with control strings. During locomotion, the machine is controlled by actuation during flight: the leg is positioned, and the Bow String retracted to store energy that is automatically released during stance. During ground contact all the strings become slack, and the hopper bounces passively off the ground with no forces or torques supported by actuators. The hip joint is attached to the body slightly above the center of mass so the body effectively hangs from the hip during ground contact and the natural pendulum forces passively stabilize body attitude. In this design a single spring provides the leg structure, elasticity, and energy storage. The high forces of ground impact are carried conservatively by the spring and hip bearing. This addresses four problems central to dynamic legged locomotion: a low-power actuator may be used for thrust by storing energy in the leg; low-force actuation may be used to position the leg; the free hip minimizes body disturbance torques; and the hopping cycle is energy efficient since negative work is eliminated and the spring has high restitution. The machine is a form of “programmable mechanism” configured by leg position and stored energy during flight to control the evolution of the bounce dynamics. The physics of the machine have been modelled in closed form using a combination of idealized analysis and empirically determined functions. These models are used by a planner that finds sequences of foot placements across known terrain to a goal position by searching a graph representing the trajectories reachable from any given landing. The planner uses heuristics to discretize the continuous control space and estimate path costs. Paths are generated in real time as needed in conjunction with a feedback controller that rejects local disturbances. The dissertation also includes graphical methods for terrain analysis, discussion of mechanical design details, details of the real-time graph-search planner and heuristics, and experimental data from the planar prototype. Acknowledgments I would especially like to thank Professor Matt Mason for his perpetual patience with me through my whole tenure as a graduate student. This thesis would not have been possible without his guidance and resources, and I am grateful for the opportunity to learn so much from him. And equally essential was Ben Brown, who has volunteered countless hours and untold energies on my behalf. I would like to thank him for agreeing to let me develop his original idea into an entire thesis of my own, and then helping me at each step of the way. Many, many others have contributed to my effort. The weekly MLAB meeting has been a continual source of inspiration for clear thinking and academic comraderie. Professors Alfred Rizzi and Illah Nourbakhsh each offered illuminating discussions about combining control and planning. Professor Daniel Koditschek, Professor Martin Buehler, William Schwind, and Professor Andrew Ruina provided valuable commentary at conference meetings. My officemate Arthur Quaid provided much patient listening and useful comments on my thesis draft. My fellow students Chris Lee and Martin Martin listened through many discussions. And I am grateful to Dr. Marc Raibert, who brought me to this work in the first place and provided much inspiration over the years. My work was supported in part by a National Science Foundation Graduate Fellowship. This work was also supported in part by a fellowship from the Engineering Research Program of the Office of Basic Energy Sciences at the Department of Energy.