Abstract

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.

The bow leg hopper is a novel locomotor design with a highly resilient leg that resembles an archer's bow. During @flight, a "thrust" actuator adds elastic energy to the leg, which is automatically released during stance to control hopping height. Laterak motion is controlled by directing the leg angle at touchdown, which determines the angle of takeoff or reflection. The leg pivots freely on a hip bearing, and is automatically decoupled from the leg-angle positioner during stance to preclude hip torques that would disturb body attitude. Upright attitude is maintained without active control by allowing the body to "hang"ffom the hip joint. Preliminary experiments with a planar prototype have demonstrated impressive per3eormance (hopping heights of 50 cm or more), high efJiciency (recovers 70% of the energy from one hop to the next) and low power requirements (45 minutes of operation on a small battery pack). Current experiments are focused on developing control and planning schemes to enable locomotion over discrete "stepping stones" and obstacles.

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We propose a model-based reinforcement learning algorithm for biped walking in which the robot learns to appropriately place the swing leg. This decision is based on a learned model of the Poincare map of the periodic walking pattern. The model maps from a state at the middle of a step and foot placement to a state at next middle of a step. We also modify the desired walking cycle frequency based on online measurements. We present simulation results, and are currently implementing this approach on an actual biped robot.