Nonlinear control of a two-link hopping robot

Abstract

Legged robots have great potential for locomotion on rugged terrain inaccessible to current wheeled or tracked mobile robots. Much of the previous work has focused on statically stable legged robots. However, dynamically stable legged robots offer the advantages of increased speed and mobility. Typically, dynamically stable legged robots are designed to have simple dynamics and therefore simple control strategies. While much progress has been made by following this approach, it excessively limits the variety of legged mechanisms that can be considered and the performance that can be achieved. Nonlinear control is advocated as a means for dealing with these limitations. An example of a dynamically stable legged robot with nonlinear dynamics was studied: a two-link hopping robot. To understand how locomotion might be achieved, the mechanism was analyzed with its foot fixed in place. With this constraint the legged robot was an underactuated double pendulum. This system has been studied previously and is known as the Acrobot. Careful study of the Acrobot equations of motion revealed a surprising set of feasible periodic trajectories with dynamics of a simple pendulum. A nonlinear control law was used to track these pendulum trajectories. With the foot of the legged robot no longer fixed, the pendulum motion produced sufficient forces to slide the foot or to launch the robot into the air. This led to two distinct gaits simulated on a computer: (1) A sliding gait was produced by a low magnitude pendulum oscillation. The foot maintained contact with the ground and slid only in one direction. (2) A hopping gait was produced in the following manner: First, a large magnitude oscillation launched the robot into the air with non-zero angular momentum. Then, rotation of the leg during this aerial phase landed the robot in a configuration where it could recover its balance. The concepts of geometric phase (holonomy) and dynamic phase were instrumental in developing the strategy for the aerial phase of the gait. Experimental results verified that the oscillations for the Acrobot could be achieved and were stable. The sliding gait was observed on the experimental setup.