Design of Asymptotically Stable Walking for a 5-Link Planar Biped Walker via Optimization

Closed-loop, asymptotically stable walking motions are designed for a 5-link, planar bipedal robot model with one degree of underactuation. Parameter optimization is applied to the hybrid zero dynamics, a 1-DOF invariant subdynamics of the full robot model, in order to create asymptotically stable orbits. Tuning the dynamics of this 1 DOF subsystem via optimization is interesting because asymptotically stable orbits of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The optimization process uses a sequential quadratic programming (SQP) algorithm and is able to satisfy kinematic and dynamic constraints while approximately minimizing energy consumption and ensuring stability. This is in contrast with traditional approaches to the design of walking controllers where approximately optimal walking (time-) trajectories are derived and then enforced on the robot using a trajectory tracking controller.