Non-linear robust control for inverted-pendulum 2D walking

We present an approach to high-level control for bipedal walking exemplified with a 2D point-mass inextensible-legs inverted-pendulum model. Balance control authority here is only from step position and trailing-leg push-off, both of which are bounded to reflect actuator limits. The controller is defined implicitly as the solution of an optimization problem. The optimization robustly avoids falling for given bounded disturbances and errors and, given that, minimizes the number of steps to reach a given target speed. The optimization can be computed in advance and stored for interpolated real-time use online. The general form of the resulting optimized controller suggests a few simple principles for regulating walking speed: 1) The robot should take bigger steps when speeding up and should also take bigger steps when slowing down 2) push-off is useful for regulating small changes in speed, but it is fully saturated or inactive for larger changes in speed. While the numerically optimized model is simple, the approach should be applicable to, and we plan to use it for, control of bipedal robots in 3D with many degrees of freedom.