We present a method for designing a walking controller for the walking robot Cornell Ranger. Our goal is a controller that can be designed using model-based optimization, and then transferred directly to the robot without the need for after-the-fact hand-tuning. The structure of the controller is hierarchical, with a high-level balance controller that plans step-to-step motions, and a lower-level joint controller that coordinates the individual joint motors to achieve the desired limb motions. The balance controller is designed through optimization, with the explicit goals of a) achieving a desired walking speed while b) minimizing energy use and c) avoiding falls due to disturbances. We demonstrate this walking controller on the Cornell Ranger, and find that the resulting gait is comparable to that of a previous (hand-tuned) controller, with regard to energy use, speed regulation, and fall prevention.

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.