Stabilization of 3D underactuated biped robots: Using posture adjustment and gait libraries to reject velocity disturbances

This paper presents a systematic, two-stage optimization process for the design and stabilization of periodic walking gaits based on the full 3D dynamic model of a robot. After designing a nominal periodic walking motion, a parametric means of adjusting the robot's posture is introduced to achieve exponential orbital stability. The parameters are determined through a finite-horizon optimization problem that emphasizes gait robustness to perturbations. This gait design and stabilization process is used to generate a library of gaits over a grid of longitudinal and lateral velocities. The discrete set of gaits is then unified through bilinear interpolation to create a single continuously defined control policy. This policy extends the controller's region of attraction, allowing the robot to handle perturbations much larger than those presented during the initial optimization. The resulting controller allows the simulated robot to recover from velocity disturbances of up to 1.4 m/s longitudinally and 0.7 m/s laterally. Preliminary experimental results are shown on an underactuated Atriasseries robot.