Online Learning of Unknown Dynamics for Model-Based Controllers in Legged Locomotion

The performance of a model-based controller can severely suffer when its model inaccurately represents the real world dynamics. We propose to learn a time-varying, locally linear residual model along the robot's current trajectory, to compensate for the prediction errors of the controller's model. Supervised learning is performed online, as the robot is running in the unknown environment, using data collected from its immediate past. We theoretically investigate our method in its general formulation, then apply it to a bipedal controller derived from the full-order dynamics of virtual constraints, and a quadrupedal controller derived from a simplified model of contact forces. For a biped in simulation, our method consistently outperforms the baseline and a recent learning-based method. We also experiment with a 12 kg quadruped in simulation and real world, where the baseline fails to walk with 10 kg of payload but our method succeeds.