Learning Terrain Dynamics: A Gaussian Process Modeling and Optimal Control Adaptation Framework Applied to Robotic Jumping

The complex dynamics characterizing deformable terrain presents significant impediments toward the real-world viability of locomotive robotics, particularly for legged machines. We explore vertical, robotic jumping as a model task for legged locomotion on presumed-uncharacterized, nonrigid terrain. By integrating Gaussian process (GP)-based regression and evaluation to estimate ground reaction forces as a function of the state, a 1-D jumper acquires the capability to learn forcing profiles exerted by its environment in tandem with achieving its control objective. The GP-based dynamical model initially assumes a baseline rigid, noncompliant surface. As part of an iterative procedure, the optimizer employing this model generates an optimal control strategy to achieve a target jump height. Experiential data recovered from execution on the true surface model are applied to train the GP, in turn, providing the optimizer a more richly informed dynamical model of the environment. The iterative control-learning procedure was rigorously evaluated in experiment, over different surface types, whereby a robotic hopper was challenged to jump to several different target heights. Each task was achieved within ten attempts, over which the terrain's dynamics were learned. With each iteration, GP predictions of ground forcing became incrementally refined, rapidly matching experimental force measurements. The few-iteration convergence demonstrates a fundamental capacity to both estimate and adapt to unknown terrain dynamics in application-realistic time scales, all with control tools amenable to robotic legged locomotion.