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

Abstract

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.

Real‐Time Remodeling of Granular Terrain for Robot Locomotion

“…Augmenting robophysics with machine learning will reduce these constraints, as evidenced by previous studies which achieved optimal control in a 1D jumping robot by iteratively adapting to deformable terrain dynamics. [39] Beyond blind learning and Bayesian optimization approaches, future studies will use a neural network-based machine learning scheme to characterize the gait and terrain interactions for both the rover and biped robots. We will capture the robots' kinematics and the surrounding terrain deformation using external depth cameras (Figure 2A) and train a learning model to describe the coupling of the robot/terrain system.…”

“…Augmenting robophysics with machine learning will reduce these constraints, as evidenced by previous studies which achieved optimal control in a 1D jumping robot by iteratively adapting to deformable terrain dynamics. [ 39 ]…”

Learning quadrupedal locomotion on deformable terrain

“…There have been efforts to control legged robots on highly soft and deformable terrains. Some of them took advantage of known properties of the terrain (10)(11)(12) or estimated the ground reaction force with a nonparametric model trained with data from prior experiences (13). However, because the ground properties and prior experiences are often not available in the outdoor environments, demonstrations of those approaches have been confined to laboratory environments.…”

“…Furthermore, the complexity of a combined model that describes the interactions between the floating-based robot and the terrain leads to an impractically complex control architecture. As a result, contemporary research on integrating the terrain model into the legged robotic control has primarily been limited to morphologically simple robots, e.g., one-dimensional (1D) hopper (10,12,13).…”