Tractable Stochastic Hybrid Model Predictive Control using Gaussian Processes for Repetitive Tasks in Unseen Environments

TL;DR

This paper introduces a computationally efficient stochastic hybrid model predictive control method using Gaussian processes, capable of adapting to changing environment modes for improved control in repetitive tasks.

Contribution

It develops an iterative mapping algorithm for mode distribution prediction and two tractable approximations of the control optimization problem, enhancing performance and reducing computation time.

Findings

Performance improved by 4-18% with approximations.

Computation times reduced up to 250x.

Controller performance increased up to 3x over iterations.

Abstract

Improving the predictive accuracy of a dynamics model is crucial to obtaining good control performance and safety from Model Predictive Controllers (MPC). One approach involves learning unmodelled (residual) dynamics, in addition to nominal models derived from first principles. Varying residual models across an environment manifest as modes of a piecewise residual (PWR) model that requires a) identifying how modes are distributed across the environment and b) solving a computationally intensive Mixed Integer Nonlinear Program (MINLP) problem for control. We develop an iterative mapping algorithm capable of predicting time-varying mode distributions. We then develop and solve two tractable approximations of the MINLP to combine with the predictor in closed-loop to solve the overall control problem. In simulation, we first demonstrate how the approximations improve performance by 4-18% in comparison to the MINLP while achieving significantly lower computation times (upto 250x faster). We then demonstrate how the proposed mapping algorithm incrementally improves controller performance (upto 3x) over multiple iterations of a trajectory tracking control task even when the mode distributions change over time.