Computation-Aware Learning for Stable Control with Gaussian Process

TL;DR

This paper introduces a novel approach to stable control in Gaussian Process models by accounting for computational uncertainty, enhancing safety and stability in resource-constrained robotic systems like quadrotors.

Contribution

It highlights the importance of computational uncertainty in GP models for control and proposes a new controller design method that incorporates this uncertainty within a convex optimization framework.

Findings

Incorporating computational uncertainty improves stability and safety.

The proposed controller outperforms traditional methods under computational constraints.

Simulations and experiments validate the effectiveness of the approach.

Abstract

In Gaussian Process (GP) dynamical model learning for robot control, particularly for systems constrained by computational resources like small quadrotors equipped with low-end processors, analyzing stability and designing a stable controller present significant challenges. This paper distinguishes between two types of uncertainty within the posteriors of GP dynamical models: the well-documented mathematical uncertainty stemming from limited data and computational uncertainty arising from constrained computational capabilities, which has been largely overlooked in prior research. Our work demonstrates that computational uncertainty, quantified through a probabilistic approximation of the inverse covariance matrix in GP dynamical models, is essential for stable control under computational constraints. We show that incorporating computational uncertainty can prevent overestimating the region of attraction, a safe subset of the state space with asymptotic stability, thus improving system safety. Building on these insights, we propose an innovative controller design methodology that integrates computational uncertainty within a second-order cone programming framework. Simulations of canonical stable control tasks and experiments of quadrotor tracking exhibit the effectiveness of our method under computational constraints.