Robotic Control Optimization Through Kernel Selection in Safe Bayesian Optimization

TL;DR

A novel learning-based control optimization method is proposed, which enhances the additive Gaussian process-based Safe Bayesian Optimization algorithm to efficiently tackle high-dimensional problems through kernel selection.

Abstract

Control system optimization has long been a fundamental challenge in robotics. While recent advancements have led to the development of control algorithms that leverage learning-based approaches, such as SafeOpt, to optimize single feedback controllers, scaling these methods to high-dimensional complex systems with multiple controllers remains an open problem. In this paper, we propose a novel learning-based control optimization method, which enhances the additive Gaussian process-based Safe Bayesian Optimization algorithm to efficiently tackle high-dimensional problems through kernel selection. We use PID controller optimization in drones as a representative example and test the method on Safe Control Gym, a benchmark designed for evaluating safe control techniques. We show that the proposed method provides a more efficient and optimal solution for high-dimensional control optimization problems, demonstrating significant improvements over existing techniques.

Figures (4)

• Figure 1: Overview of the method. First, the input and output of the system are measured to obtain a set of observations, which serve as the GP priors for calculating kernel selection. Subsequently, Bayesian optimization via additive Gaussian processes uses the most important one or several additive kernels calculated by kernel selection for optimization, iteratively selecting safe new parameters and testing the performance in the system until the optimal control parameters are obtained.
• Figure 2: Quadrotor model used for benchmark environment.
• Figure 3: Comparison of trajectory tracking results and tracking error. (a) compares the trajectory tracking curves of the initial controller and the optimal controller tuned with our method, where the blue curve is the reference trajectory, the light gray curve is the trajectory of the initial controller, the red curve is the trajectory of the optimal controller, and the yellow point is the starting point of the trajectory. (b) and (c) compare the tracking errors of the initial controller and the optimal controller on the $x$-axis and $z$-axis, respectively. The blue curve is the error of the initial controller, and the yellow curve is the error of the optimal controller.
• Figure 4: Comparison of optimization performance between our method and different baseline methods. (a) compares our method with the standard kernel selection method introduced in AdditiveGaussianProcesses, (b) compares our method with the state-of-the-art high-dimensional safe Bayesian optimization method LINEBO, (c) compares our method with unconstrained Bayesian optimization method.