Cooptimizing Safety and Performance with a Control-Constrained Formulation

TL;DR

This paper presents a novel control-constrained optimal control framework that effectively balances safety and performance in autonomous systems, using dynamic programming and HJB-PDE solutions, validated through a case study.

Contribution

It introduces a control-constrained formulation converting safety constraints into control constraints, enabling efficient solution via dynamic programming for nonlinear systems.

Findings

Controller outperforms baselines in safety and performance

Method effectively handles nonlinear system constraints

Validated with a two-dimensional case study

Abstract

Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders the cooptimization between them difficult. One school of thought is to treat this cooptimization as a constrained optimal control problem with a performance-oriented objective function and safety as a constraint. However, solving this constrained optimal control problem for general nonlinear systems remains challenging. In this work, we use the general framework of constrained optimal control, but given the safety state constraint, we convert it into an equivalent control constraint, resulting in a state and time-dependent control-constrained optimal control problem. This equivalent optimal control problem can readily be solved using the dynamic programming principle. We show the corresponding value function is a viscosity solution of a certain Hamilton-Jacobi-Bellman Partial Differential Equation (HJB-PDE). Furthermore, we demonstrate the effectiveness of our method with a two-dimensional case study, and the experiment shows that the controller synthesized using our method consistently outperforms the baselines, both in safety and performance.