Adaptive High-Order Control Barrier Function-Based Iterative LQR for Real Time Safety-Critical Motion Planning

Abstract

This letter proposes an adaptive high-order control barrier function-based iterative linear quadratic regulator (AHOCBF-ILQR) algorithm for real time safety-critical motion planning. Firstly, we propose a HOCBF-ILQR method, where a HOCBF-based controller is designed as a safety filter of ILQR to guarantee safety. Then, to address the potential infeasibility issue in HOCBF-ILQR, AHOCBF-ILQR is proposed by introducing an auxiliary variable. In AHOCBF-ILQR, only an unconstrained optimization problem and a quadratic programming need to be solved within a sampling interval. The low computation burden significantly enhances the time efficiency of AHOCBF-ILQR. Furthermore, we provide theoretical proof of the safety and feasibility of AHOCBF-ILQR. The algorithms are tested by motion planning experiments for a wheeled mobile robot, where the robot is required to navigate around static or moving obstacles that are unknown in advance. The experimental results show that AHOCBF-ILQR can solve the control inputs within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{0.05}~s$</tex-math></inline-formula> , and ensure safety.