Fast Superquadric Potential Function for Collision Avoidance of Autonomous Vehicle

In this paper, accurate collision avoidance for autonomous vehicles is achieved using an iterative linear quadratic regulator (iLQR), a nonlinear model predictive control (MPC) approach, combined with proposed fast search algorithms for the superquadric potential function to ensure real-time performance. The superquadric potential function has the advantage of being able to represent various obstacle shapes, such as circular and rectangular forms. The potential function is integrated into the MPC cost function, where its differentiation is required during the backward pass of iLQR to obtain the MPC solution. However, the high nonlinearity of the superquadric potential function poses challenges for real-time computation, hindering collision avoidance performance. To address this issue, we propose fast search algorithms that improve real-time computation of the superquadric potential function and its derivatives with sufficient accuracy. These algorithms rely on precomputed offline solution sets for the superquadric potential function, allowing efficient retrieval of suboptimal solutions during online collision avoidance. The proposed approach extends the applicability of collision avoidance systems across diverse scenarios, maintaining real-time feasibility. We rigorously validate the real-time performance and collision avoidance accuracy through high-speed test scenarios. Results confirm that our approach achieves computational complexity withinO(ϵ−1), whereas conventional nonlinear equation solvers exhibit complexity ofO(ϵ−2).