Efficient Collision Avoidance for Autonomous Vehicles in Polygonal Domains

This research addresses the trajectory planning challenges for autonomous vehicles navigating obstacles within confined environments. Utilizing numerical optimal control techniques, the study reformulates the constrained optimization problem into a nonlinear programming (NLP) framework, incorporating explicit collision avoidance constraints. We present three novel, exact formulations to describe collision constraints. The first exact formulation is derived from a proposition concerning the separation of a point and a convex set. We prove the separating proposition through De Morgan’s laws. Another two exact formulations are constructed based on the hyperplane separation theorem. Compared with the existing dual formulations and the first formulation, they significantly reduce the number of auxiliary variables to be optimized and inequality constraints within the NLP problem. Finally, the efficacy of the proposed formulations is demonstrated in the context of typical autonomous parking scenarios compared with the state-of-the-art. For generality, we design three initial guesses to assess the computational effort required for convergence to solutions when using the different collision formulations. The results illustrate that the scheme employing De Morgan’s laws performs equally well with those utilizing dual formulations, while the other two schemes based on the hyperplane separation theorem exhibit the added benefit of requiring fewer computational resources.