Exact Obstacle Avoidance for Autonomous Vehicles in Polygonal Domains

This research investigates optimization-based schemes aimed at achieving effective collision avoidance in autonomous vehicles. The study introduces three explicit formulations of collision constraints that can be applied universally to both general vehicles and obstacles regardless of whether they are represented by convex or nonconvex polygons. These formulations are devised by reformulating implicit vertex-edge constraints, exclusively designed to prevent collisions between any vertex and any edge, as explicit constraints through analytically characterizing modified signed distance functions (MSDFs), equilibrium functions, and binary variables, respectively. The proposed schemes can formulate the optimization-based planning problem involving collision avoidance as a nonlinear program (NLP), a mathematical program with equilibrium constraints, and a mixed-integer NLP, which are readily addressed using off-the-shelf solvers. Furthermore, the research examines the sensitivity of the MSDFs, indicating that the formulation can exhibit numerical sensitivity to the sign. Finally, the efficacy of the proposed schemes is demonstrated in the context of an autonomous bus parallel parking in a confined bus stop with multiple corridors. The results illustrate that all the three schemes perform equally well in terms of identifying feasible solutions, while the scheme using MSDFs avoids adding dual variables to be optimized, exhibiting the added benefit of requiring lower computational resources compared to the state of the art.