Tunnel-MILP: Path Planning with Sequential Convex Polytopes∗

This paper focuses on optimal path planning for vehicles in known environments. Previous work has presented mixed integer linear programming (MILP) formulations, which suffer from scalability issues as the number of obstacles, and hence the number of integer variables, increases. In order to address MILP scalability, a novel three-stage algorithm is presented which first computes a desirable path through the environment without considering dynamics, then generates a sequence of convex polytopes containing the desired path, and finally poses a MILP to identify a suitable dynamically feasible path. The sequence of polytopes form a safe tunnel through the environment, and integer decision variables are restricted to deciding when to enter and exit each region of the tunnel. Simulation results for this approach are presented and reveal a significant increase in the size and complexity of the environment that can be solved.