Control-Minimal Time-Assigned Path-Constrained Trajectory Optimization

Path-constrained trajectory optimization research normally focuses on time or energy optimality. However, some applications seek reference trajectories that satisfy other constraints. In this paper, we formulate a control-minimal time-assigned path-constrained trajectory optimization problem: a mobile ground robot must traverse a given path in a specific amount of time using minimal control effort. Through a nonlinear change of variables, we solve this problem using convex optimization. We evaluate our solution with an intelligent transportation scenario where an autonomous vehicle must cross an intersection in a specific amount of time while following the turn lane's geometric center.