Time-optimal path planning for flat systems with application to a wheeled mobile robot

The time-optimal path planning problem aims at bringing a system from an initial to terminal state in minimal time while obeying both geometric and dynamic constraints. Path planning problems are often decoupled into a high-level path planning stage where a feasible geometric path is determined and a low level stage where system dynamics are taken into account. The paper combines the geometric and dynamic approach into a single optimization problem for so-called differentially flat systems. The geometric path is represented as a convex combination of two or more feasible paths. Relying on differential flatness, the dynamics of the system are projected onto the path which leads to a single input system. The resulting optimization problem is transformed into a fixed end-time optimal control problem that can be initialized easily. An application to a wheeled mobile robot, a challenging non-linear system, will illustrate the proposed approach throughout the paper.