An Automated Parallel Parking Strategy Using Reach Control Theory

We propose a novel method of parallel parking using reach control theory. Reach control is a hybrid control method to achieve complex control objectives. It relies on triangulating the state space, devising a desired sequence of simplices or polytopes that a trajectory needs to pass through to complete a task, and then constructing a separate closed-loop controller on each polytope that enables the system state to move on to the next member of the sequence. For the parallel parking task, we design a state space consisting of eight polytopes, and we use an automated procedure to construct a continuous piecewise-affine controller for each polytope. Extensive simulations demonstrate the robustness of the approach: a vehicle starting from an acceptable initial position performs the maneuver safely and comes to a stop in the desired parking area.