Interactive Car Parking Simulation Based on On-line Trajectory Optimization

This paper presents an on-line trajectory optimization method to simulate the autonomous parking of a car-like vehicle in an environment with static or dynamic obstacles. We employ a stochastic and derivative-free optimization technique called Covariance Matrix Adaptation (CMA) to seamlessly integrate collision events between the car and the environment into the formulation of our autonomous parking problem without resorting to any preprocessing steps to make the problem differentiable. Given the current and target car states, our system repeatedly predicts a sequence of control inputs for a short time window to move the car to the target while shifting the window along the time axis, which facilitates on-line performance. We also present a simple and effective scheme to make our optimization robust to environmental changes by adjusting its parameters in an on-line manner. We show the effectiveness of our method through simulation results for garage parking, parallel parking, and interactive parking based on on-line user input.