Optimal approach for autonomous parallel parking of nonholonomic car-like vehicle

Over the past few years, research related to autonomous parallel parking has developed in conjunction with vehicle dynamics and mobile robotics. The parallel parking system applied to the real world would be helpful for beginner drivers and for disabled people. Parallel parking is required in our usual lives, especially on the streets of big cities where parking spaces are in demand. The purpose of this research is to develop an optimal approach for trajectory generation and at the same time obstacle avoidance for road vehicle's parking motion. It is linked to nonholonomic mobile robot maneuvering planning. Path planning and collision-free motion are two issues that always arise in nonholonomic motion planning for robotic manipulators and mobile robot navigation problems. Using the penalty function method, these two issues can be combined into a constrained optimal problem and solved by a numerical gradient method without the linearization process, as a nonlinear time optimal control problem. The configuration for collision-free motion is satisfied by state constraints, which prevents the trajectory from lying in an infeasible region which corresponds to the vehicle colliding with an obstacle. To illustrate the technique, a MATLAB program is used for simulations.