Continuous Curvature Trajectory Generation with Obstacle Avoidance for Car-Like Robots

This paper presents an extension of cubic curvature polynomial trajectory planning to include a mechanism for obstacle avoidance. Cubic polynomials have been used to describe curvature continuous trajectories for car like robots. From known start and end robot postures, (position, orientation and curvature) a continuous trajectory can be decided. We extend cubic polynomial trajectories to fourth order polynomials, and introduce a cost function, describing accumulated distance to obstacles along a trajectory, to the robot posture vector. Such trajectories, generated by a gradient descent method, satisfy continuity constraints and avoid obstacles. The method is implemented on a mobile robot system and experiments in real time trajectory planning and execution are conducted