A real-time 3D motion planning and simulation scheme for nonholonomic systems

We propose a new motion planning and simulation scheme for nonholonomic systems in this paper to provide a practical solution for these application problems taking into account of real-time obstacle avoidance and the continuous curvature path generation simultaneously in 3D unknown environment. The proposed motion planning and simulation scheme generates the motion path using a new universal Euler spiral generation algorithm, which is locally optimal based on perceived points of view. The generated Euler spiral solution can be non-symmetrical and easily implemented while maintaining a C2 continuous. It is therefore more flexible and powerful in dealing with dynamic situations in real-time, compared with current symmetrical Euler spirals solutions. Real-time solutions are particularly important in navigation in unknown environments. The universal Euler spiral algorithm proposed displays a smaller maximum curvature value and smaller mean square curvature value than the conventional symmetrical algorithm in tested cases. Another significant contribution of our work is the new motion planning scheme which extend current 2D based motion planning into three-dimensional (3D) space. In this paper, we have conducted experiments and describe simulation results including 3D motion trajectory modeling for a flight simulation.