An Asymptotically Optimal Path Planning Method with Cubic Bézier Spline

Book excerpt: This dissertation introduces a novel path planning algorithm for robotics, known as Informed SRRT#. Our algorithm integrates a local planner from SRRT, accommodating both external and internal constraints. We introduce two extra lines at the Bézier spline's endpoints, which facilitates the rewiring process. A minimum of three state connections need adjustment during rewiring to meet kinematic constraints. The effectiveness of the proposed method is demonstrated through various channels: Python-based simulations, Gazebo/Rviz -- a robot simulator and visualization tool in Robot Operating System, and real-world scenarios. In real-world experiments, the algorithm successfully maneuvered TurtleBot3 past obstacles in the physical map, leading to a smooth, streamlined and optimal navigation approach. Our results reveal that the new algorithm identifies shorter paths than SRRT while achieving the same number of node sampling iterations. However, these enhancements come with a trade-off, as the computational time of this method is slightly higher compared to traditional methods.