This paper considers the problem of designing motion planning algorithms for control-affine systems that generate collision-free paths from an initial to a final destination and can be executed using safe and dynamically-feasible controllers. We introduce the C-CLF-CBF-RRT algorithm, which produces paths with such properties and leverages rapidly exploring random trees (RRTs), control Lyapunov functions (CLFs) and control barrier functions (CBFs). We show that C-CLF-CBF-RRT is computationally efficient for a variety of different dynamics and obstacles, and establish its probabilistic completeness. We showcase the performance of C-CLF-CBF-RRT in different simulation and hardware experiments.

翻译：本文研究针对仿射控制系统的运动规划算法设计问题，该算法需生成从初始位置到目标位置的无碰撞路径，并可通过安全且动态可行的控制器执行。我们提出了C-CLF-CBF-RRT算法，该算法利用快速扩展随机树（RRT）、控制李雅普诺夫函数（CLF）和控制屏障函数（CBF）生成具备上述特性的路径。我们证明C-CLF-CBF-RRT算法对于多种不同动力学模型和障碍物场景均具有计算效率，并建立了算法的概率完备性。通过不同仿真与硬件实验，我们展示了C-CLF-CBF-RRT算法的实际性能。