Rapidly exploring random trees (RRTs) have proven effective in quickly finding feasible solutions to complex motion planning problems. RRT* is an extension of the RRT algorithm that provides probabilistic asymptotic optimality guarantees when using straight-line motion primitives. This work provides extensions to RRT and RRT* that employ fillets as motion primitives, allowing path curvature constraints to be considered when planning. Two fillets are developed, an arc-based fillet that uses circular arcs to generate paths that respect maximum curvature constraints and a spline-based fillet that uses Bezier curves to additionally respect curvature continuity requirements. Planning with these fillets is shown to far exceed the performance of RRT* using Dubin's path motion primitives, approaching the performance of planning with straight-line path primitives. Path sampling heuristics are also introduced to accelerate convergence for nonholonomic motion planning. Comparisons to established RRT* approaches are made using the Open Motion Planning Library (OMPL).

翻译：快速探索随机树（RRT）已被证明能有效快速求解复杂运动规划问题的可行解。RRT*是RRT算法的扩展，在使用直线运动基元时可提供概率渐近最优性保证。本文提出了RRT和RRT*的扩展方法，采用圆角过渡作为运动基元，使路径曲率约束能够在规划中被考虑。本文开发了两种圆角过渡：基于圆弧的圆角过渡利用圆弧生成满足最大曲率约束的路径，以及基于样条的圆角过渡采用贝塞尔曲线额外满足曲率连续性要求。实验表明，使用这些圆角过渡进行规划的性能远超基于杜宾路径运动基元的RRT*，并接近使用直线路径基元的规划性能。本文还引入了路径采样启发式方法以加速非完整运动规划的收敛。通过开放运动规划库（OMPL）与既有RRT*方法进行了对比验证。