Generating a collision-free and dynamically feasible trajectory with a better clearance in a cluttered environment is still a challenge. We propose two dynamically feasible B-spline based rapidly exploring random tree (RRT) approaches, which are named DB-RRT and FMDB-RRT, to achieve path planning and trajectory planning simultaneously for omnidirectional mobile robots. DB-RRT combines the convex hull property of the B-spline and RRT’s rapid expansion capability to generate a safe and dynamically feasible trajectory. Firstly, we analyze the tree’s sustainable growth ability and put forward the dynamically feasible region. A geometric method is proposed to judge whether finding a dynamically feasible trajectory quickly. Secondly, we design two steer functions to guide the tree’s growth, improve efficiency, and decrease the number of iterations. To further increase the clearance and reduce the randomness of the trajectory, we propose FMDB-RRT, which uses the path of fast marching to guide the rapid growth of DB-RRT. Then, assuming that the number of sampled points is sufficient to represent the dynamically feasible region, the DB-RRT is proved to be probabilistically complete. Finally, by conducting experimental comparisons with other algorithms in different environments and deploying the proposed algorithm to an omnidirectional mobile robot, the effectiveness and good performance of the algorithm have been verified.

在杂乱的环境中生成具有更好间隙的无碰撞且动态可行的轨迹仍然是一个挑战。我们提出了两种基于动态可行 B 样条的快速探索随机树 (RRT) 方法，分别称为 DB-RRT 和 FMDB-RRT，以同时实现全向移动机器人的路径规划和轨迹规划。DB-RRT 结合了 B-spline 的凸包特性和 RRT 的快速扩展能力，生成了安全且动态可行的轨迹。首先分析了树木的可持续生长能力，提出了动态可行区域。提出了一种几何方法来判断是否能快速找到动态可行的轨迹。其次，我们设计了两个转向函数来引导树的生长，提高效率，减少迭代次数。为了进一步增加间隙并降低轨迹的随机性，我们提出了FMDB-RRT，它利用快速行进的路径来引导DB-RRT的快速增长。然后，假设采样点的数量足以表示动态可行区域，则证明 DB-RRT 在概率上是完备的。最后，通过在不同环境下与其他算法进行实验对比，并将所提算法应用于全向移动机器人，验证了算法的有效性和良好的性能。DB-RRT 被证明是概率完备的。最后，通过在不同环境下与其他算法进行实验对比，并将所提算法应用于全向移动机器人，验证了算法的有效性和良好的性能。DB-RRT 被证明是概率完备的。最后，通过在不同环境下与其他算法进行实验对比，并将所提算法应用于全向移动机器人，验证了算法的有效性和良好的性能。