In this paper, a sampling-based trajectory planning algorithm for a laboratory-scale 3D gantry crane in an environment with static obstacles and subject to bounds on the velocity and acceleration of the gantry crane system is presented. The focus is on developing a fast motion planning algorithm for differentially flat systems, where intermediate results can be stored and reused for further tasks, such as replanning. The proposed approach is based on the informed optimal rapidly exploring random tree algorithm (informed RRT*), which is utilized to build trajectory trees that are reused for replanning when the start and/or target states change. In contrast to state-of-the-art approaches, the proposed motion planning algorithm incorporates a linear quadratic minimum time (LQTM) local planner. Thus, dynamic properties such as time optimality and the smoothness of the trajectory are directly considered in the proposed algorithm. Moreover, by integrating the branch-and-bound method to perform the pruning process on the trajectory tree, the proposed algorithm can eliminate points in the tree that do not contribute to finding better solutions. This helps to curb memory consumption and reduce the computational complexity during motion (re)planning. Simulation results for a validated mathematical model of a 3D gantry crane show the feasibility of the proposed approach.

翻译：本文提出了一种用于实验室规模三维桥式起重机在静态障碍物环境中的采样轨迹规划算法，该算法受限于桥式起重机系统的速度和加速度边界。研究重点在于为微分平坦系统开发快速运动规划算法，其中中间结果可存储并用于后续任务（如重规划）。所提方法基于知情最优快速探索随机树算法（informed RRT*），利用该算法构建轨迹树，当起始状态和/或目标状态发生变化时，可重复使用该轨迹树进行重规划。与现有技术相比，所提运动规划算法集成了线性二次型最小时间（LQTM）局部规划器。因此，时间最优性和轨迹平滑性等动态特性在所提算法中得到了直接考虑。此外，通过集成分支定界方法对轨迹树进行剪枝，所提算法可以剔除树中无助于寻找更优解的点。这有助于抑制内存消耗，并降低运动（重）规划过程中的计算复杂度。针对经过验证的三维桥式起重机数学模型的仿真结果证明了所提方法的可行性。