A Numerical Algorithm for Optimal Trajectory Planning Problems with Multiple Constraints and Its Application to Nonholonomic Systems
A Numerical Algorithm for Optimal Trajectory Planning Problems with Multiple Constraints and Its Application to Nonholonomic Systems
复制标题
多约束最优轨迹规划问题的数值算法及其在非完整系统中的应用
DOI：
10.7210/jrsj.19.260
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
A. Mohri
中科院分区：
文献类型：
--
作者：
Makoto Iwamura;Motoji Yamamoto;A. Mohri
本文提出了一种求解多约束条件下最优轨迹规划问题的梯度型迭代算法。由于同时生成考虑所有约束条件的轨迹过于困难，我们在轨迹生成过程中引入了优先级排序的概念。在该算法中，根据约束的优先级顺序对标称轨迹进行迭代改进。在梯度函数的基础上，分层合成梯度函数，使低优先级约束的收敛速度不改变高优先级约束的收敛速度。验证了该算法的收敛性。本文还提出了一种改进算法在求解非完整系统问题时收敛性的方法。三自由度平面自由关节机械臂轨迹规划仿真结果表明了该算法的有效性。
In this paper, we propose a novel gradient-type iterative algorithm for solving the optimal trajectory planning problems with multiple constraints. Since it is too difficult to generate trajectories considering all constraints at the same time, we introduce the concept of the order of priority into the trajectory generation procedure. In the proposed algorithm, a nominal trajectory is iteratively improved considering the order of priority of the constraints. The procedure is executed based on the gradient function which is synthesized in a hierarchical manner so that the convergence rate of the constraint with lower priority does not change the one with higher priority. The convergence properties of the proposed algorithm are examined. A method to improve the convergence properties when we apply the algorithm to the problem of nonholonomic systems is also proposed. The simulation results of planning trajectories for a 3-DOF planar free-joint manipulator show the effectiveness of the proposed algorithm.