This article presents a dual-optimization trajectory planning algorithm, which consists of the optimal path planning and the optimal motion profile planning for robot manipulators, where the path planning is based on parametric curves. In path planning, a virtual-knot interpolation is proposed for the paths required to pass through all control points, so the common curves, such as Bézier curves and B-splines, can be incorporated into it. Besides, an optimal B-spline is proposed to generate a smoother and shorter path, and this scheme is especially suitable for closed paths. In motion profile planning, a generalized formulation of time-optimal velocity profiles is proposed, which can be implemented to any types of motion profiles with equality and inequality constraints. Also, a multisegment cubic velocity profile is proposed by solving a multiobjective optimization problem. Furthermore, a case study of a dispensing robot is investigated through the proposed dual-optimization algorithm applied to numerical simulations and experimental work.

中文翻译：

---

基于参数曲线的机器人机械手双优化轨迹规划

本文提出了一种双优化轨迹规划算法，该算法由机器人机械手的最优路径规划和最优运动轨迹规划组成，其中路径规划基于参数曲线。在路径规划中，对需要通过所有控制点的路径提出了虚拟节点插值，因此可以将常见的曲线，如贝塞尔曲线和B样条曲线纳入其中。此外，提出了一个最优的 B 样条来生成更平滑和更短的路径，该方案特别适用于封闭路径。在运动剖面规划中，提出了时间最优速度剖面的广义公式，它可以实施到具有等式和不等式约束的任何类型的运动剖面。还，通过解决多目标优化问题，提出了多段立方速度剖面。此外，通过应用于数值模拟和实验工作的拟议双重优化算法，对分配机器人的案例研究进行了研究。