最后，应用近似化方法和黎曼度量方法，研究了机器人最优轨迹规划的问题。
In the end, the problem of robot trajectory planning is investigated by the linearization method and Riemannian metric.
它为工业机器人在非线性运动学约束条件下的时间最优轨迹规划及控制问题提供了一种较好的解决方案。
It provides a better solution to the problem of industrial robot's time optimal trajectory planning and control under the nonlinear kinematical constraints.
本文首先介绍了国内外喷漆机器人离线编程系统的研究现状及意义，提出了喷枪最优轨迹规划问题(OTPP)。
This paper first describes the research purport and current research level of the off-line programming system for painting robot, and points out the Optimal Trajectory Planning Problems (OTPP).
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