Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots
Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots
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DOI：
10.7936/k7r78c8n
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发表时间：
2012
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2012年圣路易斯华盛顿大学系统科学与数学科学博士菲利普·弗里曼的论文《轨迹约束冗余度机器人的最小跳跃轨迹规划》研究顾问：Heinz Schaettler教授在本文中，我们为冗余度机器人的轨迹跟踪问题提出了一种生成最小跳跃轨迹的有效方法。我们证明了高抖动是一种局部现象，因此重点优化了使用传统轨迹生成方法时出现的高抖动区域。证明了最优轨迹位于自运动流形的叶层上，并利用这一性质将问题表示为最小维Bolza最优控制问题。基于伪谱优化方法的思想，提出了一种数值算法，并将其应用于两个冗余自由度平面机器人结构的算例。与已有的轨迹生成方法相比，该算法将算例的积分抖动分别降低了75%和13%。峰值抖动分别降低了98%和33%。最后，给出了一个实时测量刀尖跟随误差的实时控制器，以准确跟踪规划的轨迹。
OF THE THESIS Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots by Philip Freeman Doctor of Science in System Science and Mathematics Washington University in St. Louis, 2012 Research Advisor: Professor Heinz Schaettler In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip’s following error.