Orientation planning in task space using quaternion polynomials

M. Shahbazi, Navvab Kashiri, D. Caldwell, N. Tsagarakis
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引用次数: 3

Abstract

This paper introduces a computationally fast method for orientation trajectory planning in point-to-point motion tasks when the angular velocity and acceleration at the endpoints are constrained. Addressing such a problem with existing spherical-interpolation-based methods (in the context of unit quaternion) is not straightforward, since the inherent complexities of spherical curves necessitate task-specific tunings for satisfying all the boundary conditions. To tackle such a difficulty, we propound an interpolation function on the basis of standard polynomials in time with quaternion coefficients. We introduce a novel algorithm to determine varying polynomial coefficients in a way that the unit length of interpolated quaternion can be guaranteed. The performance of the developed planning algorithms is illustrated through a functional analysis and via simulation experiments on an anthropomorphic robotic arm. The results corroborate the merits of the presented approach especially in respecting arbitrary boundary conditions.
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基于四元数多项式的任务空间定向规划
本文介绍了一种点到点运动任务中,当端点处的角速度和加速度有约束时,定位轨迹规划的快速计算方法。用现有的基于球面插值的方法(在单位四元数的背景下)解决这样的问题并不简单,因为球面曲线固有的复杂性需要特定于任务的调优来满足所有的边界条件。为了解决这一难题,我们提出了一个基于四元数系数的标准时间多项式的插值函数。在保证插值四元数单位长度的前提下,提出了一种确定变多项式系数的新算法。通过功能分析和拟人机械臂的仿真实验,说明了所开发的规划算法的性能。结果证实了该方法的优点,特别是在考虑任意边界条件时。
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