Joint motion planning of industrial robot based on hybrid polynomial interpolation

基于混合多项式插值的工业机器人关节运动规划

¹ School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
² College of Engineering, Honghe University, Mengzi 661199, China

Received: 26 April 2021

Abstract

To plan an industrial robot's point-to-point joint motion that has velocity constraints, the cubic polynomial interpolation planning method has angular acceleration discontinuity. The quintic polynomial interpolation planning method needs to set in advance the angular acceleration values of target points and easily causes angular velocity fluctuation. Because of the existence of quintic polynomials, hybrid polynomial planning 3-5-…-5-3 also easily causes large angular velocity fluctuation. To solve these problems, a hybrid polynomial interpolation planning method based on cubic and quartic polynomial interpolation is proposed. Cubic polynomial interpolation planning is applied to the first planning, and quartic polynomial interpolation planning is used for the rest of planning. The planning method can not only specify the angular velocities of intermediate target points but also ensure the continuity of angular acceleration. In addition, there is no need to set in advance the angular acceleration values of target points so as to avoid the angular velocity fluctuation caused by the unreasonable presetting of angular acceleration. Furthermore, in order to avoid excessive peaks of angular velocity during the joint motion planning, a calculation method for finding out reasonable motion time is put forward, under which the larger speed at two target points is taken as maximum, thus making the planned angular velocity fluctuation small. A case study is performed to verify the rationality and effectiveness of the planning method. Compared with the other two planning methods used for the case study, our planning method can effectively solve the problems of point-to-point joint motion planning with velocity constrains, therefore being beneficial to the working performance and service life of an industrial robot.

摘要

对于工业机器人速度约束的点到点关节运动规划, 三次多项式规划存在角加速度不连续的问题, 五次多项式规划方法需要预先设定目标点的角加速度值, 容易引起角速度较大波动, 3-5-…-5-3混合多项式规划因为五次多项式的存在, 同样容易引起角速度较大波动。针对这些问题, 提出一种三次多项式与四次多项式混合规划方法, 第一段运动规划采用三次多项式插值, 其余规划都采用四次多项式插值, 在指定中间目标点角速度的同时, 确保角加速度的连续性, 且无需预先设定角加速度的值, 避免角加速度预设定值不合理引起的角速度较大波动。并且为了避免运动规划中出现角速度峰值过大, 提出了运动时间的计算方法, 并设定2个目标点处较大速度为最大值, 使得规划的角速度波动较小。通过算例验证了所提方法的合理性和有效性, 与其他2种规划方法进行比较, 有效解决了速度约束的点到点关节运动规划存在的问题, 有利于提升工业机器人的工作性能和使用寿命。