﻿ 基于构形平面的冗余机械臂轨迹规划方法<sup>*</sup>
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Trajectory planning method for redundant manipulator based on configuration plane
WANG Anqi, WEI Yanhui, HAN Han, XU Lixue
College of Automation, Harbin Engineering University, Harbin 150001, China
Received: 2017-11-29; Accepted: 2018-04-08; Published online: 2018-05-17 12:57
Foundation item: National Science and Technology Department International Science and Technology Cooperation Project (2014DFR10010); Defense Industrial Technology Development Program (A0420132202); Thirteen Five Navy Pre-research (J040717005); Natural Science Foundation of Heilongjiang Province of China (E2017024)
Corresponding author. WEI Yanhui.E-mail:wyhhit@163.com
Abstract: This paper proposes a novel method for solving the problem of multi-goal redundant manipulator trajectory planning. Specifically, Specifically, the trajectory planning path for a redundant manipulator is a complicated process with the joint constraint and the limit of spatial obstacle. First, to ensure stability of the manipulator motion, the work configuration of a redundant manipulator can be composed of multiple joint axes, which are connected in sequence. Second, by using the spatial geometry method, spatial trajectory planning for a redundant manipulator can be performed based on the configuration plane. Third, the optimized spatial path can be quickly obtained, which achieves multi-goal trajectory planning using the method of spatial vector leading, obstacle avoidance path comparing and choosing. Finally, a simulation using a 7-DOF redundant manipulator is conducted. The simulation result shows that the path planning problem can be solved quickly and intuitively by this method. Further, it does not depend on the work configuration of the manipulator and can be applied to redundant manipulators with more degrees of freedom.
Keywords: redundant manipulator     configuration plane     space geometry     trajectory planning     space obstacle avoidance

1 机械臂的构形平面 1.1 构形平面的划分

 图 1 构形平面示意图 Fig. 1 Schematic diagram of configuration plane

1.2 构形平面的运动学表达形式

 图 2 构形平面的运动学模型 Fig. 2 Kinematic model of configuration plane

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2 冗余机械臂轨迹规划 2.1 问题提出

1) 空间避障要求:空间避障常用的方法是对空间障碍物用简单三维图形进行包覆, 避免空间机械臂本体发生干涉和碰撞。

2) 运动轨迹:按照任务要求进行机械臂末端运动, 同时运动要求平稳快速, 常用的方法是在关节空间内对机械臂关节进行多次样条曲线插补, 实现运动轨迹平滑和运动平稳。

3) 能量优化:在众多的运动规划中, 通常要求机械臂各关节的运动角度、运动速度和运动加速度的指标最优, 常用的方法是通过对机械臂各关节的运动量(角度、速度和加速度)进行叠加统计, 在这样的方法中往往容易忽略各关节在相同运动角度和速度条件下消耗的能量不同, 靠近基座的关节消耗的能量相对靠近机械臂末端的关节消耗的能量要大很多。

2.2 空间障碍物检测方法

 图 3 构形平面内的障碍物干涉检测 Fig. 3 Interference detection of obstacles within configuration planes

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2.3 机械臂关节约束

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2.4 冗余机械臂的构形平面空间位置确定

 图 4 空间构形平面位置确定 Fig. 4 Determining space position of configuration planes

 图 5 已知轨迹点的构形平面规划 Fig. 5 Configuration plane planning based on known trajectory points

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3 仿真实例

3.1 7自由度机械臂建模

 关节名称 运动范围/(°) 关节参数尺寸/mm 关节1 -180≤θ1≤180 d1=350 关节2 -190≤θ2≤10 d2=450 关节3 -100≤θ3≤100 d3=350 关节4 -100≤θ4≤100 d4=150 关节5 -150≤θ5≤150 d5=145 关节6 -100≤θ6≤100 d6=150 关节7 -180≤θ7≤180 d7=160

 图 6 7自由度冗余机械臂运动模型 Fig. 6 Kinematic model of a 7-DOF redundant manipulator
3.2 构形平面划分

 图 7 冗余机械臂构形平面划分 Fig. 7 Division of configuration plane of a redundant manipulator
3.3 规划任务

 图 8 机械臂插补轨迹点的坐标 Fig. 8 Coordinates of trajectory interpolation points of manipulator

 图 9 机械臂各关节在插补点的角度 Fig. 9 Joint angles of manipulator when end-effector is located in trajectory points
4 结论

1) 总结串联形式的机器人结构特点和工作方式, 引出构形平面概念, 建立了构形平面表达式。该方法能够分解复杂的冗余机械臂拓扑结构, 为运动学求解、轨迹规划、空间避障工作奠定基础。

2) 以构形平面为基础, 通过空间矢量引导的方式对构形平面进行空间位置确定, 进而确定较为合理的冗余机械臂空间位形。该方法避免了采用传统解析方法即依赖机器人构形形式和自由度, 也避免了数值方法中求解精度和求解速度问题, 具有实用性和通用性。

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#### 文章信息

WANG Anqi, WEI Yanhui, HAN Han, XU Lixue

Trajectory planning method for redundant manipulator based on configuration plane

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(9): 1991-1997
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0746