Time-optimal trajectory planning based on improved genetic algorithm
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摘要: 提出一种工业机器人时间最优轨迹规划方法。将机器人关节空间的轨迹视为拟合关键点的三次样条曲线，以最优时间为目标建立最优时间轨迹规划的数学模型，同时考虑关节轨迹速度、加速度和加加速度的约束，结合目标函数值和约束条件提出一种用于进化算法的排序方法，以改进遗传算法为例优化关节空间的三次样条轨迹。应用谢菲尔德(Sheffield)遗传算法工具箱计算遗传算法优化结果，以D-H法建立机器人运动学模型，结合Roboticstoolbox构建机器人的三维仿真模型，建立对机器人三次样条轨迹优化的仿真环境。对斯坦福机器人仿真实验结果表明，与传统的模式搜索法相比，改进遗传算法优化的轨迹总时间明显降低。Abstract: A time-optimal trajectory planning method for industrial robots is proposed. The trajectory of robot joint space is regarded as the cubic spline curve fitting the key points. The mathematical model of optimal time trajectory planning was established with the objective of optimal time. At the same time, the constraints of joint trajectory velocity, acceleration and acceleration were considered. Combining the objective function value and constraint conditions, a sorting method for evolutionary algorithm was proposed, and the cubic spline trajectory of joint space was optimized with the improved genetic algorithm as an example. The Sheffield genetic algorithm toolbox was used to calculate the optimization results of genetic algorithm, and the D-H method was used to establish the robot kinematics model. Combined with the Robotics Toolbox, the 3D simulation model of the robot was built, and the simulation environment for cubic spline trajectory optimization of the robot was established. The simulation results of Stanford robot show that compared with the traditional pattern search method, the total trajectory time of the improved genetic algorithm is significantly reduced.
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表 1 轴承圆柱滚子自动化测量工艺路径过程
关键点 p1 p2 p3 p4 p5 p6 p7 p8 目的 工作原点 接近 抓取 测量 接近 分类 移开 回位 位姿 X/m 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.4 Y/ m 0.5 0.5 0.5 -0.5 -0.5 -0.5 0.5 0.4 Z/m 0.5 0.5 0.5 0.5 0 0.5 0.5 0.5 R/rad 0 0 0 0 0 0 0 0 P/rad 0 0 0 0 0 0 0 0 Y/rad 0 0 0 0 0 0 0 0 
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表 2 机器人DH参数
a/rad α/rad d/m θ/rad 1 0 -π/2 0.412 0 2 0 π/2 0.154 0 3 0 0 0 0 4 0 -π/2 0 0 5 0 π/2 0 0 6 0 0 0.263 0
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表 3 机器人各关节的约束
约束 关节 1 2 3 4 5 6 vjmax/(rad/s) 1.74 1.66 2.00 2.61 2.27 1.92 ajmax/(rad/s2) 0.87 0.70 1.50 1.22 1.57 1.40 jjmax/(rad/s3) 1.05 1.05 1.50 1.22 1.31 1.22
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表 4 机器人移动路线关键点对应关节角度
关键点 关节/rad 1 2 3 4 5 6 p1 0.764 1.022 8.288 -3.142 1.022 2.378 p2 -2.334 1.476 -7.102 3.142 1.476 -0.807 p3 0.764 1.022 8.288 -3.142 1.022 2.378 p4 -0.807 1.022 8.288 0.000 -1.022 0.807 p5 2.378 1.477 -7.102 3.142 1.476 0.764 p6 -0.807 1.022 8.288 0.000 -1.022 0.807 p7 0.764 1.022 8.288 -3.142 1.022 2.378 p8 -2.329 -0.918 7.119 0.000 0.918 2.329
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表 5 优化路径时间间隔对比
序号 优化方法 改进遗传算法 模式搜索法 h1 5.338 7 7.289 0 h2 5.378 7 8.374 3 h3 3.331 5 7.947 2 h4 5.488 6 8.602 4 h5 5.497 2 8.626 6 h6 4.561 6 8.026 0 h7 6.199 9 8.503 0 总计 36.180 4 57.368 6 对比增长 -36.93%
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