基于时间最短的冲压机器人轨迹规划
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摘要
针对一种4自由度串联冲压机器人的自动上下料过程,在机器人的初始位姿与目标位姿已知,而运动时间和路径不确定的前提下,以最大限度提高机器人工作效率为目标,以工程实际中关节驱动力、驱动速度和工艺过程为约束条件,进行了单工作周期时间最短优化研究。首先采用D-H参数法建立机器人的连杆坐标系,列出关节变换矩阵和运动学方程,通过微分变换法求出机器人的雅克比矩阵,采用牛顿-欧拉法得出各关节力矩的表达式;然后以时间为参数,运用5次多项式拟合关节位移变化轨迹;最后采用二分法求解满足各关节速度约束和力(矩)约束的最优运动时间,从而生成各关节运动轨迹,并且进行了对比实验。结果表明,该轨迹规划方法能有效地缩短冲压机器人的工作周期。
For the automatic loading and unloading process of a 4-DOF series stamping robot,with the known initial position and target position of the robot but the uncertain movement time and path,taking the joint driving force,the driving velocity and the process in the engineering practice as the constraint conditions,the shortest optimization period of a single working cycle was carried out to maximize the improvement of the robot work efficiency. Firstly,the link-pole coordinate system of the robot was established by the D-H method,and the transformation matrix of joints and the kinematics equations were listed. Therefore,the Jacobi matrix of the robot was obtained by the differential transformation method,and the expressions of the joint moment were obtained by the Newton-Euler method. Secondly,the displacement trajectory of joint was fitted with quintic polynomial,while the motion time was parameterized. Finally,the optimal motion time of the robot was calculated to satisfy the velocity and force( moment) limitation of the joint by the bisection method. Thus,a new corresponding trajectory was generated,and a contrast experiment was carried out. The results show that it can effectively shorten the work period of stamping robot by this trajectory planning method.
For the automatic loading and unloading process of a 4-DOF series stamping robot,with the known initial position and target position of the robot but the uncertain movement time and path,taking the joint driving force,the driving velocity and the process in the engineering practice as the constraint conditions,the shortest optimization period of a single working cycle was carried out to maximize the improvement of the robot work efficiency. Firstly,the link-pole coordinate system of the robot was established by the D-H method,and the transformation matrix of joints and the kinematics equations were listed. Therefore,the Jacobi matrix of the robot was obtained by the differential transformation method,and the expressions of the joint moment were obtained by the Newton-Euler method. Secondly,the displacement trajectory of joint was fitted with quintic polynomial,while the motion time was parameterized. Finally,the optimal motion time of the robot was calculated to satisfy the velocity and force( moment) limitation of the joint by the bisection method. Thus,a new corresponding trajectory was generated,and a contrast experiment was carried out. The results show that it can effectively shorten the work period of stamping robot by this trajectory planning method.
引文
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[4]翟敬梅,应灿,张铁,等.双机器人协同焊接的轨迹优化[J].焊接学报,2015,36(1):91-95.Zhai J M,Ying C,Zhang T,et al.Trajectory optimization of tworobot welding coordination[J].Transactions of the China Welding Institution,2015,36(1):91-95.
[5]杨玉维,赵新华,孙启湲,等.基于多体动力学特性的机械手时间最优轨迹规划[J].机械工程学报,2014,50(7):8-14.Yang Y W,Zhao X H,Sun Q Y,et al.Trajectory optimization of manipulator for minimum working time based on multi-body dynamic characters[J].Journal of Mechanical Engineering,2014,50(7):8-14.
[6]Li B,Shao Z J.Simultaneous dynamic optimization:A trajectory planning method for no holonomic car-like robots[J].Advances in Engineering Software,2015,87:30-42.
[7]王艳艳,刘开周,封锡盛.AUV纯方位目标跟踪轨迹优化方法[J].机器人,2014,36(2):179-184.Wang Y Y,Liu K Z,Feng X S.Optimal AUV trajectories for bearings-only tracking[J].Robot,2014,36(2):179-184.
[8]Devendra P G,Manish K.Optimization techniques applied to multiple manipulators for path planning and torque minimization[J].Engineering Applications of Artificial Intelligence,2002,15:241-252.
[9]祁若龙,周维佳,王铁军.一种基于遗传算法的空间机械臂避障轨迹规划方法[J].机器人,2014,36(3):263-270.Qi R L,Zhou W J,Wang T J.An obstacle avoidance trajectory planning scheme for space manipulators based on genetic algorithm[J].Robot,2014,36(3):263-270.
[10]Denavit J,Hartenberg R.A kinematic notation for lower pair mechanisms based on matrices[J].Journal of Applied Mechanics,1955,(22):215-221.
[11]张志强.大型机器人冲压线上下料技术研究[D].秦皇岛:燕山大学,2012.Zhang Z Q.A Study of Loading/Unloading Technology on Large Robotic Automatic Press Lines[D].Qinhuangdao:Yanshan University,2012.