基于A^(*)算法与组合函数的分拣机械臂轨迹规划

Sorting Robotic Arm Trajectory Planning Based on A^(*) Algorithm and Combination Function

为提高常用铸件分拣机械臂路径较长、工作效率低、轨迹与加速度不平滑的问题,提出一种将A算法和组合函数相融合的轨迹规划方法。根据Modified DH法对铸件分拣机械臂进行正运动学分析与计算,采用代数法求解机械臂逆解。通过设置A^(*)算法中启发式函数,使其带有一定方向遍历路径点,寻找最优最短路径,对折线路径轨迹采用三次均匀B样条曲线平滑,得到了光滑轨迹图。为保证加速度、速度平滑性,设计了一种将矩形函数和摆线函数相结合的组合函数,推导了其角位移、角速度、角加速度函数表达式。通过MATLAB仿真模拟得到的五次多项式插值的关节运动学曲线,并与所设计函数曲线对比分析,仿真结果表明所设计的组合函数更加平稳,且角加速度极值被限定,降低了一定程度的机械冲击和振动,确保机械臂工作平稳。

In order to improve the problems of long path,low work efficiency,and unsmooth trajectory and acceleration of commonly used casting sorting manipulators,a trajectory planning method integrating A^(*) algorithm and combination function is proposed.According to the Modified DH method,the positive kinematics of the manipulator are analyzed and calculated,and the algebraic method is used to solve the manipulator inverse.By setting the heuristic function in the A^(*) algorithm to traverse the path points with a certain direction to find the optimal shortest path,the triple-uniform B-spline curve is used to smooth the path trajectory of the polyline line,and the smooth trajectory graph is obtained.In order to ensure the acceleration and smoothness of velocity,a combination function combining rectangular function and cycloid function is designed,and the expressions of angular displacement,angular velocity and angular acceleration are derived.The joint kinematics curve of the five-degree polynomial interpolation obtained by MATLAB simulation and comparison and analysis with the designed function curve determine that the designed combination function is more stable,and the angular acceleration extremum is limited,which reduces a certain degree of mechanical shock and vibration and ensures the smooth work of the robotic arm.