A Trajectory Planning Method For Six Degree-of-Freedom Robots Taking Into Account of End Effector Motion Error

A trajectory planning method for six degree-of-freedom robots taking into accounts of end effector motion error, wherein:

• key trajectory points are obtained at equal interval of an end effector continuous trajectory;
• interpolation programming is carried out for the angular positions of each joint obtained by inverse solution of the spinor kinematics model;
• at first, take the number of the key trajectory points as variable to control an end effector tracking error within a required range, then take the intervals as design variables, and take maximum angular velocity, angular acceleration and angular jerk of each joint as constraint conditions, take minimum tracking error as the optimization objective to optimize the trajectory so as to obtain the planned trajectory with high planning efficiency, small tracking error and smooth movement;
• comprising the steps of:
• step (1), a forward and an inverse kinematics model are established for the robot based on screw theory;
• step (2), on the end effector continuous trajectory, take N+1 key trajectory points at equal interval and get N track segments, with N representing the number of track segments;
• trajectory nodes of each joint are obtained by the inverse kinematics model, a cubic modified spline curve was used for interpolation programming to obtain time-related curves of angular displacement, angular velocity, angular acceleration and angular jerk;
• step (3), the tracking error model is established by taking points on the angular displacement curve every 20 milliseconds (ms) and calculating the end effector position through the forward kinematics model;
• the tracking errors of the end effector position points are calculated;
• a maximum tracking error max(Em) was extracted, Em is track tracking error, m is the number of joint node groups;
• step (4), Tn represents a time interval of the track segment n, take Tn=t, 1≤n≤N, plan the trajectory and calculate the maximum tracking error max(Em) following the above steps;
• if the accuracy requirement max(Em)<Emax is not met, Emax being the maximum tracking error defined according to the operation task, take N+1, and then calculate the error again, loop the calculation until the tracking error meets the condition;
• time interval t and motion accuracy limit Emax are determined according to specific task requirements;
• and
• step (5), when N is determined, taking the time intervals as the design variable, the angular velocity, angular acceleration and angular jerk of each joints as constraints, and the minimum tracking error as the optimization objective to optimize the trajectory and obtain an optimized trajectory.