Robotic Arm Trajectory Planning

Abstract

we addressed the task of trajectory planning, which involves the preliminary determination of the programmed motion of degrees of mobility over a specified time interval as a key aspect of kinematic control for robot manipulators. We framed this problem as a mathematical programming challenge. Depending on the requirements for the gripper’s movement, such as bypassing specific trajectory points or transitioning between initial and final points along arbitrary paths, we defined constraints. These constraints include limits on the velocities and accelerations of generalized coordinates to ensure smooth manipulator motion along the trajectory, as well as smoothness conditions imposed on the trajectory itself.
We considered the movement time across all trajectory points, the power of the drives, and other factors as potential target functions. We proposed using the positioning error as the primary criterion, noting that this error varies within the envelope for different configurations of the robotic arm at specific trajectory points. We quantified the positioning error of the gripper near a given point using the quadratic norm of deviations, which depends on the generalized coordinates, their deviations, and the kinematic parameters of the mechanism (e.g., link lengths). This error exhibits maxima and minima within the range of these parameters. By identifying positions where the error reaches its minimum, we demonstrated that the trajectory can be planned precisely through these points, optimizing accuracy.