Spline Based Trajectory Planning for Cooperative Crane Lifts

This paper reports the work done towards planning the trajectory for cooperative crane lifts. The location of the hook points between the pick and place positions are determined using a path-planner. These are inputs to the trajectory planner. The goal of the trajectory planner is to connect all the path-points while ensuring the overshoots, velocities, accelerations and jerk for each degree of freedom to be within acceptable limits for the system. A number of alternate techniques are available for defining the trajectory between the path-points. This paper reports on the evaluation of algebraic and trigonometric splines for trajectory planning. Splines of various orders were initially evaluated for a single joint. This evaluation found that 4th order trigonometric splines were most appropriate. Hence, this was applied to a lift problem involving the 2x4 DOF cooperative manipulator system and the results are presented.