Optimal Time-Jerk Trajectory Generation for Robot Manipulators

Abstract

This work presents a method to obtain minimum-time smooth motion trajectories for robot manipulators. The strategy is to design the trajectory as a combination of cubic splines for position, velocity and acceleration using seven degree polynomials to ensure that the initial and final conditions are set to zero. The spline is obtained with an optimization based in L-BFGS-B (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) with weighing between the accumulated time or jerk, which are part of the cost equation to let the user generate the trajectory according to the specific task. The proposed method is implemented in a Sawyer robot and, under the premise of precisely passing through the required knots, the spline motion is compared with functions from the manufacturer that directly provide tools for kinematic inversion to show the advantage of our approach.