A Convex Optimization Method to Time-Optimal Trajectory Planning With Jerk Constraint for Industrial Robotic Manipulators

This paper proposes a convex time-optimal trajectory planning method for industrial robotic manipulators with jerk constraints. To achieve smooth and efficient trajectories, the square of the pseudo velocity profile is constructed using a cubic uniform B-spline, and a linear relationship is defined with the control points of the B-spline to preserve convexity in the pseudo states. Bi-linear and non-convex jerk constraints are introduced in the optimization problem, and a convex restriction method is applied to achieve convexity. The proposed method is evaluated through three case studies: two contour following tasks and a pick-and-place task. Comparative optimization results demonstrate that the proposed method achieves time optimality and trajectory smoothness simultaneously in the reformulated and jerk-restricted optimization problem. The proposed method provides a practical approach to address the non-convexity of jerk constraints in trajectory optimization for industrial robotic manipulators.
Note to Practitioners
—This work was motivated by the challenge of generating smooth and time-optimal trajectories for industrial manipulators while considering jerk and dynamic constraints. Existing approaches typically use multi-objective methods that treat jerk constraints as soft constraints. In contrast, this work proposes a B-spline-based convex optimization method that treats jerk constraints as hard constraints. Three case studies are conducted, involving butterfly-type, door-type and ‘OPTEC’-type paths, with the UR5 cooperative robot. The numerical and experimental results demonstrate that the proposed method sacrifices some time optimality to achieve trajectory smoothness and computational efficiency due to the convex restriction reformulation of the jerk constraints. Moreover, the proposed method is applicable to general industrial manipulators. Supplementary video is available at https://youtu.be/gVz5IuPKD-o.