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.