Time-Jerk Optimal Robotic Trajectory Planning Under Jerk and Continuity Constraints via Convex Optimization

This paper proposes a robot trajectory planning method focused on time and jerk optimization under compound constraints. First, the robot path-tracking task is parameterized by incorporating both kinematic and dynamic constraints in joint and Cartesian spaces, establishing a time-optimal trajectory optimization model. To achieve C3 continuity in joint motion, joint-motion continuity conditions are analyzed, and optimization variables are reconstructed using piecewise cubic splines with corresponding continuity constraints. Considering the nonlinear and nonconvex characteristics of jerk constraints, the time-optimal planning model is decomposed into two second-order cone programming (SOCP) subproblems, achieving linear convexification of the original problem. Additionally, the objective function is improved to optimize both time and joint jerk simultaneously. Experimental results confirm that the proposed method effectively improves robot efficiency and trajectory smoothness.