On the Performance of Jerk-Constrained Time-Optimal Trajectory Planning for Industrial Manipulators

TL;DR

The paper tackles time-optimal trajectory planning for industrial manipulators under jerk (third-order) constraints. It introduces a novel Sequential Linear Program (SLP) that conservatively linearizes nonlinear jerk inequalities, enabling iterative convergence to jerk-constrained, time-optimal trajectories. Through simulations and real-robot experiments on a 7-DOF Kawasaki arm, it demonstrates that enforcing jerk limits reduces peak power by about 25% and RMS torque by about 50%, with only modest increases in motion duration and real-time solvability (sub-10 ms per instance). The approach offers smoother, more energy-efficient, and more trackable motions, providing a practical pathway to safer and more durable industrial automation.

Abstract

Jerk-constrained trajectories offer a wide range of advantages that collectively improve the performance of robotic systems, including increased energy efficiency, durability, and safety. In this paper, we present a novel approach to jerk-constrained time-optimal trajectory planning (TOTP), which follows a specified path while satisfying up to third-order constraints to ensure safety and smooth motion. One significant challenge in jerk-constrained TOTP is a non-convex formulation arising from the inclusion of third-order constraints. Approximating inequality constraints can be particularly challenging because the resulting solutions may violate the actual constraints. We address this problem by leveraging convexity within the proposed formulation to form conservative inequality constraints. We then obtain the desired trajectories by solving an $\boldsymbol n$-dimensional Sequential Linear Program (SLP) iteratively until convergence. Lastly, we evaluate in a real robot the performance of trajectories generated with and without jerk limits in terms of peak power, torque efficiency, and tracking capability.

Figures (6)

• Figure 1: Two-Stage Motion Planning and Control Architecture: The path generator creates a collision-free path, which is fed into the time-optimal trajectory planner to compute the desired trajectory satisfying robot hardware limits. Subsequently, the predictive proportional-integral (PPI) controller generates high-frequency joint commands with feedback.
• Figure 2: Test motion snapshots. A: Front place motion to move boxes from a conveyor to the top of a virtual stack of packages. B: Pre-pick motion preparing to pick a box from a conveyor: C. Bottom place motion to place boxes onto the bottom of the truck. D: Post-place motion to return to the ready pose after placing boxes. E and F show box unloading motions, which return the box from a stack of packages to the conveyor with and without jerk constraints. Without jerk constraints, the robot's suction gripper is also more likely to lose grasp of the box.
• Figure 3: Comparison of the velocity curve for the pre-pick motion (Fig. \ref{['fig:snapshot']}B) computed from TOPP-RA pham2018new without jerk limits (black), zhang2013practical with pseudo jerk limits (blue) and the proposed approach with jerk limits (red).
• Figure 4: Algorithm performance comparison on real-robot for the front place motion (Fig. \ref{['fig:snapshot']}A): A shows tracking performance of the algorithms with and without jerk limits by comparing the desired, commanded, and actual joint position and velocity. B shows the corresponding estimated torque and power.
• Figure 5: Time-optimal trajectory generated for the front place motion (Fig. \ref{['fig:snapshot']}A) without jerk limits (blue) and with jerk limits (red).