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

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.

Real-Time Model Predictive Control for Industrial Manipulators with Singularity-Tolerant Hierarchical Task Control

This paper proposes a real-time model predictive control (MPC) scheme to execute multiple tasks using robots over a finite-time horizon. In industrial robotic applications, we must carefully consider multiple constraints for avoiding joint position, velocity, and torque limits. In addition, singularity-free and smooth motions require executing tasks continuously and safely. Instead of formulating nonlinear MPC problems, we devise linear MPC problems using kinematic and dynamic models linearized along nominal trajectories produced by hierarchical controllers. These linear MPC problems are solvable via the use of Quadratic Programming; therefore, we significantly reduce the computation time of the proposed MPC framework so the resulting update frequency is higher than 1 kHz. Our proposed MPC framework is more efficient in reducing task tracking errors than a baseline based on operational space control (OSC). We validate our approach in numerical simulations and in real experiments using an industrial manipulator. More specifically, we deploy our method in two practical scenarios for robotic logistics: 1) controlling a robot carrying heavy payloads while accounting for torque limits, and 2) controlling the end-effector while avoiding singularities.