A Closed-Form Cooperative Avoidance Control for Multiple m-DOF Manipulators

Multi-manipulator cooperative systems are widely deployed in industrial assembly, intelligent manufacturing and other fields, but collision safety and efficient motion coordination during coordinated operation remain key challenges. In this paper, a novel cooperative control strategy based on relative velocity information is derived to guarantee collision-free maneuvers for multiple m-degree-of-freedom (m-DOF) manipulator systems with general Lagrangian dynamics. One key advantage is that it ensures reliable safety while achieving smoother avoidance maneuvers, reduced interference with objective tasks, lower energy consumption, and improved task efficiency; notably, the avoidance control depends not only on the relative distance between manipulators but also on their relative motion, making it less conservative as manipulators avoid unnecessary spreading during collision avoidance. Another is that it integrates collision avoidance, disturbance attenuation, and deadlock elimination into a unified closed-form control law, which yields a closed-form solution and is easy to implement in engineering practice. Theoretically, this paper adopts the generalized Lyapunov stability theory to rigorously prove the asymptotic convergence and persistent collision-free property. Finally, simulation results on a dual two-DOF manipulator system further verify the effectiveness and reliability of the proposed control strategy.