Cooperative Load Manipulation with Three 3R Robot Arms: Emergent Force Sharing via Lotka–Volterra Ecological Dynamics Under Virtual Impedance Control

This paper presents a novel control architecture for cooperative load manipulation using three 3R serial robot arms arranged symmetrically around a shared payload. The major contribution of this paper to existing literature is the use of a competitive ecological model as the force-sharing mechanism. In this approach, each robot is treated as a species competing for a common resource, and the inter-species interaction matrix governs how the 150 N total load is distributed among the three agents at every instant. The Lotka-Volterra dynamics feed into a virtual impedance layer in which an emergent load trajectory P(t) evolves according to a mass–damper equation driven by the net end-effector forces. Joint trajectories are resolved at each time step through a Jacobian inverse kinematics solver with exponential moving average warm-start, and a low-pass filter on the Lotka-Volterra output suppresses transient oscillations. The result is a fully closed-loop system in which the load’s spatial trajectory is not prescribed but emerges from the collective force dynamics. A key property of the architecture is its self-regulated disturbance recovery: when a sigmoid-ramped perturbation reduces the dominant robot’s effective force contribution between t = 12 s and t = 14 s, the ecological competition naturally redistributes load across the remaining agents without any explicit re-planning or supervisory intervention. This self-regulating behavior arises directly from the limit-cycle structure of the Lotka-Volterra equilibrium.