Cooperative Passivity-Based Control of Nonlinear Mechanical Systems

In this work, we propose two cooperative passivity-based control methods for networks of mechanical systems. By cooperatively synchronizing the end-effector coordinates of the individual agents, we achieve cooperation between systems of different types. The underlying passivity property of our control approaches ensures that cooperation is stable and robust. Neither of the two approaches rely on the modeling information of neighbors, locally, which simplifies the interconnection of applicable systems and makes the approaches modular in their use. Our first approach is a generalized cooperative Interconnection-and-Damping Assignment passivity-based control (IDA-PBC) scheme for networks of fully actuated and underactuated systems. Our approach leverages the definition of end-effector coordinates in existing single-agent IDA-PBC solutions for underactuated systems to satisfy the matching conditions, independently of the cooperative control input. Accordingly, our approach integrates a large set of existing single-agent solutions and facilitates cooperative control between these and fully actuated systems. Our second approach proposes agent outputs composed of their end-effector coordinates and velocities to guarantee cooperative stability for networks of fully actuated systems in the presence of communication delays. We validate both approaches in simulation and experiments.