Distributed end-effector formation control for networked 2-DoF flexible-joint manipulators with partially underactuated agents

The presence of faulty or underactuated manipulators can disrupt the end-effector formation keeping of a team of manipulators. This paper investigates the distributed end-effector formation control of networked planar two-link manipulators with flexible joints, emphasizing cases where some agents are underactuated. The underactuated agents can be active–passive (AP) manipulators, where only the first joint is actuated; passive–active (PA) manipulators, where only the second joint is actuated; or a combination thereof. First, we establish an equilibrium property for the discussed underactuated manipulators with flexible joints. Building upon this property, we introduce the novel concept of virtual end-effectors for manipulators, whose positions serve as intermediate variables in the controller design. Then, we extend the distance-based and displacement-based formation controllers to accommodate this group of manipulators by coupling virtual end-effectors, rather than actual end-effectors used in existing works. Finally, we investigate the set of desired and reachable shapes for the networked end-effectors to highlight how the presence of underactuated manipulators affects the applicability of the proposed controllers. This analysis demonstrates that the distance-based method accommodates more underactuated manipulators in the group than the displacement-based method. We validate both our analysis and the proposed distributed controllers through numerical simulations.