Distributed Force/Position Optimization Dynamics for Cooperative Unknown Payload Manipulation

We consider the problem of manipulating an unknown payload using multiple agents. The objective is to find both optimal grasping positions and input forces for agents to apply so that the resulting linear and angular velocities make the rigid object track a reference. The associated optimization problem is split into force and position subproblems. The primal–dual gradient dynamics for the force subproblem can be completely decoupled into local dynamics that each agent can implement using only local measurements. The proximal gradient dynamics for the position subproblem require only local object shape information and relative positions between adjacent agents. We prove that combining the optimization dynamics for these subproblems yields an algorithm that converges to a locally optimal point for the joint force-position problem, and provide numerical simulations that demonstrate its performance on practical problems.