Primal–Dual Gradient Dynamics for Cooperative Unknown Payload Manipulation without Communication

We consider the problem of manipulating an unknown payload using multiple, non-communicating agents. The objective is to find an optimal input force of each agent so that linear and angular velocity of a rigid object tracks a reference velocity. We show that the primal-dual gradient dynamics for the associated optimization program can be completely decoupled into local dynamics that each agent can implement using only their own measurements. We prove that the proposed optimization dynamics converge locally at an exponential rate, and provide numerical simulations that demonstrate their performance on practical problems.