Distributed Object Transport of Mobile Manipulators with Optimal Manipulable Coordination

This paper addresses a distributed projected control algorithm for networked mobile manipulators to achieve a task of object transport with optimal manipulable coordination between robot arm and mobile platform. The task is designed as a distributed non-convex optimization problem with time-varying coupled equality constraints. To eliminate the time-varying term in the optimization problem, the task variables are first introduced. The non-convex cost function is then proved convex under a sufficient condition by selecting a proper displacement vector. Moreover, a modified Lagrangian function containing local multipliers and a nonsmooth penalty function is constructed to handle the coupled equality constraints in a distributed manner. Therefore, a fully distributed projected control algorithm is proposed to achieve the object transport task based on the primal-dual subgradient dynamics. We prove the convergence of the algorithm utilizing the Lyapunov stability theory and the invariance principle. Under the proposed control algorithm, the object transport is accomplished with optimal manipulable coordination, which is further validated through numerical simulations.