Fully Distributed Real-Time MPC for Cooperative Mobile Manipulation Via Box-iLQR and ADMM with an Object-Centric Planar Projection

Abstract

We propose a emph{fully distributed} real-time model predictive control framework for transporting a single rigid object with multiple mobile manipulators. Each robot rapidly solves a local optimal control problem via Box-iLQR, while ADMM enforces consensus on the shared object state without centralized computation. The core idea is an object-centric planar orthographic projection that reduces the whole-body state and input dimensions, substantially lowering the computational load of linearization and the Riccati backward pass. Simulations demonstrate accurate trajectory tracking and consistent convergence. Specifically, the proposed dimension-reduced Box-iLQR solver operates at an average of 6.32 ms per iteration—approximately 4 times faster than a full 6-DoF model and cutting the computational cost of SQP-based methods nearly in half. Despite this significant reduction, our controller achieves comparable tracking accuracy, offering a practical alternative for real-time cooperative manipulation under limited compute and communication resources. The framework scales naturally with the number of robots and provides a concise and effective design for cooperative mobile manipulation grounded in real-time distributed optimization.