Frequency-Shaped Primal-Dual Optimization for Distributed Model Predictive Control of Nonlinear Multi-Agent Systems

This letter proposes a distributed model predictive control (DMPC) method for multi-agent systems with smooth nonlinear dynamics and constraints, including pairwise distance constraints for collision avoidance. We cast the finite-horizon DMPC problem as a coupled optimization and apply a fully distributed generalized primal-dual gradient method that requires only neighbor-to-neighbor communication to solve the optimization problem. The update law for the optimization is built from diagonal transfer-function blocks that enable frequency-domain shaping of the iteration dynamics to mitigate oscillations and improve convergence. We show that any equilibrium satisfies the Karush-Kuhn-Tucker (KKT) conditions of the original DMPC problem and prove local convergence under a strong monotonicity assumption around a KKT-point. In a four-robot example, frequency-shaped tuning reduces KKT residuals by one to two orders of magnitude and yields collision-free trajectories comparable to a centralized MPC benchmark.