Nonlinear Density-Driven Optimal Control (D2OC) for Multi-Agent Spatial Coverage via Sequential Convex Programming

2026-10-03

AI Summary

This study addresses the spatial coverage problem for nonlinear multi-agent systems subject to control constraints. It extends the density-driven control framework to nonlinear dynamics by formulating an optimization objective based on the Wasserstein distance metric. Efficient distributed solutions are achieved through local linearization combined with sequential convex programming, while finite-horizon error bounds are established to ensure theoretical rigor. The proposed algorithm significantly reduces computational complexity while fully preserving the distribution-driven characteristics of the original framework. Simulation results demonstrate that its coverage performance is comparable to that of nonlinear model predictive control (MPC), yet with substantially shorter computation times, thereby achieving an effective balance between accuracy and efficiency.

Abstract

This paper presents a nonlinear extension of Density-Driven Optimal Control (D2OC) for multi-agent spatial coverage with prescribed density distributions. Rather than assigning individual target locations, D2OC drives the collective spatial distribution of agents toward a desired density through a Wasserstein-based objective. We extend this framework to multi-step finite-horizon control for discrete-time control-affine nonlinear systems using sequential convex programming. At each control update, the nonlinear dynamics are locally linearized over the prediction horizon, yielding a strictly convex quadratic program that preserves the Wasserstein barycentric structure while directly incorporating input constraints. We further characterize the effect of constrained control deviations and nonlinear Taylor remainders on the accuracy of the local linear prediction, establishing an explicit finite-horizon error bound and a two-step specialization for receding-horizon implementation. The resulting method retains the decentralized, distribution-driven nature of D2OC while providing a computationally efficient optimization procedure for nonlinear multi-agent systems. Simulations with unicycle and quadrotor teams show coverage performance comparable to nonlinear model predictive control, while substantially reducing computation time. These results demonstrate a tractable and theoretically characterized framework for density-driven spatial coverage under nonlinear dynamics.

Problem

• Multi-agent spatial coverage
• Density-driven optimal control
• Nonlinear dynamics
• Wasserstein distance
• Sequential convex programming

Innovation

• Density-Driven Optimal Control
• Sequential Convex Programming
• Wasserstein Distance
• Multi-Agent Spatial Coverage
• Nonlinear Model Predictive Control