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.
Figures & tables
Fig. 1: Five-unicycle team trajectories: (a) NMPC baseline and (b) proposed method. Reference samples are shaded by weight; crosses and circles denote initial and final positions.
Fig. 2: Unicycle team over ten seeds: (a) Wasserstein distance between the time-averaged agent distribution ρk and reference density ν and (b) Ratio of ∣∣ek+2∣∣ to the proposed bound.
Fig. 3: Four-quadrotor team trajectories: (a) NMPC baseline and (b) proposed method. Crosses and circles denote initial and final positions.
Fig. 4: Quadrotor team over ten seeds: (a) Wasserstein distance between ρk and ν , and (b) Ratio of ∣∣ek+2∣∣ to the proposed bound.