Conflict-Predictive Variable Horizons in Multi-Drone Distributed Model Predictive Control

Linda Mümken; Michael Schwung; Stefan Lier; Andreas Schwung

cs.ROSep 7, 2026

Conflict-Predictive Variable Horizons in Multi-Drone Distributed Model Predictive Control

Authors: Linda Mümken, Michael Schwung, Stefan Lier, Andreas Schwung

Organizations: Department of Automation Technology, South Westphalia University of Applied Sciences, 59494 Soest, Germany · Institute of Automation and Computer Control, Ruhr University Bochum, 44801 Bochum, Germany · Department of Logistics and Supply Chain Management, South Westphalia University of Applied Sciences, 59872 Meschede, Germany

Abstract

In distributed model predictive control for multi-drone collision avoidance, a fixed prediction horizon forces a compromise: a short horizon is inexpensive but reacts late to approaching neighbors, whereas a long one anticipates conflicts at a per-step cost that grows superlinearly with its length. We propose a conflict-predictive variable horizon that each drone sets locally, leaving the distributed model predictive control itself unchanged. From a short history of observed positions, a drone extrapolates the flight lines of its neighbors, tests each against its own using confidence funnels that narrow with prediction range, and obtains each time to conflict in closed form. The horizon is then the smallest admissible value whose planning window covers the farthest predicted conflict. It collapses to its minimum in clear airspace and grows only when a conflict lies ahead. Provided this minimum meets a single computable feasibility bound, we prove that recursive feasibility and asymptotic stability are preserved for every horizon the policy can select. These guarantees hold for a linear model, and a cascaded inner loop reduces each quadrotor's translational dynamics to a perturbed double integrator, so they carry over to the linearized quadrotor model and, as practical stability, to the full nonlinear one. In simulation on dense antipodal-swap benchmarks, the variable horizon reduces both per-step solver cost and total computation well below those of a long fixed horizon, and it maintains separation in every run, which a short fixed horizon of comparable per-step cost does not.

Figures & tables

Panel of Figure 1 — Fig. 1: Proposed scheme on $N$ drones sharing the airspace $\Omega$ . Each drone observes the neighbor positions $\mathbf{p}_{j}$ and runs the same local loop. The predictor $p_{T}$ turns the observations into flight lines $\hat{\mathbf{p}}_{j}$ , the policy $H_{p}$ sets the horizon $H_{i}$ from the funnel conflict test, and the DMPC turns the state $\mathbf{x}_{i}$ into the control input $\mathbf{u}_{i}$ . The horizon is the only quantity that the scheme changes in the otherwise unchanged DMPC. All signals are taken at step $k$ .

Fig. 2: Confidence funnels in a four-drone swap (3D, color-coded). Each funnel runs along a drone’s predicted flight line (dashed), starting at the initial radius $r_{\max}$ and narrowing to the lower bound $r_{\mathrm{f}}$ ( Definition III.1 ). Dotted lines trace the paths already flown. The funnels shown are those predicted by a single drone, but as the simulation shares positions by broadcast, every drone observes the same histories and predicts the same funnels.

Model	$\bar{e}$
Double integrator	$\bar{\rho}+C\beta$
Linearized quadrotor	$\bar{\rho}+C\beta+\bar{\xi}$
Nonlinear quadrotor	$\bar{\rho}+C\beta+\\|\boldsymbol{\xi}_{\mathrm{nl}}\\|_{\infty}$

TABLE I: Feedback perturbation bound across the three model classes.

Fig. 3: Closed-loop trajectories under the variable horizon for the six benchmark scenarios, in open ( $20^{3}\,\mathrm{m}^{3}$ , top) and tight ( $5^{3}\,\mathrm{m}^{3}$ , bottom) airspace. Circles mark the start positions, stars the goals, and the gray curves on the floor are the horizontal projections. One representative seed is shown per scenario, since overlaying all $20$ would obscure the individual paths.

Fig. 4: Per-step solver and prediction cost across the six scenarios, log scale, as means over $20$ seeds per scenario and strategy.

Fig. 5: Total computation per scenario for the three strategies, log scale, as means over $20$ seeds. Labels give the total-time ratio of the long fixed horizon to the variable horizon. The asterisk marks the eight-drone open scenario, where the long fixed horizon exceeds the $500\,$ s budget in every seed.

Panel of Figure 7 — Fig. 6: Minimum pairwise distance in the four-drone open scenario (top) and tight scenario (bottom): seed mean per strategy with min–max envelope over $20$ seeds. The contact boundary is $2r_{\min}=0.8\,$ m.

Scenario	short fixed	variable	long fixed
$N{=}2$ , $20^{3}$	$0.84$	$1.12$	$1.34$
$N{=}4$ , $20^{3}$	$0.81$	$0.86$	$1.07$
$N{=}8$ , $20^{3}$	$0.78^{\dagger}$	$0.81$	$0.83^{*}$
$N{=}2$ , $5^{3}$	$0.80$	$0.80$	$0.80$
$N{=}4$ , $5^{3}$	$0.80$	$0.80$	$0.81$
$N{=}8$ , $5^{3}$	$0.80$	$0.80$	$0.81$

TABLE II: Worst-case closest approach [m] over

20

seeds per scenario.

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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Distributed Model Predictive Control with Adaptive Safety Zones for Multi-Fleet Drone Operations

Linda Mümken, Diyar Altinses, Michael Schwung, Stefan Lier+1

Department of Automation Technology South Westphalia University of Applied Sciences, Soest, Germany · Institute of Automation and Computer Control, Ruhr University Bochum, 44801 Bochum, Germany · Department of Logistics and Supply Chain Management, South Westphalia University of Applied Sciences, Meschede, Germany

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Autonomous drone swarms in space-constrained environments such as warehouses, inspection corridors, and urban delivery routes must share limited airspace safely at high vehicle density. Existing approaches rely on fixed safety zones sized for worst-case velocity, which wastes airspace in congested scenarios. We replace the fixed radius with an adaptive, speed-dependent safety sphere whose size scales with braking distance: tight at low speeds, expanded at high speeds. We develop both a centralized model predictive control (MPC) formulation and a distributed MPC (DMPC) in which each drone optimizes locally from detected neighbors, accommodating mixed fleets with non-cooperative agents. We prove feasibility up to the geometric packing limit evaluated at the minimum radius, establish Lyapunov stability under sufficient conditions on the adaptation parameter, drone density, and prediction horizon, and extend these guarantees to the distributed setting via a contraction condition that preserves the centralized stability margins. We further derive modified sphere-packing capacity bounds and a throughput-optimal crossing speed for narrow passages. Simulations confirm that the adaptive framework remains feasible where fixed-radius methods fail: it roughly doubles the admissible drone count, reduces traversal time through constrained passages by about 25 percent, and enables passage through openings impassable to static safety zones. The centralized variant realizes a larger fraction of the theoretical capacity, while the distributed variant offers a more realistic deployment model for mixed-fleet operations under the same safety guarantees.

Abstract

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