DMPC-SWARM: Distributed MPC for UAV Swarms

• DMPC-SWARM is a distributed model predictive control framework that uses receding-horizon optimization and trajectory exchange to coordinate UAV and multirobot swarms.
• It integrates various formulations—from event-triggered off-board computation to on-demand collision constraints and decentralized learning—to reduce communication load and conservative planning.
• Empirical studies and hardware experiments validate its scalability and safety, demonstrating significant reductions in computational time and improved collision avoidance.

DMPC-SWARM denotes a class of distributed model predictive control architectures for UAV and multirobot swarms in which coupled motion-planning, collision-avoidance, and formation-control problems are solved in receding-horizon form through local or partially local optimizations that exchange predicted trajectories, state estimates, or consensus variables. In the recent arXiv literature, closely related methods described under the DMPC-SWARM label include event-triggered ground-offloaded planning for UAV swarms (Gräfe et al., 2022), online trajectory generation with on-demand collision avoidance (Luis et al., 2019), decentralized agile quadrotor collision avoidance based on ORCA and flatness-based MPC (Arul et al., 2019), communication-efficient trajectory-prediction-assisted DMPC (Yan et al., 2024), distributed learning-based predictive control with explicit closed-loop policies (Zhang et al., 2024), and a nano-UAV implementation combining event-triggered off-board computing with a stateless wireless mesh and message-loss recovery (Gräfe et al., 28 Aug 2025). This suggests that DMPC-SWARM is best understood as a research lineage rather than a single canonical algorithm.

1. Core formulation and system models

At its most standard, DMPC-SWARM assigns each agent $i$ a local prediction model, a finite horizon, a stage cost, and state/input/safety constraints, then executes only the first control action before shifting the horizon. In the event-triggered UAV-swarm formulation, each vehicle is modeled by the linear time-invariant discrete-time system

$x_i(k+1)=A\,x_i(k)+B\,u_i(k),$

with

$$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$

where $p_i\in\mathbb R^3$ is position, $v_i\in\mathbb R^3$ velocity, and $y_i\in\mathbb R^{n-6}$ additional internal states (Gräfe et al., 2022). The local decision variables over horizon $H$ are predicted state and input sequences $X_i(k)$ and $U_i(k)$, and the optimization minimizes a quadratic tracking-and-effort objective subject to dynamics, box constraints, a terminal constraint $x_i(k+H\mid k)\in\mathcal X_{f,i}$, and pairwise collision-avoidance constraints (Gräfe et al., 2022).

A second widely used formulation parameterizes future trajectories directly. In the online multi-robot motion-planning variant, each agent uses a linear discrete-time trajectory-tracking model

$x_i(k+1)=A\,x_i(k)+B\,u_i(k),$0

and samples the continuous control trajectory on the horizon by concatenating $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$1 Bézier curves of degree $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$2. The control points $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$3 become the QP decision variables, while physical limits are imposed by sampling the curves and their derivatives up to order $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$4 and encoding the bounds as linear inequalities on $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$5 (Luis et al., 2019).

For agile quadrotors, the modeling layer can be richer. The decentralized collision-avoidance method DCAD begins from the full 12-dimensional nonlinear quadrotor dynamics and then exploits differential flatness with flat outputs $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$6. Through exact feed-forward linearization, the dynamics are transformed into the linear decoupled form

$x_i(k+1)=A\,x_i(k)+B\,u_i(k),$7

which is then discretized and embedded in an MPC with velocity, acceleration, jerk, and collision constraints (Arul et al., 2019). This formulation is explicitly downwash conscious and incorporates Kalman filtering to address uncertainty in sensed position and velocity data (Arul et al., 2019).

Later work generalizes beyond repeated online QP solves. Distributed learning-based predictive control formulates the multirobot problem as a nonlinear coupled finite-horizon MPC with dynamics

$x_i(k+1)=A\,x_i(k)+B\,u_i(k),$8

local stage costs $x_i(k+1)=A\,x_i(k)+B\,u_i(k),$9, and coupling sets $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$0, then learns explicit closed-loop policies to avoid numerical optimization during deployment (Zhang et al., 2024). A plausible implication is that DMPC-SWARM now spans both optimizer-centric and policy-centric implementations.

2. Collision avoidance, constraint handling, and local objectives

The principal technical distinction among DMPC-SWARM variants lies in how they encode inter-agent safety. In the event-triggered UAV architecture, pairwise avoidance is enforced through time-variant buffered Voronoi cells (TV-BVC). For each sample $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$1, the constraint

$$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$2

is built from previously predicted relative positions, where $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$3 is the minimum allowed inter-UAV distance. By enforcing these linear constraints at sufficiently many points along the horizon, continuous-time collision-free operation is guaranteed (Gräfe et al., 2022).

The online trajectory-generation approach replaces full Voronoi partitioning by an on-demand mechanism. Each agent first detects whether a predicted collision with neighbor $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$4 exists within the horizon through the earliest index

$$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$5

defines an activation set $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$6 of imminent conflicts, and adds linearized separating-hyperplane constraints only for $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$7. Slack variables $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$8 soften these constraints, while the local objective combines terminal position error, smoothness or energy regularization, and violation penalties (Luis et al., 2019). The paper explicitly states that this is far less conservative than full buffered-Voronoi methods (Luis et al., 2019).

In DCAD, collision constraints are built from Optimal Reciprocal Collision Avoidance (ORCA) half-spaces. At each prediction step, agent $$x_i(k)=\begin{bmatrix} p_i(k)\ v_i(k)\ y_i(k) \end{bmatrix},$$9 enforces

$p_i\in\mathbb R^3$0

and extends the geometry through a sphere-oriented-ellipsoid Minkowski model so that a higher vehicle’s downwash region is respected. The method then inflates these shapes by the maximal standard deviation of the neighbor’s position covariance from a Kalman filter (Arul et al., 2019). This is a notably different safety mechanism from TV-BVC or on-demand hyperplane constraints, but it remains compatible with linear or linearized MPC.

Communication-constrained DMPC introduces a broader constraint stack. In the cluttered-environment formulation, the local QP includes dynamics feasibility, Bézier continuity, agent-agent collision avoidance, cohesion, and agent-obstacle avoidance: $p_i\in\mathbb R^3$1

$p_i\in\mathbb R^3$2

$p_i\in\mathbb R^3$3

with nonnegative slacks $p_i\in\mathbb R^3$4. Its stage cost combines migration to the goal, control effort, inter-agent and agent-obstacle repulsion, and cohesion (Yan et al., 2024).

A common misconception is that DMPC-SWARM always relies on a single safety formalism. The literature instead shows several distinct mechanisms—TV-BVC, on-demand linearized collision constraints, ORCA half-spaces with downwash geometry, soft-safe-cohesive Bézier constraints, and barrier-augmented safe learning—embedded in the same receding-horizon coordination paradigm (Gräfe et al., 2022).

3. Distributed coordination, communication, and triggering

Distributed coordination in DMPC-SWARM ranges from purely peer-to-peer trajectory exchange to architectures that offload planning to ground-based computation units. In the online trajectory-generation framework, each agent broadcasts its predicted trajectory $p_i\in\mathbb R^3$5 to its neighbors, collects $p_i\in\mathbb R^3$6, solves its local QP in parallel, and re-broadcasts its updated prediction. Because each QP only depends on one-hop neighbors in $p_i\in\mathbb R^3$7, the computation parallelizes naturally (Luis et al., 2019). DCAD adopts a similar decentralized pattern, exchanging state estimates, covariances, and optionally the first few steps of predicted trajectories with neighbors within a sensing radius $p_i\in\mathbb R^3$8, with communication rates matched to the MPC rate (Arul et al., 2019).

The event-triggered UAV-swarm architecture of 2022 introduces a different organization. There are $p_i\in\mathbb R^3$9 stationary ground-based computation units and $v_i\in\mathbb R^3$0 UAVs, with $v_i\in\mathbb R^3$1, and communication proceeds in synchronous rounds of length

$v_i\in\mathbb R^3$2

During the communication slot, all agents broadcast their most recent state or planned trajectory in a many-to-all flood so that every CU and UAV begins the next round with a consistent global view of trajectories. An event trigger then selects which $v_i\in\mathbb R^3$3 of the $v_i\in\mathbb R^3$4 UAV trajectories should be replanned in the coming round (Gräfe et al., 2022). The Priority-Based Trigger assigns each UAV a scalar score

$v_i\in\mathbb R^3$5

combining tracking error, time since last replanning, and a blocking measure (Gräfe et al., 2022).

The 2025 nano-UAV implementation retains the same event-triggered off-board idea but embeds it in a specific communication stack. All UAVs and compute units are synchronized into fixed-length rounds by the Mixer wireless protocol, with a computation phase and a communication phase. Each CU updates “information-trackers” $v_i\in\mathbb R^3$6, runs the event trigger if all trackers are up-to-date, solves one local MPC, and broadcasts a trajectory message. If any tracker is deprecated because of missing messages, the CU enters message-loss-recovery mode and requests the missing trajectory. Priority values can be Round-Robin, Distance-based, or Hybrid, and they are unified by max-consensus across CUs (Gräfe et al., 28 Aug 2025).

Self-triggering provides a further reduction in communication. For asynchronous nonlinear multi-agent systems with bounded delays, each agent solves a local min-max MPC at its own triggering instants, evaluates value functions $v_i\in\mathbb R^3$7 for candidate triggering intervals $v_i\in\mathbb R^3$8, and chooses the largest interval whose worst-case cost does not exceed the one-step update cost: $v_i\in\mathbb R^3$9 The agent then broadcasts a predicted trajectory and waits until the next triggering instant $y_i\in\mathbb R^{n-6}$0 (Wei et al., 2021).

These designs show that “distributed” does not imply a single networking pattern. Depending on the formulation, DMPC-SWARM may mean local peer-to-peer exchange, centralized many-to-all flooding with off-board compute, asynchronous self-triggering, or a hybrid architecture with consensus over trigger priorities and message-loss recovery (Gräfe et al., 28 Aug 2025).

4. Theoretical guarantees

The strongest theoretical results in DMPC-SWARM concern recursive feasibility and collision avoidance. In the event-triggered ground-offloaded formulation, Lemma 1 proves safety at sample points, Theorem 1 establishes recursive feasibility under the terminal constraint and TV-BVC conditions even if some agents are not replanned, and Theorem 2 shows continuous-time collision avoidance when the TV-BVC sampling grid is dense enough and

$y_i\in\mathbb R^{n-6}$1

The proof strategy combines standard MPC Lyapunov-like arguments with buffered Voronoi geometry (Gräfe et al., 2022).

The nano-UAV implementation extends these guarantees to more realistic communication conditions. Under one-round communication delay, arbitrary message losses detected through information-trackers, and bounded tracking error, Lemma 1 proves correctness of information-trackers, Lemma 2 proves tracker agreement across computation units, Theorem 1 proves recursive feasibility and collision-free reference generation, and Theorem 2 establishes actual continuous-time separation: $y_i\in\mathbb R^{n-6}$2 provided the tracking error bound satisfies

$y_i\in\mathbb R^{n-6}$3

The paper explicitly states that safety is maintained despite one-round delay, arbitrary message losses, and bounded tracking error (Gräfe et al., 28 Aug 2025).

In the asynchronous self-triggered min-max setting, a consistency constraint restricts the deviation between a newly optimized trajectory and the last broadcast one,

$y_i\in\mathbb R^{n-6}$4

so that previously broadcast predictions remain usable even under time-varying delays. Under Lipschitz dynamics, bounded disturbances and delays, and a robust positive-invariant terminal set, Theorem 1 guarantees recursive feasibility and input-to-state practical stability at update instants (Wei et al., 2021).

Optimization-theoretic guarantees also appear in distributed solution methods. For cooperative formation control, ADMM is globally convergent for convex QP formulations, while decentralized SQP for non-convex QCQP subproblems enjoys local convergence under standard SQP assumptions, including LICQ, strict complementarity, and a strong second-order sufficient condition (Stomberg et al., 2023). In the spatial-temporal D-PDDP framework, ADMM primal and dual residuals converge to zero under mild convexity assumptions on the constraint-indicator terms plus local fast convergence of PDDP, and spectral tuning of the penalty parameter is proposed to reduce the number of algorithmic iterations (Zheng et al., 20 Oct 2025).

Learning-based variants preserve an MPC-style stability narrative. Distributed policy learning selects terminal cost weights $y_i\in\mathbb R^{n-6}$5 through a Lyapunov equation and imposes a baseline-upper-bound condition

$y_i\in\mathbb R^{n-6}$6

so that policy-learning updates decrease the cost until convergence and closed-loop asymptotic stability follows (Zhang et al., 2024). A plausible implication is that DMPC-SWARM now includes both classical recursive-feasibility proofs and stability arguments mediated by learned policy approximators.

5. Empirical performance and hardware realizations

Reported results show that DMPC-SWARM has progressed from simulation-only studies to hardware-in-the-loop and fully distributed swarm experiments. The numerical evidence is heterogeneous because the papers evaluate different dynamics, communication models, and optimization back-ends, but several recurring themes are clear: communication reduction, reduced conservatism relative to buffered-Voronoi baselines, and real-time feasibility on swarms ranging from a few robots to tens of thousands of simulated agents.

Variant	Setup	Reported outcome
Event-triggered off-board ET-DMPC (Gräfe et al., 2022)	Up to $y_i\in\mathbb R^{n-6}$7, $y_i\in\mathbb R^{n-6}$8, $y_i\in\mathbb R^{n-6}$9 m$H$0 arena	$H$1 reduction in communication load, $H$2 savings in cumulative computation time, $H$3 target reach vs. $H$4 round-robin
On-demand DMPC (Luis et al., 2019)	Up to 60 agents in $H$5 m$H$6	$H$7 success rates up to 30 agents; average transition times reduce by $H$8 vs. BVC
DCAD (Arul et al., 2019)	8 agents, up to $H$9 m/s nominal speed	0 collisions up to $X_i(k)$0 m/s; at $X_i(k)$1 m/s, 21/250 collisions vs. ORCA 151/250 and AVO 128/250
Prediction-assisted DMPC (Yan et al., 2024)	Funnel environment, $X_i(k)$2	VAE+EG+KKT total cost $X_i(k)$3 k vs. oracle DMPC $X_i(k)$4 k; communication load cut by up to $X_i(k)$5
DMPC-Swarm on nano UAVs (Gräfe et al., 28 Aug 2025)	16 Crazyflie 2.1, 3 laptops, real wireless mesh	$X_i(k)$6 many-to-all delivery per round; formation change $X_i(k)$7 s with 1 CU and $X_i(k)$8 s with 3 CUs

Hardware validation is a consistent feature. The online trajectory-generation method was implemented in C++/ROS on an 8-core Xeon workstation, replanning at $X_i(k)$9 Hz and sending commands at $U_i(k)$0 Hz, with qpOASES solve times from $U_i(k)$1 ms for 2 agents to $U_i(k)$2 ms for 20 agents. Experiments with 2–20 Crazyflie 2.0 quadrotors validated safe online transitions, and a “hula-hoop” scenario with 10 drones passing through a 30 cm aperture was completed in 28 s (Luis et al., 2019).

The 2022 event-triggered off-board framework was further tested in hardware-in-the-loop with six Crazyflie quadcopters tracked by a motion-capture system and controlled via a single on-ground computation unit using a linear triple-integrator model. The reported trajectories were collision-free, smooth, and easily executed by the on-board PD controllers (Gräfe et al., 2022).

DCAD reports mean per-agent compute time of approximately $U_i(k)$3 ms on a modern CPU core with $U_i(k)$4 and up to 10 neighbors, versus approximately $U_i(k)$5 ms in the compared nonlinear MPC implementation, while maintaining trajectory length and time-to-goal within $U_i(k)$6 of the obstacle-free optimal (Arul et al., 2019). Cooperative DMPC via decentralized real-time optimization gives median solve times of 6.6 ms per MPC step for a convex chain-formation QP and 33.8 ms for a non-convex minimum-distance problem, with communication accounting for $U_i(k)$7–$U_i(k)$8 of ADMM or dSQP execution time (Stomberg et al., 2023).

The largest simulated scale appears in distributed learning-based predictive control, where online learning time per step grows approximately $U_i(k)$9 from 0.02 s for $x_i(k+H\mid k)\in\mathcal X_{f,i}$0 to 14.6 s for $x_i(k+H\mid k)\in\mathcal X_{f,i}$1 on a laptop, while direct policy deployment ranges from $x_i(k+H\mid k)\in\mathcal X_{f,i}$2 s to 0.28 s. The same work reports deployment to robot populations up to $x_i(k+H\mid k)\in\mathcal X_{f,i}$3 units, Gazebo multirotor experiments with $x_i(k+H\mid k)\in\mathcal X_{f,i}$4, and $x_i(k+H\mid k)\in\mathcal X_{f,i}$5–$x_i(k+H\mid k)\in\mathcal X_{f,i}$6 speed-up over classical DMPC implementations using IPOPT or fmincon (Zhang et al., 2024).

6. Variants, limitations, and current directions

DMPC-SWARM now encompasses several distinct research directions. One direction seeks lower communication and computation through event-triggering, off-board replanning, and stateless many-to-all wireless flooding (Gräfe et al., 2022). A second direction reduces conservatism through on-demand collision constraints and sparse neighbor interactions rather than full buffered partitions (Luis et al., 2019). A third direction incorporates richer dynamics and uncertainty models, as in flatness-based quadrotor MPC with downwash-aware ORCA constraints and Kalman-filter-based covariance inflation (Arul et al., 2019). More recent directions couple DMPC with learned trajectory prediction under limited communication (Yan et al., 2024) or replace online numerical optimization by distributed actor-critic policy learning with barrier-augmented safety shaping (Zhang et al., 2024).

The literature also identifies several limitations. The online trajectory-generation study notes that, as agent density exceeds approximately 30 in $x_i(k+H\mid k)\in\mathcal X_{f,i}$7 m$x_i(k+H\mid k)\in\mathcal X_{f,i}$8, collisions become more frequent and relaxations larger, motivating hierarchical or waypoint planners or stronger constraint tightening; it also explicitly assumes perfect, delay-free neighbor broadcasts (Luis et al., 2019). The nano-UAV implementation states that safety cannot be guaranteed if the tracking error bound is violated by extreme gusts, because the analysis assumes $x_i(k+H\mid k)\in\mathcal X_{f,i}$9 (Gräfe et al., 28 Aug 2025). The decentralized formation-control implementation emphasizes that communication latency becomes critical for larger swarms and denser graphs, and observes experimentally that communication may dominate runtime (Stomberg et al., 2023).

A further point of variation concerns where computation resides. Some formulations run one local QP per agent in parallel on-board or on workstation-class processors (Luis et al., 2019), whereas others deliberately move heavy computation off the UAV to reduce on-board weight and power consumption and to introduce active redundancy against computation-unit failures (Gräfe et al., 2022). By contrast, distributed learning-based predictive control argues that scalability for nonlinear multirobot systems may require explicit policies rather than periodic numerical optimization at all (Zhang et al., 2024). This suggests that the main contemporary debate is no longer whether DMPC can coordinate swarms, but which combination of optimization, communication, prediction, and learning yields the best trade-off between safety guarantees, scalability, and deployability.

The most recent extensions push DMPC-SWARM toward broader optimal-control formulations. Distributed spatial-temporal trajectory optimization introduces free final time, safe-copy variables, ADMM-based consensus, and Parameterized Differential Dynamic Programming as a local solver, together with adaptive spectral-gradient tuning of the ADMM penalty parameter (Zheng et al., 20 Oct 2025). Taken together with prediction-assisted and policy-learning variants, these developments indicate that DMPC-SWARM is evolving from a narrowly defined local-QP coordination method into a broader framework for safety-critical, communication-aware, and increasingly heterogeneous swarm control.