FF-MPCC: High-speed Agile Formation Flight with Model Predictive Contouring Control

Aditya Dandwate; Vit Kratky; Parakh M. Gupta; Martin Saska; Robert Penicka

cs.ROAug 21, 2026

FF-MPCC: High-speed Agile Formation Flight with Model Predictive Contouring Control

Authors: Aditya Dandwate, Vit Kratky, Parakh M. Gupta, Martin Saska, Robert Penicka

Organizations: Multi-robot Systems Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic

Abstract

Flying in a prescribed formation in an agile manner remains a challenging problem in the field of UAVs, particularly when following highly-demanding trajectories that require flight at platform limits. We address this problem by proposing a novel decentralized approach to formation flight along a given path that integrates formation maintenance into the MPCC framework, allowing UAVs to adapt their progression along complex paths while respecting individual dynamic constraints and maintaining the desired formation. To this end, we introduce a novel reparametrization and synchronization method for dynamic formation geometries together with a decentralized approach to determine the desired positions for the individual UAVs. The proposed approach allows the formation to coordinate high-speed path following without compromising formation integrity. The proposed approach is validated through extensive simulation and real-world experiments involving scenarios with varying complexity of paths and changes of required formation shape on the fly. In comparison to time-parameterized trajectory tracking, we demonstrate improved formation maintenance by 65% in high-speed flight with velocities up to 21 m/s, while achieving comparable times required to reach the goal.

Figures & tables

Panel of Figure 1 — Fig. 1 : Deployment of the proposed approach in a real-world scenario with three UAV navigating along a straight line with transition from triangular to straight line formation with speeds up to $21\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ .

Panel of Figure 2 — Fig. 2 : Geometric error formulation for a three-UAV formation at time-step $k$ . The current position of UAV $D_{i}$ is denoted by $\bm{p}_{k}^{i}$ , with $\bm{p}_{k}^{c}$ representing the formation center. The target geometry positions are defined by $\bm{\lambda}^{i}$ , from which the formation errors $\bm{e}_{f}^{i}$ are calculated. The total tracking error $\bm{e}^{1}$ is the vector sum of the contour error $\bm{e}_{c}^{1}$ and lag error $\bm{e}_{l}^{1}$ , which are defined relative to the reference position $\bm{p}_{r}^{1}(\theta_{k})$ on the arc-length parametrized reference path.

Panel of Figure 3 — Fig. 3 : Visualization of the formation geometry generation over the normalized path parameter $\tau_{\text{norm}}=\tau/\tau_{\max}$ . The example illustrates the smooth interpolation between defined static key-frames through dynamic transition intervals.

Panel of Figure 4 — Fig. 4 : Distributed rigid-body fitting. The green and red dashed triangles denote the desired fitted and the current formation, respectively. The target position $\bm{\lambda}_{\mathrm{ego}}$ is computed from the estimated positions of $D_{0}$ and $D_{1}$ . Each UAV performs the procedure independently using local information.

Panel of Figure 5 — Fig. 5 : Ablation study of the influence of configuration parameter $q_{f}$ on formation completion time and formation accuracy metrics evaluated using 3 agents scenarios. Performance profiles are color-coded by parameter value.

Path type	Formation	Alignment	Path length [m]	PMM+NMPC			FF-MPCC
Path type	Formation	Alignment	Path length [m]	SFTE [m]	MAPDE [m]	Time [s]	SFTE [m]	MAPDE [m]	Time [s]
Straight Line	Triangle	Yes	60	0.095	0.056	4.406	0.093	0.049	5.341
Straight Line	Triangle-Line	Yes	60	0.935	0.532	4.443	0.250	0.176	5.084
Straight Line	Triangle-Line-Triangle	Yes	60	1.764	1.051	4.927	1.195	0.397	6.361
Spiral	Triangle	Yes	62.93	2.643	0.116	6.139	0.262	0.081	5.963
Spiral	Triangle-Line	Yes	62.93	3.371	0.305	5.910	0.223	0.107	6.285

TABLE I : Comparison of the baseline PMM+NMPC and the proposed FF-MPCC in formation flight scenarios. All simualtions are conducted with identical constant gains, and the reported results are averaged over 20 trials per scenario.

Panel of Figure 7 — Fig. 6 : Trajectory comparison between the baseline PMM+NMPC and FF-MPCC for a sine-wave path with a triangle-line-triangle formation geometry. Dashed lines denote the reference trajectories generated by each method, solid lines the trajectories flown by the individual UAVs.

Fig. 7 : Scatter of actual UAV positions around the reference shape after transformation to the reference frame for the Sine Wave with static Triangle formation listed in Table I . The dashed triangle denotes the desired formation. The formation is centered at its centroid, with UAV 1 defining the orientation of the reference frame.

Panel of Figure 9 — Fig. 8 : Real-world validation experiments. The top image in each column shows the reconstructed trajectories, while the bottom image shows the corresponding captured experimental scene. The global formation path for both scenarios is a straight line, where a) depicts a transitional geometry from triangle to straight line while b) shows a static triangular geometry.

Multi-Robot Formation Control

Multi-robot formation control coordinates robots to maintain, change, or navigate in groups while meeting task and safety constraints.

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Laboratory of Intelligent Systems, Ecole Polytechnique Federale de Lausanne (EPFL), CH1015 Lausanne, Switzerland

Robot Trajectory Tracking Aerial Robotics Nonlinear MPC Model Predictive Control

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Flapping-wing micro aerial vehicles offer quieter and safer operation than rotary-wing drones, yet achieving precise autonomous control of bird-scale ornithopters remains challenging: lift, airspeed, and turning authority are tightly coupled and governed by only a few control inputs. Conventional cascaded controllers treat altitude, speed, and heading independently, producing persistent tracking errors during complex maneuvers, while time-parameterized trajectory tracking requires predefined speed profiles that existing methods cannot robustly produce for these coupled dynamics. We address both limitations simultaneously with a Model Predictive Contouring Control (MPCC) approach that tracks arc-length-parameterized trajectories while optimizing progress online, eliminating the need for predefined timing. However, MPCC requires a dynamical model that captures the coupled aerodynamics without exceeding the computational budget of real-time nonlinear optimization. Here, we propose a compact, continuously differentiable model that captures the dominant couplings of bird-scale ornithopters, enabling real-time predictive control. We validated the method with the XFly ornithopter flying along circular and three-dimensional racing trajectories and achieved a mean deviation from the reference trajectory between 6.5 and 9 cm at speeds up to 3 m/s, which represents an almost 10-fold improvement over prior ornithopter control methods.

Abstract

Multi-Robot Formation Control

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