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
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 21ms−1 .
Fig. 2 : Geometric error formulation for a three-UAV formation at time-step k . The current position of UAV Di is denoted by pki , with pkc representing the formation center. The target geometry positions are defined by λi , from which the formation errors efi are calculated. The total tracking error e1 is the vector sum of the contour error ec1 and lag error el1 , which are defined relative to the reference position pr1(θk) on the arc-length parametrized reference path.
Fig. 3 : Visualization of the formation geometry generation over the normalized path parameter τnorm=τ/τmax . The example illustrates the smooth interpolation between defined static key-frames through dynamic transition intervals.
Fig. 4 : Distributed rigid-body fitting. The green and red dashed triangles denote the desired fitted and the current formation, respectively. The target position λego is computed from the estimated positions of D0 and D1 . Each UAV performs the procedure independently using local information.
Fig. 5 : Ablation study of the influence of configuration parameter qf 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
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.
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.
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.
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.
Charbel Toumieh, Jack Zeng, Niel Mistry +1
Laboratory of Intelligent Systems, Ecole Polytechnique Federale de Lausanne (EPFL), CH1015 Lausanne, Switzerland
This work proposes the L1 Adaptive Model Predictive Path Integral (L1-MPPI). It cascades L1 adaptive control with the Model Predictive Path Integral (MPPI) to improve tracking of high-speed UAV trajectories. Thanks to the L1augmentation, the tracking remains accurate even under model uncertainties and external disturbances, such as an additional payload or a mismatch in the modeled aerodynamic drag. In contrast to existing MPPI approaches for UAV control that do not explicitly model aerodynamic effects, varying payloads, and typically neglect the dynamics of low-level motor controllers, our L1-MPPI approach enhances the dynamic model used in the MPPI by incorporating the low-level flight controller and motor dynamics, as well as an iterative mixing scheme that reflects the approach of the low-level controller. The proposed method demonstrates improved tracking performance in both simulation and the real world, even when the UAV is subjected to an unknown payload. In flight with 35% mass increase, our approach lowers the RMSE by 58.61% with respect to plain MPPI. Compared to the same MPPI using an online mass estimator in place of the L1 augmentation, the RMSE is lower by 38.59%. During the real-world experiments the UAV reaches speeds up to 13.50 m/s and accelerations up to 2.5 g.
Lukáš Kotek, Ondřej Procházka, Vojtěch Vonásek +2
Multi-robot Systems Group, Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
Aiming at the problem that obstacle avoidance flexibility and formation integrity are difficult to coexist in multi-UAV formation motion in complex obstacle environments , and that the traditional artificial potential field (APF) method easily falls into local optima, a cooperative obstacle avoidance algorithm for multi-UAV formations integrating BI-APF-RRT and affine transformation is proposed. First, abandoning the traditional APF centroid path planning method , a goal-biased Bidirectional Artificial Potential Field method RRT (BI-APF-RRT) algorithm is adopted to conduct global collision-free path planning for the centroid of the leader formation. By introducing an improved artificial potential field and cubic B-spline interpolation, the smoothness and rapid convergence of the global path are ensured. Secondly, using the generated global path as the guiding trajectory for the formation's centroid , combined with an affine transformation matrix (including non-uniform scaling and rotation) , the formation can adaptively deform based on the distance to obstacles while moving along the optimal path. Finally, the followers track the leaders through a distributed control law , enabling the entire formation to safely cross complex obstacle areas without disassembling.
Yiliang Wu, Weican Chen, Yendo Hu
College of Marine Information Engineering, Jimei University, Xiamen, China