Multi-quadrotor systems interconnected via structurally unknown forces and moments
Authors: Kaiyue Xing, Shivansh Pratap Singh, Sarthak Mishra, Di Liu, Spandan Roy, Simone Baldi, Leonid Fridman
Organizations: Self-Organizing Mobility Lab, School of Mathematics, Southeast University, Nanjing 210096, China · Robotics Research Center, International Institute of Information Technology Hyderabad, India · Department of Electrical and Electronic Engineering, Imperial College, London SW7 2BT, U.K. · Universidad Nacional Autónoma de México (UNAM), Facultad de Ingenieria, 04510, Mexico City, Mexico
This work addresses the challenge of controlling multi-quadrotor systems subject to tight uncertain couplings. We consider interconnection forces and moments among the quadrotors to be state-dependent functions of the coordination errors, without assuming knowledge of their functional/parametric structures, e.g., no linear-in-parameters assumptions are made. We only rely on general state-dependent quadratic bounds valid for several Euler-Lagrange mechanical systems. We propose a coordination strategy embedding adaptive laws dedicated to compensating for the lack of structural knowledge. Unlike conventional decoupled position-attitude designs, we present a coupled stability analysis accounting for the position-attitude couplings induced by the interconnection forces and moments. The analysis, along with real experiments involving cooperative aerial transportation of rope-interconnected payloads, demonstrates the effectiveness of the proposed solution in compensating for these complex interconnections. Comparative experiments show that, when a payload drop induces a disturbance propagating through the ropes across the whole formation, the proposed strategy reduces significantly post-disturbance transients.
Figures & tables
Fig. 1: Schematic of a cooperative aerial transportation scenario (left): it is not trivial to model the functional/parametric structure of the interconnection forces and moments generated through the rope-interconnected payloads. External disturbances like a payload drop (right) would generate even more complex and uncertain interconnection terms. This work considers interconnection forces and moments as state-dependent functions of the coordination errors among the quadrotors (coupled along position and attitude dynamics), with no knowledge of their functional/parametric structure.
Fig. 2: Experimental setup for cooperative aerial transportation (top left). Snapshots before (top right) and right after (bottom right) payload drop. Tracking performance with the proposed controller (bottom left).
Fig. 3: Comparison of position and attitude coordination errors among the controllers. The orange vertical line denotes the payload-drop instant.
Fig. 4: Comparison of position-rate and attitude-rate coordination errors among the controllers. The orange vertical line denotes the payload-drop instant.
Position loop rate
50 Hz
Attitude loop rate
100 Hz
Inner rate loop / mixer rate
400 Hz
State estimation
RTK-GNSS + IMU, PX4 EKF2
Estimator output rate
100 Hz
Thrust saturation
25 N ( ≈ 200% of hover)
Roll/pitch command saturation
±25∘
TABLE I: Implementation and communication parameters
Metric
Controller
RMSE
Common-window
Total
Peak
Recovery
before D
RMSE
RMSE
@ D
time (s)
∥ep∥ (m)
Controller 1
0.391
1.495
1.170
2.730
n/r
Controller 2
0.325
0.706
0.575
1.724
13.36
Proposed
0.200
0.242
0.223
0.595
2.36
∥eq∥ (rad)
Controller 1
0.113
0.436
0.337
1.007
n/r
Controller 2
0.092
0.212
0.169
0.609
10.58
TABLE II: Performance Comparison of Different Controllers under Three Repeated Payload-Drop Experiments
Controller
eτ,1%
eτ,2%
eτ,3%
Controller 1
0.37%
0.72%
0.68%
Controller 2
0.37%
0.72%
0.58%
Proposed
0.38%
0.68%
0.69%
TABLE III: Percentage error between computed and allocated control inputs
Fig. 5: Computed rotor speeds under the payload-drop disturbance. Rows: (a) Controller 1, (b) Controller 2 and (c) Proposed controller. Columns: quadrotors i=1,2,3 . Each panel shows the four entries of Ωi=[Ωi,1,Ωi,2,Ωi,3,Ωi,4]⊤ , as if they would be computed from ( 30 ) before control allocation. Front-right and rear-left rotors spin counter-clockwise (CCW), while front-left and rear-right rotors spin clockwise (CW). The dashed line marks the release at D=20 s: after it, quadrotors 1 and 2 settle at lower speeds because they no longer carry part of the released payload.
Fig. 6: Allocated rotor speeds for the same flights as Fig. 5 , with the same layout and axes: rows (a)–(c) are the controllers, and columns are drones i=1,2,3 . Each panel shows the four entries of Ωi=[Ωi,1,Ωi,2,Ωi,3,Ωi,4]⊤ obtained from ( 30 ) after control allocation. Front-right and rear-left rotors spin CCW, while front-left and rear-right rotors spin CW. The allocated speeds well align to the computed ones. The dashed line marks the payload release at D=20 s.
This paper presents a dual-quadrotor hook- suspended transport system for cooperative aerial manipulation of a payload that is not rigidly attached to a fixed point along the cable. Two quadrotors are connected by a single inextensible cable that passes through a frictionless hook mounted on the payload, allowing the cable to slide between its two segments. This introduces a cable-distribution variable that couples the quadrotor motion, cable geometry, and payload dynamics. A feasible reference-generation framework is formulated using the desired payload pose, cable distribution, and system shape while satisfying the cable-length constraint and elliptical workspace. The quadrotors track the geometrically generated trajectories while maintaining positive cable tension and respecting actuator limits. The payload pose is estimated from the system geometry, and its measured position is used only to validate the desired trajectory. The approach is evaluated through experimental demonstrations.
Sebastian Tilaguy Lezama, Diego S D'Antonio
Distributed Multi-Agent Robotic Systems (∆MARS Lab), Department of Electrical and Computer Engineering, Oakland University, Rochester, MI 48309, USA
Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.
Pei-An Hsieh, Fengjun Yang, Nikolai Matni +1
1GRASP Laboratory, University of Pennsylvania, PA, USA
Multi-quadrotor passage planning requires coordinated spatial routes and passage times under vehicle dynamics and actuation constraints. Optimizing these decisions jointly couples temporal allocation, nonlinear motion, and inter-vehicle interactions, creating a computational challenge for local trajectory generation. We propose a learning-optimization framework that predicts spatial waypoints and ordered passage events for independently solved quadrotor planners. A common physical time grid aligns the vehicles, with intermediate events fixed by the networks and terminal progress optimized locally to permit different completion metrics. Differentiable sequential convex programming incorporates rigid-body dynamics and rotor-thrust bounds, allowing collision and completion gradients to train both networks through the generated trajectories. In a two-quadrotor evaluation across 24 layouts, the adapted policy passes physical feasibility and sampled separation checks in all five held-out layouts. Their mean completion metric decreases by 1.52% relative to the inherited policy. The median forward time is 21.01 ms on the held-out exchange layout with matching numerical trajectory references. These results demonstrate that learned spatial and event parameters can coordinate independent rigid-body planners while preserving local vehicle constraints in the evaluated scenarios.
Yunhan Shi, Jia Deng, Zehao Jia +2
School of Astronautics, Beihang University, Beijing 100191, China · Astroup(Beijing) Technology Co., Ltd.