Multi-quadrotor systems interconnected via structurally unknown forces and moments

Kaiyue Xing; Shivansh Pratap Singh; Sarthak Mishra; Di Liu; Spandan Roy; Simone Baldi; Leonid Fridman

cs.ROOct 31, 2026

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

Abstract

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 ( $\approx$ 200% of hover)
Roll/pitch command saturation	$\pm 25^{\circ}$

TABLE I: Implementation and communication parameters

Metric	Controller	RMSE	Common-window	Total	Peak	Recovery
		before D	RMSE	RMSE	@ D	time (s)
$\\|e_{p}\\|$ (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
$\\|e_{q}\\|$ (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	$e_{\tau,1}^{\%}$	$e_{\tau,2}^{\%}$	$e_{\tau,3}^{\%}$
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 $\Omega_{i}=[\Omega_{i,1},\Omega_{i,2},\Omega_{i,3},\Omega_{i,4}]^{\top}$ , 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 $\Omega_{i}=[\Omega_{i,1},\Omega_{i,2},\Omega_{i,3},\Omega_{i,4}]^{\top}$ 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.

Robotic Control

Robotic control studies how machines use sensing and computation to produce reliable movement and interaction in changing environments.

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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.

Abstract

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