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Cooperative Aerial Transportation of a Payload with a Sliding Cable Attachment

Sebastian Tilaguy Lezama, Diego S D'Antonio

arXiv:2610.13665v1cs.ROcs.MA

TL;DR

Cooperative transport methods generally assume fixed cable attachments, leaving sliding cable redistribution through a payload-mounted hook unaddressed. This paper introduces a dual-quadrotor system and geometrically generated references for indirect payload positioning; experiments show accurate indirect tracking, with performance sensitive to configuration.

  • Problem

    Prior cooperative cable-transport approaches generally assume fixed attachment points and do not address cable-length redistribution through a sliding payload-mounted hook.

    Source: §I · p. 1

  • Method

    The DQ-HSTS uses two quadrotors on a cable sliding through a payload-mounted hook, with references parameterized by payload pose, cable distribution, and system shape for indirect tracking.

    Source: §I · p. 1, C. Onboard Quadrotor Trajectory… · p. 4

  • Results

    Experiments showed accurate indirect payload-position tracking, although performance was sensitive to λ and γ and deteriorated as γ increased.

    Source: §V · p. 6

  • Takeaways & Limitations

    The DQ-HSTS achieved effective transportation through geometric reconstruction and indirect position control using quadrotor references.

    Source: §V · p. 6

    Direct closed-loop payload control was beyond the study’s scope; future work will incorporate payload-state feedback to improve robustness against cable dynamics, payload swing, tracking errors, and modeling uncertainties.

    Source: §V · p. 6

Abstract

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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.

I. INTRODUCTION

Cooperative cable-suspended transport distributes payload weight across multiple UAVs, but prior methods generally assume fixed cable attachments and omit redistribution through a payload-mounted sliding hook. The DQ-HSTS addresses this gap with parameterized trajectory generation and coordinated tracking under constraints.

I. INTRODUCTION

  • Cable-suspended transport can separate payloads from aerial platforms, reduce direct disturbance transmission, and support attachment or release in flight.Cooperative systems distribute payload weight and coordinate cable forces, addressing limitations of single-UAV lifting.Source: §I · p. 1
  • Prior work spans trajectory generation, cooperative transport, hook-based grasping, and constrained full-pose manipulation.The cited methods include differential flatness, coordinated rotorcraft motion, inertial sensing, and nonlinear model predictive control.Source: §I · p. 1
  • Prior cooperative cable-transport methods generally assume fixed attachment points and omit cable-length redistribution through a sliding payload-mounted hook.This leaves the hook-induced coupling among UAV motion, cable geometry, payload dynamics, and cable distribution unaddressed.Source: §I · p. 1

II. SLIDING HOOK-PAYLOAD

  • The DQ-HSTS connects two quadrotors with one cable that slides through a frictionless hook rigidly attached to the payload.Sliding redistributes total cable length between the two segments.Source: §I · p. 1, §II · p. 2

I. INTRODUCTION

  • The work formulates trajectory generation using payload pose, cable distribution λ, and system shape γ, then coordinates trajectory tracking under tension, geometric, and actuator constraints.The approach is validated experimentally.Source: §I · p. 1

A. System Description and Kinematics

The DQ-HSTS models two quadrotors connected by a taut, inextensible cable that slides through a frictionless payload-mounted hook. Cable geometry and segment forces couple the vehicle and payload dynamics.

A. System Description and Kinematics

  • The cable is massless, inextensible, perfectly flexible, and taut, and slides through a frictionless hook fixed to the payload at a constant distance.Under this assumption, both cable segments have equal tension.Source: A. System Description and Kinematics · p. 2, B. System Dynamics · p. 2
  • The analysis restricts the system to the vertical Π_y,z plane and quadrotor and payload rotation to pitch about the out-of-plane x-axis.The underlying dynamics are governed by three-dimensional Newton–Euler equations.Source: A. System Description and Kinematics · p. 2
  • The hook divides the fixed total cable length L into segments ℓ_l = λL and ℓ_r = (1 − λ)L, with λ specifying the left-segment fraction.The segment lengths are not independently actuated; they change through passive cable sliding.Source: A. System Description and Kinematics · p. 2, B. System Dynamics · p. 2
  • For fixed quadrotor positions, the cable-length constraint confines the hook to an ellipse with the vehicles at its foci; admissible suspended configurations use its lower half.In three dimensions, the corresponding surface is a prolate spheroid.Source: A. System Description and Kinematics · p. 2

B. System Dynamics

  • Each quadrotor’s cable force is determined by the shared tension and the direction from the hook to that vehicle.The cable forces on the two quadrotors are −T e_l and −T e_r.Source: B. System Dynamics · p. 2
  • The payload is modeled as a rigid body, with the hook offset from its center of mass by r_h = d_h R_ϕp e_z.The hook is rigidly attached at a constant distance d_h above the payload center of mass.Source: B. System Dynamics · p. 2, A. System Description and Kinematics · p. 2

C. Problem Formulation

The control problem separates geometrically feasible reference generation from quadrotor trajectory tracking. Both stages must account for cable constraints and maintain a physically admissible, tensioned configuration.

C. Problem Formulation

  • The control objective is bifurcated because recovering the system state requires integrating geometric constraints with dynamics around the unactuated sliding variable λ.The two stages are reference generation and trajectory tracking.Source: C. Problem Formulation · p. 2
  • Reference generation determines feasible cable-distribution λ and system-shape γ trajectories from a desired payload-position trajectory and fixed cable length L.The resulting hook and quadrotor references must satisfy inextensible cable constraints and avoid known workspace obstacles.Source: C. Problem Formulation · p. 2
  • Quadrotor tracking must generate the cable tensions needed to manipulate the payload while keeping the cable taut and preserving the lower-half-ellipse hook configuration.The approach assumes positive tension and sufficient actuation capacity for reference tracking.Source: C. Problem Formulation · p. 3

III. TRAJECTORY GENERATION AND CONTROL

The control architecture uses two cascaded stages, beginning with payload reference generation. Desired waypoints encode payload position, cable distribution, and cable angle to define the reference trajectory.

III. TRAJECTORY GENERATION AND CONTROL

  • The architecture divides indirect payload-position control into two cascaded stages that address the formulated control problems.Source: §III · p. 3

A. Payload Reference Generation

B. Vehicles Trajectory Transformation from the Payload

The payload reference is transformed into desired hook and quadrotor states using the rigid hook attachment and the system’s cable geometry. Cable distribution and shape determine quadrotor placement under a balanced-motion assumption.

B. Vehicles Trajectory Transformation from the Payload

C. Onboard Quadrotor Trajectory Tracking and Indirect Payload Control

Quadrotors track geometrically reconstructed position, velocity, and acceleration references to control payload motion indirectly. The onboard controller uses vehicle state estimates, while cable tension and modeling effects remain disturbances.

C. Onboard Quadrotor Trajectory Tracking and Indirect Payload Control

  • Payload position is controlled indirectly by having both quadrotors track the geometrically reconstructed desired position, velocity, and acceleration, without payload-level feedback.Source: C. Onboard Quadrotor Trajectory… · p. 4
  • The Crazyflie Mellinger controller uses onboard estimates of position, velocity, attitude, and angular velocity to generate the desired force.Source: C. Onboard Quadrotor Trajectory… · p. 4
  • Cable tension, payload swing, and modeling errors act as unmodeled disturbances, so successful tracking requires smooth references, a taut cable, accurate geometry, and adequate quadrotor actuation.Source: C. Onboard Quadrotor Trajectory… · p. 4

IV. EXPERIMENTS

Experiments test fixed-position payload control under varying cable parameters, trajectory tracking, and transport beneath a ceiling obstacle. A third quadrotor’s payload measurements validate the trajectory but do not provide feedback.

IV. EXPERIMENTS

  • The three experiments vary λd or γd while holding payload position fixed, track a moving payload with both parameters oscillating, and transport beneath a ceiling obstacle.Source: §IV · p. 4
  • The platform uses two Crazyflie 2.1 Brushless nano-quadrotors connected by a 1 m cable, with references transmitted from a control computer.Source: §IV · p. 4
  • A third Crazyflie acts as the payload, and its measurements are used only for validation, not feedback.Source: §IV · p. 4

A. Experiment i: Constant Payload Position

The hover tests vary cable distribution and system shape to assess payload-position performance. Position-error changes differ by axis, with higher γ associated with greater lateral spread and asymmetric λ with increased disturbance sensitivity.

A. Experiment i: Constant Payload Position

  • RMSEλ was 0.061 and RMSEγ was 0.027rad in the varying-λ experiment.The experiment compared payload hover performance under different λ and γ references.Source: A. Experiment i: Constant Payload… · pp. 4–5
  • At γ=π/4, the reported mean zp error changed from 0.3cm to −5.7cm, which the authors relate to increased cable tension proportional to 1/cosγ.The passage repeats the γ=π/4 label for both values; the authors state the change is expected because increased tension overloads the quadrotors.Source: A. Experiment i: Constant Payload… · p. 5
  • σyp rose from 1.9cm at γ=π/12 to 5.6cm at γ=π/4, where residual hook friction was more pronounced.The model assumes a frictionless hook, but residual friction in the setup can drag the hook along the cable and contribute to lateral tracking error.Source: A. Experiment i: Constant Payload… · p. 5
  • Changing λ from 0.5 to 0.25 shifted mean yp error from −0.2cm to −7.0cm, while mean zp error stayed near −1cm.The reported mean zp errors were −0.8cm at λ=0.5 and −1.2cm at λ=0.25.Source: A. Experiment i: Constant Payload… · p. 5
  • The asymmetric λ=0.25 configuration can increase disturbance sensitivity and promote horizontal load oscillation, with lateral cable-force effects contributing more to yp error than xp error.The passage relates this pattern to the greater bias observed in yp.Source: A. Experiment i: Constant Payload… · p. 5

B. Experiment ii: Tracking a payload trajectory while λ and γ oscillate

The experiment tests circular payload path-following while λ and γ oscillate across three cases. Payload tracking errors were similar across cases despite larger parameter-estimation errors in some cases, and the authors report tracking under the Vmax constraint.

B. Experiment ii: Tracking a payload trajectory while λ and γ oscillate

  • Payload trajectory tracking errors were similar across the three cases, around RMSExp = 3cm, despite the experiment’s λ and γ oscillations.The largest mean Euclidean payload tracking error was in case 2, with xp = 3.2cm; the authors report the indirect strategy tracked under the Vmax constraint.Source: B. Experiment ii: Tracking a payload… · p. 5
  • The largest reported λ estimation error was RMSEλ = 0.05 in case 2, and the largest γ estimation error was RMSEγ = 0.11rad in case 3.The circular trajectory was evaluated in three cases with oscillating λ and γ references.Source: B. Experiment ii: Tracking a payload… · p. 5

C. Experiment iii: Transporting the payload beneath a ceiling obstacle

The obstacle mission transports the payload horizontally beneath a low ceiling by varying λ and γ. The maneuver had a mean payload tracking error of 3.19cm while limiting the tension increase associated with increasing γ alone.

C. Experiment iii: Transporting the payload beneath a ceiling obstacle

V. CONCLUSIONS

The DQ-HSTS uses a sliding cable through a payload-mounted hook, adding cable-length distribution as a configuration degree of freedom. Experiments demonstrate indirect payload-position tracking, while revealing sensitivity to system shape and the potential of cable distribution for obstacle avoidance.

V. CONCLUSIONS

  • The DQ-HSTS connects two quadrotors with one cable sliding through a frictionless payload-mounted hook, allowing segment lengths to vary while preserving the desired payload position.This makes cable-length distribution λ an additional configuration degree of freedom.Source: §V · p. 6
  • Experiments showed accurate indirect payload-position tracking, although performance deteriorated as γ increased.Under quasistatic equilibrium, required cable tension increases with γ, consistent with lower mean payload height at larger γ.Source: §V · p. 6
  • Pre-calculating λ and γ enabled obstacle avoidance while maintaining a constant payload trajectory and position error within the range demonstrated previously.The experiment illustrates λ's potential to avoid relying exclusively on γ, which is correlated with the load carried by the drones.Source: §V · p. 6
  • Overall, the system transported the payload through geometric reconstruction and indirect position control using quadrotor references.Source: §V · p. 6
  • Direct closed-loop payload control was outside this study's scope; future work will incorporate payload-state feedback to improve robustness to cable dynamics, swing, tracking errors, and modeling uncertainties.Source: §V · p. 6
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