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Compact Force Sensor for Dual-UAV Cable-Suspended Payload Transport with Tension-Aware Outer-Loop Control

Andrea Delbene, Giorgio Cannata, Giorgio Carlini, Filippo Sante, Marco Baglietto

arXiv:2609.31035v1cs.RO

TL;DR

Reliable cooperative transport is difficult when cable tensions must be handled under position uncertainty. This work combines direct force sensing with decentralized tension-aware cascade control; simulations and indoor tests report improved stability, coordination, and disturbance rejection.

  • Problem

    Reliable dual-UAV payload transport must address cable-tension measurement and control when position information is uncertain.

    Source: §I · pp. 1–2

  • Method

    The framework combines a compact three-axis force sensor with decentralized cascade control that accounts for cable tension and requires limited inter-UAV information sharing.

    Source: §I · p. 2

  • Results

    The proposed sensor and controller showed improved stability, coordination, and disturbance rejection in simulations and indoor payload-drop and narrow-passage tests.

    Source: §VII · pp. 7–8

  • Takeaways & Limitations

    Measured tensions provide cleaner feedback than the estimator and improve UAV-payload stability, especially in x-motion after the payload drop.

    Source: 2) Experiment · p. 7

    The sensor response becomes slightly nonlinear around its x- and y-axis mechanical singularities, where higher-order regression is needed.

    Source: C. Calibration · p. 4

Abstract

from arXiv · show

Cooperative payload transportation using multiple \textit{Unmanned Aerial Vehicles} (UAVs) poses challenges in stability, coordination, and robustness, especially under external disturbances and unmodeled dynamics. This work proposes a dual-UAV payload transportation framework supported by a compact, custom-designed force sensor measuring the interaction force at the UAV cable anchor point. The sensor design and mathematical model are presented, and its performance is characterized through static and dynamic tests evaluating linearity, hysteresis, repeatability, and crossload. The control architecture follows a cascade structure: fast inner loops handle vehicle stabilization, while outer loops are designed to compensate for the measured forces. The approach is validated through simulations and indoor experiments under position uncertainty. Payload-drop and constrained-space tests assess the proposed sensing and control architecture against literature-based distributed references, showing improved stabilization, coordination, and disturbance rejection. A video of the experiments is available at: https://youtu.be/rIw9-fvV8Qw.

I. INTRODUCTION

Cable-suspended payload transport supports pose control and formation changes, but decentralized control and reliable tension measurement remain challenges. This work introduces a compact force sensor and a tension-aware cascade controller for dual-UAV transport.

I. INTRODUCTION

  • Flexible cables support full payload pose control and formation changes for collision avoidance, unlike more rigid connection approaches.The cited alternatives include robotic arms, grippers or magnets, and rigid bars.Source: §I · p. 1
  • State-based tension estimates depend on state estimation and model fidelity, and can respond with delays to abrupt force changes.Such approaches may also require informative measurements and communication to reconstruct the full system state.Source: §I · p. 1
  • Commercial force sensors provide direct, high-rate, model-independent measurements, but can add weight and integration complexity.Three-axis force reconstruction from a uniaxial sensor can require extra hardware, while the cited optical sensor is more delicate and typically less accurate than strain-gauge or capacitive sensors.Source: §I · p. 2
  • The paper develops a compact three-axis sensor and decentralized cascade control that accounts for cable tension, with limited information sharing between UAVs.Each UAV uses its own state and exchanges minimal data for state transitions.Source: §I · p. 2

II. SYSTEM MODELING

The system model describes two quadrotors carrying a payload on equal-length flexible cables. It defines inertial and body-fixed frames, states, and the forces and torques used in the translational and rotational dynamics.

II. SYSTEM MODELING

  • The modeled system has two quadrotors transporting a payload through equal-length flexible cables.The UAV and payload attachment points are offset from their centers of mass.Source: §II · p. 2
  • The model uses an inertial North-East-Down frame and local body-fixed frames for each UAV and the payload, with the z-axis pointing downwards.Each UAV state includes position, linear velocity, orientation, and angular velocity; the payload state is defined analogously.Source: §II · p. 2
  • Newton–Euler dynamics use thrust and control torque for the UAVs, gravity, mass and inertia, and cable-tension vectors acting on the vehicles and payload.Rotation matrices map body-fixed frames to the inertial frame.Source: §II · p. 2

A. Sensor Description

The sensor combines four load cells, supporting electronics, and a cross-shaped anchor structure. The paper reconstructs the three-axis cable tension from cell measurements using force and moment equilibrium, assuming negligible cell displacement.

A. Sensor Description

  • Four strain-gauge load cells in a Wheatstone bridge are integrated into a compact structure, with a cross-shaped support linking the UAV to the payload.Each cell supports up to 5 kg, has 0.05% Full Scale precision, and 120% Full Scale overload capacity.Source: A. Sensor Description · p. 2
  • A centrally housed PCB digitizes and conditions the load-cell signals using four parallel converters, selected to maximize sampling frequency despite greater power use and footprint.Each converter operates at 240 samples per second with 12-bit resolution; differential amplifiers provide gain and act as anti-aliasing filters.Source: A. Sensor Description · p. 2
  • The sensor’s base supports the cells and board, while a cross structure links the cells to the cable anchor point.The figure also shows top and bottom views of the load cells and electronic board.Source: Figure 2 · p. 3

B. Measures to Force

  • Static force and moment equilibrium reconstruct the anchor-point tension from the four cell readings; direct force balance recovers only the vertical component, so lateral components require moment balance.The reconstruction assumes negligible load-cell displacement and that each reading represents the true force applied to its cell.Source: B. Measures to Force · p. 3

C. Calibration

Calibration shows improved z-axis non-linearity and crossload after correction, while x/y tests reveal weaker performance near mechanical singularities. The section also describes static and dynamic characterization and reports the sensor’s practical tradeoffs against commercial alternatives.

C. Calibration

  • Static calibration averages the first 3,000 raw force outputs from each cell under a reference load, and a four-sample moving average adds about 6 ms of delay.The delay is described as acceptable for the 100 Hz outer control loop.Source: C. Calibration · p. 3
  • Around x/y mechanical singularities, performance indexes were approximately twice those on the z-axis; this application stays far from those conditions, with operating thresholds or regression switching left for future work.The x/y tests showed slight nonlinearity requiring higher-order regression.Source: C. Calibration · p. 4
  • The sensor is a cost-valid alternative to commercial solutions, though its dimensions and mass are higher and its acquisition rate is lower than most alternatives but remains suitable for the target application.It uses I²C and a custom Python/ROS2 script rather than the USB, CAN, or Ethernet hardware/drivers required by other sensors.Source: C. Calibration · p. 4, Table I · p. 4
  • In the dynamic test, manual roll and pitch tilts up to approximately ±70° produced a linear relation between expected force and sensor output, aside from small scaling factors.The test used applied weights and fused MoCap/onboard IMU orientation; controlled step-force instrumentation remains preferable for precise dynamic characterization.Source: C. Calibration · p. 4
  • 1% FS non-linearity fell to 0.5% FS after linear-regression correction, while crossload fell from 3.8% FS to 0.6% FS after matrix compensation.The z-axis characterization used incremental weights up to 5.5 kg over 10 loading/unloading cycles.Source: C. Calibration · pp. 3–4, Figure 4 · p. 4

IV. CONTROL ARCHITECTURE

The control strategy uses a decentralized cascade in which each UAV computes references from onboard estimates without payload or other-UAV data. The outer loop runs at 100 Hz, and the method is intended to demonstrate sensor-based in-flight tension compensation with a simple controller.

IV. CONTROL ARCHITECTURE

  • Each UAV computes its own references from onboard estimates in a decentralized cascade, without payload or other-UAV data; the outer loop runs at 100 Hz.The approach demonstrates in-flight tension compensation with the custom force sensor, while more advanced schemes are left for future work.Source: §IV · p. 4

A. Position Control

The position loop adjusts its position target using tension feedback, while the velocity loop converts commanded velocity into desired acceleration. The section also describes how sensor-characterization metrics are plotted across applied weights.

A. Position Control

  • The position target is adjusted using tension feedback, and a proportional position controller provides velocity setpoints.The tension error is defined relative to nominal static tension, using a lightly low-pass-filtered tension measurement.Source: A. Position Control · p. 4
  • Fig. 5 plots hysteresis, non-linearity, repeatability, and crossload (% FS) by applied weight relative to z-axis measurements.Boxes span Q1–Q3, horizontal lines mark medians, and wicks show observed minima and maxima.Source: Figure 5 · p. 5

B. Velocity Control

  • The velocity block computes desired accelerations from the commanded velocity vector with a PID controller.Its velocity state is low-pass filtered.Source: B. Velocity Control · p. 5

C. Thrust and Attitude Mapping

The mapping converts acceleration commands and desired yaw into thrust and attitude references for the low-level loops. It constructs desired axes from the desired force direction and yaw heading, then extracts a quaternion from the resulting rotation matrix.

C. Thrust and Attitude Mapping

  • Acceleration commands and desired yaw are mapped into thrust and attitude references for the low-level loops.The thrust command uses the force vector’s z-component, corrected for vehicle tilt.Source: C. Thrust and Attitude Mapping · p. 5
  • The desired z-axis is aligned opposite the normalized desired force, while the yaw heading vector determines the other desired axes through orthogonalization.The desired y-axis is formed from the cross product of the z-axis and heading vector; the x-axis follows from the y- and z-axes.Source: C. Thrust and Attitude Mapping · p. 5
  • The desired rotation matrix is formed from the three desired axes, and the attitude quaternion is extracted from that matrix.The trigonometric shorthand defines cosine and sine for any angle.Source: C. Thrust and Attitude Mapping · p. 5

V. EXPERIMENTAL SETUP

The software architecture uses ROS2 for high-level control and planning and PX4 for low-level control, with the same software structure in simulation and experiments. The hardware comprises two modified quadrotors, motion-capture feedback, and a marked payload suspended on nylon cables.

A. Software Architecture

  • ROS2 runs high-level control and planning while PX4 handles low-level loops and actuator commands, with uXRCE-DDS linking them in simulation and experiments.Gazebo is used only in simulation, and QGroundControl supports telemetry, mission planning, and pre-flight tuning.Source: A. Software Architecture · p. 5
  • A decentralized state machine runs on both UAVs and synchronizes transitions through ready signals published over ROS2 topics on the shared Wi-Fi network.Source: A. Software Architecture · p. 5

B. Hardware Architecture

  • The experimental platform consists of two modified Holybro x500 v2 quadrotors, each equipped with a Pixhawk 6C running PX4 and a Raspberry Pi 4 running Ubuntu with ROS2 and executing high-level nodes.Source: B. Hardware Architecture · p. 5
  • Fig. 7 shows the payload-drop and constrained-space motion composites, with successive instants marked A0–A3 and B0–B4.The constrained-space test’s desired top-view trajectories are shown separately, and return paths are mirrored.Source: Figure 7 · p. 6

C. System Evaluation

The evaluation combines payload-drop tests and narrow-passage maneuvers with simulation and indoor comparisons against distributed references. Position-feedback robustness is tested by adding independent random noise and slowly varying bias to the two UAVs’ positions.

VI. RESULTS

  • Trials use two UAVs carrying a 1 kg payload on approximately 1.5 m cables, with takeoff and move transitions triggered after both vehicles remain within 0.3 m of their setpoints for 1 s.The reported graphs show UAV and payload states detected by the motion-capture system.Source: C. System Evaluation · p. 6, §VI · p. 6

C. System Evaluation

  • The evaluation compares the proposed sensor with tensions estimated from in indoor experiments and uses the distributed geometric controller in as a simulation reference.The methods use limited inter-UAV communication, no payload-state knowledge, and onboard-measured or locally estimated cable tensions.Source: C. System Evaluation · p. 6
  • Position uncertainty is modeled with white Gaussian noise and a slowly varying first-order Gauss–Markov bias, using independent noise sequences for the two UAVs.Source: C. System Evaluation · p. 6

Test A - Payload Drop

  • In Test A, the UAVs take off with slack cables, translate 2 m to drop the payload from a box, then stabilize the resulting cable forces and payload oscillations.The test proceeds through the depicted A0–A3 stages.Source: Test A - Payload Drop · p. 6

1) Simulation:

The simulations exposed oscillations under position uncertainty, while indoor tests compared force-sensor measurements with estimated tensions. In the narrow-passage maneuver, the response remained smooth overall, though x-y tracking degraded during obstacle crossings.

1) Simulation:

  • With exact Gazebo tensions, the controller handled Takeoff and initially reduced post-drop y deviation, but later missed the z setpoint and oscillated during stabilization.The oscillations persisted at steady state and were attributed as likely arising from direct compensation under position uncertainty.Source: Figure 8 · p. 6, 1) Simulation · p. 6

2) Experiment:

  • During Takeoff, estimated tensions deviated from sensor measurements, with near-constant component biases and chattering likely amplified by position uncertainty.After the drop, estimates agreed more closely in some components, but biases and outliers reappeared, particularly for UAV2.Source: Figure 9 · p. 7, 2) Experiment · p. 7
  • Measured tensions provided cleaner feedback than the estimator and improved UAV-payload stability, especially in x-motion after the payload drop.The sensor also captured a small tension increase from a tightening UAV2 cable that the estimator did not show.Source: Figure 10 · p. 7, 2) Experiment · p. 7

Test B - Narrow Passage Maneuvers

  • During the 11-second narrow-passage round trip, the response stayed smooth and z tensions tracked targets, while x-y tracking degraded during obstacle crossings.Tracking deviations were largest for UAV1 along y during the crossings; desired tensions were robustly tracked in the remaining intervals.Source: Test B - Narrow Passage Maneuvers · p. 7

VII. CONCLUSIONS

The conclusion presents a dual-UAV transport framework combining direct cable-tension sensing with decentralized cascade control. Simulations and indoor tests showed improved stability, coordination, and disturbance rejection; future work targets hardware and controller improvements.

VII. CONCLUSIONS

  • The framework combines a custom force sensor for direct cable-tension measurement with decentralized cascade control, validated in simulation and indoor payload-drop and narrow-passage tests.The reported results showed improved stability, coordination, and disturbance rejection.Source: §VII · pp. 7–8
  • Future sensor improvements include reducing support weight, compensating temperature drift, increasing data rate, defining operating limits, and improving dust and splash resistance.The conclusion also identifies more advanced decentralized control strategies as future work.Source: §VII · p. 8
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