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Quaternion-based Unscented Kalman Filter for Robust Wrench Estimation of Human-UAV Physical Interaction

Hussein Naser, Hashim A. Hashim, Mojtaba Ahmadi

Abstract

This paper introduces an advanced Quaternion-based Unscented Kalman Filter (QUKF) for real-time, robust estimation of system states and external wrenches in assistive aerial payload transportation systems that engage in direct physical interaction. Unlike conventional filtering techniques, the proposed approach employs a unit-quaternion representation to inherently avoid singularities and ensure globally consistent, drift-free estimation of the platform's pose and interaction wrenches. A rigorous quaternion-based dynamic model is formulated to capture coupled translational and rotational dynamics under interaction forces. Building on this model, a comprehensive QUKF framework is established for state prediction, measurement updates, and external wrench estimation. The proposed formulation fully preserves the nonlinear characteristics of rotational motion, enabling more accurate and numerically stable estimation during physical interaction compared to linearized filtering schemes. Extensive simulations validate the effectiveness of the QUKF, showing significant improvements over the Extended Kalman Filter (EKF). Specifically, the QUKF achieved a 79.41\% reduction in Root Mean Squared Error (RMSE) for torque estimation, with average RMSE improvements of 79\% and 56\%, for position and angular rates, respectively. These findings demonstrate enhanced robustness to measurement noise and modeling uncertainties, providing a reliable foundation for safe, stable, and responsive human-UAV physical interaction in cooperative payload transportation tasks.

Quaternion-based Unscented Kalman Filter for Robust Wrench Estimation of Human-UAV Physical Interaction

Abstract

This paper introduces an advanced Quaternion-based Unscented Kalman Filter (QUKF) for real-time, robust estimation of system states and external wrenches in assistive aerial payload transportation systems that engage in direct physical interaction. Unlike conventional filtering techniques, the proposed approach employs a unit-quaternion representation to inherently avoid singularities and ensure globally consistent, drift-free estimation of the platform's pose and interaction wrenches. A rigorous quaternion-based dynamic model is formulated to capture coupled translational and rotational dynamics under interaction forces. Building on this model, a comprehensive QUKF framework is established for state prediction, measurement updates, and external wrench estimation. The proposed formulation fully preserves the nonlinear characteristics of rotational motion, enabling more accurate and numerically stable estimation during physical interaction compared to linearized filtering schemes. Extensive simulations validate the effectiveness of the QUKF, showing significant improvements over the Extended Kalman Filter (EKF). Specifically, the QUKF achieved a 79.41\% reduction in Root Mean Squared Error (RMSE) for torque estimation, with average RMSE improvements of 79\% and 56\%, for position and angular rates, respectively. These findings demonstrate enhanced robustness to measurement noise and modeling uncertainties, providing a reliable foundation for safe, stable, and responsive human-UAV physical interaction in cooperative payload transportation tasks.

Paper Structure

This paper contains 30 sections, 68 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. The Force Sensing Challenge in Aerial Systems
  4. Related Work in Sensorless Force Estimation
  5. Motivation and Contributions
  6. Preliminaries
  7. Notation
  8. Representation of a rigid-body attitude in 3D space
  9. Special Orthogonal Group $SO(3)$
  10. Euler angles
  11. Angle-axis
  12. Rodriguez vector
  13. Quaternion
  14. Summation, subtraction, and weighted average
  15. Problem formulation
  16. ...and 15 more sections

Figures (6)

  • Figure 1: Free body diagram of the system components.
  • Figure 2: Schematic block diagram of the control system.
  • Figure 3: Trajectory of the assistive system under human guidance in 3D space, with red arrows indicating applied forces.
  • Figure 4: Position and linear velocity estimation with normalized errors: A performance comparison between the proposed QUKF and baseline EKF.
  • Figure 5: Orientation and angular velocity estimation with normalized errors: A performance comparison between the proposed QUKF and baseline EKF.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Remark 1