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Impedance and Stability Targeted Adaptation for Aerial Manipulator with Unknown Coupling Dynamics

Amitabh Sharma, Saksham Gupta, Shivansh Pratap Singh, Rishabh Dev Yadav, Hongyu Song, Wei Pan, Spandan Roy, Simone Baldi

TL;DR

The paper tackles the challenge of compliant execution for aerial manipulators under unknown coupling dynamics by introducing an adaptive impedance controller that does not require prior system dynamics or coupling-force models. It defines an auxiliary error and adaptive laws to bound system uncertainties, and proves closed-loop uniform ultimate boundedness via Lyapunov analysis. Experimental payload-catching tests on a quadrotor-based AAM show significant improvements in stability and tracking compared with CSC and PSC baselines, including avoidance of crashes at higher payloads. The approach enables robust, fully integrated impedance behavior during dynamic interactions, with potential extensions to real-time impedance tuning for more complex manipulation tasks.

Abstract

Stable aerial manipulation during dynamic tasks such as object catching, perching, or contact with rigid surfaces necessarily requires compliant behavior, which is often achieved via impedance control. Successful manipulation depends on how effectively the impedance control can tackle the unavoidable coupling forces between the aerial vehicle and the manipulator. However, the existing impedance controllers for aerial manipulator either ignore these coupling forces (in partitioned system compliance methods) or require their precise knowledge (in complete system compliance methods). Unfortunately, such forces are very difficult to model, if at all possible. To solve this long-standing control challenge, we introduce an impedance controller for aerial manipulator which does not rely on a priori knowledge of the system dynamics and of the coupling forces. The impedance control design can address unknown coupling forces, along with system parametric uncertainties, via suitably designed adaptive laws. The closed-loop system stability is proved analytically and experimental results with a payload-catching scenario demonstrate significant improvements in overall stability and tracking over the state-of-the-art impedance controllers using either partitioned or complete system compliance.

Impedance and Stability Targeted Adaptation for Aerial Manipulator with Unknown Coupling Dynamics

TL;DR

The paper tackles the challenge of compliant execution for aerial manipulators under unknown coupling dynamics by introducing an adaptive impedance controller that does not require prior system dynamics or coupling-force models. It defines an auxiliary error and adaptive laws to bound system uncertainties, and proves closed-loop uniform ultimate boundedness via Lyapunov analysis. Experimental payload-catching tests on a quadrotor-based AAM show significant improvements in stability and tracking compared with CSC and PSC baselines, including avoidance of crashes at higher payloads. The approach enables robust, fully integrated impedance behavior during dynamic interactions, with potential extensions to real-time impedance tuning for more complex manipulation tasks.

Abstract

Stable aerial manipulation during dynamic tasks such as object catching, perching, or contact with rigid surfaces necessarily requires compliant behavior, which is often achieved via impedance control. Successful manipulation depends on how effectively the impedance control can tackle the unavoidable coupling forces between the aerial vehicle and the manipulator. However, the existing impedance controllers for aerial manipulator either ignore these coupling forces (in partitioned system compliance methods) or require their precise knowledge (in complete system compliance methods). Unfortunately, such forces are very difficult to model, if at all possible. To solve this long-standing control challenge, we introduce an impedance controller for aerial manipulator which does not rely on a priori knowledge of the system dynamics and of the coupling forces. The impedance control design can address unknown coupling forces, along with system parametric uncertainties, via suitably designed adaptive laws. The closed-loop system stability is proved analytically and experimental results with a payload-catching scenario demonstrate significant improvements in overall stability and tracking over the state-of-the-art impedance controllers using either partitioned or complete system compliance.

Paper Structure

This paper contains 12 sections, 1 theorem, 31 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Dynamics and Control Problem Formulation
  3. Control Objective and Challenge
  4. Proposed Adaptive Impedance Control and Analysis
  5. Impedance Dynamics
  6. Overall Control Law
  7. Experimental Results and Analysis
  8. Experimental Setup
  9. Experimental Scenarios, Results, and Analysis
  10. Scenario
  11. Results and Analysis
  12. Conclusion

Key Result

Theorem 1

Under Assumption assum_1 and Properties prop_1--prop_2, the closed-loop trajectories of step4 with control law control_law with adaptive law adaptive_1 and adaptive_law_full remains uniformly ultimately bounded (UUB), implying boundedness of $\mathbf{e}, \dot{\mathbf{e}}, \Delta \mathcal{I}$.

Figures (9)

  • Figure 1: A quadrotor-based AAM with an $n$-link manipulator catching an object (with relevant coordinate frames).
  • Figure 2: Hardware setup for the AAM.
  • Figure 3: Sequence of operations with the proposed controller: (a) Takeoff, (b) Follows trajectory while arm expands to pick payload, (c) Payload catching during flight and stabilization, (d) Transporting the payload, (e)-(g) Return to original position. The quadrotor is tethered for safety.
  • Figure 4: Tracking error comparison for $0.1$ kg payload (the vertical black like denotes the time the payload is caught).
  • Figure 5: Arm angles for $0.1$ kg payload (the vertical black like denotes the time the payload is caught).
  • ...and 4 more figures

Theorems & Definitions (3)

  • Remark 1: Selection of $\boldsymbol{\mathbf{M}}_d$, $\boldsymbol{\mathbf{K}}_d$ and $\boldsymbol{\mathbf{K}}_p$
  • Theorem 1
  • Remark 2: Role of $\zeta$