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Learning-Based Geometric Leader-Follower Control for Cooperative Rigid-Payload Transport with Aerial Manipulators

Omayra Yago Nieto, Leonardo Colombo

Abstract

This paper presents a learning-based tracking control framework for cooperative transport of a rigid payload by multiple aerial manipulators under rigid grasp constraints. A unified geometric model is developed, yielding a coupled agent--payload differential--algebraic system that explicitly captures contact wrenches, payload dynamics, and internal force redundancy. A leader--follower architecture is adopted in which a designated leader generates a desired payload wrench based on geometric tracking errors, while the remaining agents realize this wrench through constraint-consistent force allocation. Unknown disturbances and modeling uncertainties are compensated using Gaussian Process (GP) regression. High-probability bounds on the learning error are explicitly incorporated into the control design, combining GP feedforward compensation with geometric feedback. Lyapunov analysis establishes uniform ultimate boundedness of the payload tracking errors with high probability, with an ultimate bound that scales with the GP predictive uncertainty.

Learning-Based Geometric Leader-Follower Control for Cooperative Rigid-Payload Transport with Aerial Manipulators

Abstract

This paper presents a learning-based tracking control framework for cooperative transport of a rigid payload by multiple aerial manipulators under rigid grasp constraints. A unified geometric model is developed, yielding a coupled agent--payload differential--algebraic system that explicitly captures contact wrenches, payload dynamics, and internal force redundancy. A leader--follower architecture is adopted in which a designated leader generates a desired payload wrench based on geometric tracking errors, while the remaining agents realize this wrench through constraint-consistent force allocation. Unknown disturbances and modeling uncertainties are compensated using Gaussian Process (GP) regression. High-probability bounds on the learning error are explicitly incorporated into the control design, combining GP feedforward compensation with geometric feedback. Lyapunov analysis establishes uniform ultimate boundedness of the payload tracking errors with high probability, with an ultimate bound that scales with the GP predictive uncertainty.
Paper Structure (11 sections, 5 theorems, 46 equations, 4 figures)

This paper contains 11 sections, 5 theorems, 46 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Modeling: Single and Cooperative Aerial Manipulators
  3. Aerial manipulator as a multibody system.
  4. Cooperative aerial manipulation system
  5. Learning with Gaussian Processes
  6. Learning-based Tracking Control
  7. Control objective and leader--follower architecture
  8. Nominal payload wrench tracking
  9. Nominal tracking control under rigid grasp constraints
  10. Learning-based tracking control
  11. Simulation Results

Key Result

Lemma 1

Suppose Assumptions 1 and 3 hold, and that the GP models for the agents and the payload are trained on the (frozen) data sets $\mathcal{D}^{\mathrm{end}}_j$ and $\mathcal{D}^{\mathrm{end}}_L$, respectively. Let $\mu_j(\cdot),\Sigma_j(\cdot)$ and $\mu_L(\cdot),\Sigma_L(\cdot)$ denote the correspondin Here $\beta_j(\delta_j)\in\mathbb{R}^{9}$ and $\beta_L(\delta_L)\in\mathbb{R}^{6}$ are vectors with

Figures (4)

  • Figure 1: Payload tracking on $SE(3)$ for (C1)--(C3). Top: position error norm $\|e_p(t)\|$. Bottom: attitude error measure $\Psi(t)$. Ultimate bounds decrease from (C1) to (C2) to (C3), consistent with Theorem \ref{['thm:learning_tracking']}.
  • Figure 2: Payload wrench mismatch $\|\Delta W(t)\|$ for (C1)--(C3). Agent learning reduces the interface disturbance entering the payload error dynamics.
  • Figure 3: Uncertainty measures along the closed-loop trajectory for (C1)--(C3). Top: payload-level uncertainty $\sigma_L(t)$ decreases when payload learning is enabled (C2--C3). Bottom: agent-level uncertainty $\sigma_A(t)$ decreases only when agent learning is enabled (C3); thus $\sigma_A(t)$ remains essentially unchanged from (C1) to (C2).
  • Figure 4: Norms of the estimated applied contact forces for each agent. The forces remain bounded throughout the maneuver and show no high-frequency chattering. The bottom panel shows the internal-force input magnitude $\|\eta(t)\|$; when activated, $\eta$ redistributes contact forces along internal directions without affecting the net payload wrench (Lemma 2).

Theorems & Definitions (16)

  • Remark 1
  • Remark 2
  • Lemma 1: Adapted from Srinivas2012
  • proof
  • Remark 3
  • Lemma 2
  • proof
  • Proposition 1
  • proof
  • Remark 4
  • ...and 6 more