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Observer-Based Estimation and Hydrostatic Inertia Modeling for Cooperative Transport of Variable-Inertia Loads with Quadrotors

Jacob Goodman, Leonardo Colombo, Juan Giribet

Abstract

We address load-parameter estimation in cooperative aerial transport with time-varying mass and inertia, as in fluid-carrying payloads. Using an intrinsic manifold model of the multi-quadrotor-load dynamics, we combine a geometric tracking controller with an observer for parameter identification. We estimate mass from measurable kinematics and commanded forces, and handle variable inertia via an inertia surrogate that reproduces the load's rotational dynamics for control and state propagation. Instead of real-time identification of the true inertia tensor, driven by high-dimensional internal fluid motion, we leverage known tank geometry and fluid-mechanical structure to pre-compute inertia tensors and update them through a lookup table indexed by fill level and attitude. The surrogate is justified via the incompressible Navier-Stokes equations in the translating/rotating load frame: when effective forcing is gravity-dominated (i.e., translational/rotational accelerations and especially jerk are limited), the fluid approaches hydrostatic equilibrium and the free surface is well approximated by a plane orthogonal to the body-frame gravity direction.

Observer-Based Estimation and Hydrostatic Inertia Modeling for Cooperative Transport of Variable-Inertia Loads with Quadrotors

Abstract

We address load-parameter estimation in cooperative aerial transport with time-varying mass and inertia, as in fluid-carrying payloads. Using an intrinsic manifold model of the multi-quadrotor-load dynamics, we combine a geometric tracking controller with an observer for parameter identification. We estimate mass from measurable kinematics and commanded forces, and handle variable inertia via an inertia surrogate that reproduces the load's rotational dynamics for control and state propagation. Instead of real-time identification of the true inertia tensor, driven by high-dimensional internal fluid motion, we leverage known tank geometry and fluid-mechanical structure to pre-compute inertia tensors and update them through a lookup table indexed by fill level and attitude. The surrogate is justified via the incompressible Navier-Stokes equations in the translating/rotating load frame: when effective forcing is gravity-dominated (i.e., translational/rotational accelerations and especially jerk are limited), the fluid approaches hydrostatic equilibrium and the free surface is well approximated by a plane orthogonal to the body-frame gravity direction.
Paper Structure (8 sections, 2 theorems, 51 equations, 3 figures)

This paper contains 8 sections, 2 theorems, 51 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Modelization and Control Design
  3. Estimation of Load Mass and Moment of Inertia
  4. Mass Estimation
  5. Constant Mass Model
  6. Inertia Estimation
  7. Simulation Results
  8. Appendix

Key Result

Lemma 1

Let $\xi(t) \in C^1(\mathbb{R}, \mathbb{R}^n)$ satisfy $\dot{\xi} = -A\xi + D$ for some $A \in C^0(\mathbb{R}, \text{Sym}(n))$ and $D \in C^0(\mathbb{R}, \mathbb{R}^{n})$. Suppose that $\exists \mu, T, M > 0$ such that for all $t \ge 0$, where $\lambda_{\min}(A(\tau))^+ = \max\{\lambda_{\min}(A(\tau)), 0\}$. Then, $\xi$ is exponentially input-to-state stable (eISS) with respect to the inputs $D$.

Figures (3)

  • Figure 1: Load position trajectory $x_L(t)$ under (top) constant mass and (bottom) exponentially decaying mass.
  • Figure 2: True and estimated load mass for the two simulation scenarios.
  • Figure 3: Diagonal elements of the inertia tensor $J_L(t)$ (true vs. estimated) for both mass models.

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Proposition III.1