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Safe and Stable Teleoperation of Quadrotor UAVs under Haptic Shared Autonomy

Dawei Zhang, Roberto Tron

TL;DR

A novel approach that aims to address both safety and stability of a haptic teleoperation system within a framework of Haptic Shared Autonomy (HSA), using Control Barrier Functions (CBFs) to generate the control input that follows the user’s input as closely as possible while guaranteeing safety.

Abstract

We present a novel approach that aims to address both safety and stability of a haptic teleoperation system within a framework of Haptic Shared Autonomy (HSA). We use Control Barrier Functions (CBFs) to generate the control input that follows the user's input as closely as possible while guaranteeing safety. In the context of stability of the human-in-the-loop system, we limit the force feedback perceived by the user via a small $L_2$-gain, which is achieved by limiting the control and the force feedback via a differential constraint. Specifically, with the property of HSA, we propose two pathways to design the control and the force feedback: Sequential Control Force (SCF) and Joint Control Force (JCF). Both designs can achieve safety and stability but with different responses to the user's commands. We conducted experimental simulations to evaluate and investigate the properties of the designed methods. We also tested the proposed method on a physical quadrotor UAV and a haptic interface.

Safe and Stable Teleoperation of Quadrotor UAVs under Haptic Shared Autonomy

TL;DR

A novel approach that aims to address both safety and stability of a haptic teleoperation system within a framework of Haptic Shared Autonomy (HSA), using Control Barrier Functions (CBFs) to generate the control input that follows the user’s input as closely as possible while guaranteeing safety.

Abstract

We present a novel approach that aims to address both safety and stability of a haptic teleoperation system within a framework of Haptic Shared Autonomy (HSA). We use Control Barrier Functions (CBFs) to generate the control input that follows the user's input as closely as possible while guaranteeing safety. In the context of stability of the human-in-the-loop system, we limit the force feedback perceived by the user via a small -gain, which is achieved by limiting the control and the force feedback via a differential constraint. Specifically, with the property of HSA, we propose two pathways to design the control and the force feedback: Sequential Control Force (SCF) and Joint Control Force (JCF). Both designs can achieve safety and stability but with different responses to the user's commands. We conducted experimental simulations to evaluate and investigate the properties of the designed methods. We also tested the proposed method on a physical quadrotor UAV and a haptic interface.
Paper Structure (40 sections, 2 theorems, 53 equations, 16 figures, 1 table)

This paper contains 40 sections, 2 theorems, 53 equations, 16 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. System modeling
  4. Contributions
  5. Preliminaries
  6. Control Barrier Functions
  7. State Space Model
  8. Lie derivatives
  9. Safety Set
  10. CBFs for Second Order Systems
  11. $\mathcal{L}_2$-gain
  12. Methods
  13. Limiting $F$ via Finite-$\mathcal{L}_2$-gain
  14. Energy design
  15. Energy tank
  16. ...and 25 more sections

Key Result

Theorem 1

Assume that both Human system and Robot system are finite-gain $\mathcal{L}_2$ stable with $\mathcal{L}_2$ gains of $\gamma_1$ and $\gamma_2$: $\lVert u_{\text{ref}}\rVert_2 \leq \gamma_1\lVert\tilde{F}\rVert_2 + \beta_1$ and $\lVert F\rVert_2 \leq \gamma_2\lVert\tilde{u}_{\textrm{ref}}\rVert_2 + \b

Figures (16)

  • Figure 1: An architecture of the proposed haptic teleoperation system.
  • Figure 2: Feedback connection of the haptic teleoperation architecture. Note that the Human system and the Robot system are the same with the two systems highlighted by the blue boxes in Fig. \ref{['fig:architecture']}.
  • Figure 3: Comparison of stability performance between the condition with small $\mathcal{L}_2$-gain method and the condition without small $\mathcal{L}_2$-gain method.
  • Figure 4: Trajectories of the quadrotor under the condition without $\mathcal{L}_2$-gain method (above) and the condition with $\mathcal{L}_2$-gain method (below). The blue dot represents the start position while the red dot the end position. Yellow circles denote the obstacles.
  • Figure 5: Results of the human's commanded velocity and the force feedback in a two-dimensional simulation.
  • ...and 11 more figures

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Theorem 1: Theorem 5.6, page 218, khalil2002nonlinear
  • Proposition 1
  • proof