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Range-Only Dynamic Output Feedback Controller for Safe and Secure Target Circumnavigation

Anand Singh, Anoop Jain

TL;DR

This paper addresses the problem of circumnavigating an unknown target by a unicycle robot while ensuring it maintains a desired safe distance and remains within the sensing region around the target throughout its motion.

Abstract

The safety and security of robotic systems are paramount when navigating around a hostile target. This paper addresses the problem of circumnavigating an unknown target by a unicycle robot while ensuring it maintains a desired safe distance and remains within the sensing region around the target throughout its motion. The proposed control design methodology is based on the construction of a joint Lyapunov function that incorporates: (i) a quadratic potential function characterizing the desired target-circumnavigation objective, and (ii) a barrier Lyapunov function-based potential term to enforce safety and sensing constraints on the robot's motion. A notable feature of the proposed control design is its reliance exclusively on local range measurements between the robot and the target, realized using a dynamic output feedback controller that treats the range as the only observable output for feedback. Using the Lyapunov stability theory, we show that the desired equilibrium of the closed-loop system is asymptotically stable, and the prescribed safety and security constraints are met under the proposed controllers. We also obtain restrictive bounds on the post-design signals and provide both simulation and experimental results to validate the theoretical contributions.

Range-Only Dynamic Output Feedback Controller for Safe and Secure Target Circumnavigation

TL;DR

This paper addresses the problem of circumnavigating an unknown target by a unicycle robot while ensuring it maintains a desired safe distance and remains within the sensing region around the target throughout its motion.

Abstract

The safety and security of robotic systems are paramount when navigating around a hostile target. This paper addresses the problem of circumnavigating an unknown target by a unicycle robot while ensuring it maintains a desired safe distance and remains within the sensing region around the target throughout its motion. The proposed control design methodology is based on the construction of a joint Lyapunov function that incorporates: (i) a quadratic potential function characterizing the desired target-circumnavigation objective, and (ii) a barrier Lyapunov function-based potential term to enforce safety and sensing constraints on the robot's motion. A notable feature of the proposed control design is its reliance exclusively on local range measurements between the robot and the target, realized using a dynamic output feedback controller that treats the range as the only observable output for feedback. Using the Lyapunov stability theory, we show that the desired equilibrium of the closed-loop system is asymptotically stable, and the prescribed safety and security constraints are met under the proposed controllers. We also obtain restrictive bounds on the post-design signals and provide both simulation and experimental results to validate the theoretical contributions.
Paper Structure (14 sections, 5 theorems, 28 equations, 4 figures)

This paper contains 14 sections, 5 theorems, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model, Problem Description and Solution Methodology
  3. System Model and Problem Description
  4. Solution Methodology
  5. Lyapunov Functions and Control Design
  6. Constructions of Lyapunov Functions
  7. Control Design
  8. Availability of range and range-rate measurements
  9. Availability of range-only measurements
  10. Analysis of Post-Design Signals
  11. Simulation and Experimental Results
  12. Simulations
  13. Experiments
  14. Conclusion and Future Remarks

Key Result

Lemma 1

For any positive constants $k_a$ and $k_b$, let $\mathcal{Z} \triangleq \{\xi \in \mathbb{R}: -k_a < \xi < k_b\} \subset \mathbb{R}$ and $\mathcal{N} \triangleq \mathbb{R}^\ell \times \mathcal{Z} \subset \mathbb{R}^{\ell+1}$ be the open sets. Consider the system $\dot{\eta} = h(t, \eta)$, where $\et

Figures (4)

  • Figure 1: Safe and secure target circumnavigation by a unicycle robot: An illustration of the problem.
  • Figure 2: Robot's trajectory and time evolution of radial error \ref{['radial_error']}, range and control law \ref{['control_2a']} under range-only controller \ref{['control_2']}.
  • Figure 3: Khepera IV robot and MoCap validation setup.
  • Figure 4: Experimental results for Khepera IV robot using range only measurements.

Theorems & Definitions (12)

  • Definition 1: Barrier Lyapunov Function (BLF) tee2009barrier
  • Lemma 1: Convergence under BLF tee2009barrier
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 1
  • Theorem 3: Availability of range and range-rate measurements
  • proof
  • Theorem 4: Availability of range-only measurements
  • ...and 2 more