Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Implementation of Time-Varying Controllers for a Nonholonomic Mobile Robot: Experimental Studies

Alexander Zuyev, Victoria Grushkovskaya, Sebastian Eisner

TL;DR

The presented experimental results demonstrate the possibility of stabilizing the reference position of the robot using feedback controls with practically acceptable parameters and the admissibility problem of a gradient flow is investigated.

Abstract

We consider a kinematic model of a wheeled mobile robot controlled by translational and angular velocities. For this class of nonholonomic systems, a family of time-varying feedback controllers was proposed in our previous works using gradient flow approximation techniques. In the present study, these controllers are implemented on a TurtleBot3 Burger (TB3) mobile robot to provide experimental validation of the stabilization problem with oscillating input signals. In addition, the admissibility problem of a gradient flow is investigated to justify the construction of a Lyapunov function candidate. The presented experimental results demonstrate the possibility of stabilizing the reference position of the robot using feedback controls with practically acceptable parameters.

Implementation of Time-Varying Controllers for a Nonholonomic Mobile Robot: Experimental Studies

TL;DR

The presented experimental results demonstrate the possibility of stabilizing the reference position of the robot using feedback controls with practically acceptable parameters and the admissibility problem of a gradient flow is investigated.

Abstract

We consider a kinematic model of a wheeled mobile robot controlled by translational and angular velocities. For this class of nonholonomic systems, a family of time-varying feedback controllers was proposed in our previous works using gradient flow approximation techniques. In the present study, these controllers are implemented on a TurtleBot3 Burger (TB3) mobile robot to provide experimental validation of the stabilization problem with oscillating input signals. In addition, the admissibility problem of a gradient flow is investigated to justify the construction of a Lyapunov function candidate. The presented experimental results demonstrate the possibility of stabilizing the reference position of the robot using feedback controls with practically acceptable parameters.
Paper Structure (7 sections, 1 theorem, 17 equations, 5 figures, 1 table)

This paper contains 7 sections, 1 theorem, 17 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Stabilizing Controls for the Unicycle Kinematics
  3. Justification for the Lyapunov Function Candidate
  4. Experimental Implementation
  5. Experimental Setup
  6. Experimental Results
  7. Conclusions and Future Work

Key Result

lemma thmcounterlemma

For $x,p\in {\mathbb R}^3$, define Then

Figures (5)

  • Figure 1: Left: TurtleBot3 Burger; Right: TB3 marker configuration
  • Figure 2: Experiment 1 -- Parameter set $(P1)$: continuous-time vs. sampling.
  • Figure 3: Experiment 2 -- Parameter set $(P2)$: continuous-time vs. sampling.
  • Figure 4: Experiment 3 -- Parameter set $(P3)$: continuous-time vs. sampling.
  • Figure 5: Experiment 4 -- Parameter set $(P4)$: continuous-time vs. sampling.

Theorems & Definitions (2)

  • lemma thmcounterlemma
  • proof