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Finite-Time Trajectory Tracking of a Four wheeled Mecanum Mobile Robot

Anil B, Mayank Pandey, Sneha Gajbhiye

Abstract

Four Wheeled Mecanum Robot (FWMR) possess the capability to move in any direction on a plane making it a cornerstone system in modern industrial operations. Despite the extreme maneuverability offered by FWMR, the practical implementation or real-time simulation of Mecanum wheel robots encounters substantial challenges in trajectory tracking control. In this research work, we present a finite-time control law using backstepping technique to perform stabilization and trajectory tracking objectives for a FWMR system. A rigorous stability proof is presented and explicit computation of the finite-time is provided. For tracking objective, we demonstrate the results taking an S-shaped trajectory inclined towards collision avoidance applications. Simulation validation in real time using Gazebo-ROS on a Mecanum robot model is carried out which complies with the theoretical results.

Finite-Time Trajectory Tracking of a Four wheeled Mecanum Mobile Robot

Abstract

Four Wheeled Mecanum Robot (FWMR) possess the capability to move in any direction on a plane making it a cornerstone system in modern industrial operations. Despite the extreme maneuverability offered by FWMR, the practical implementation or real-time simulation of Mecanum wheel robots encounters substantial challenges in trajectory tracking control. In this research work, we present a finite-time control law using backstepping technique to perform stabilization and trajectory tracking objectives for a FWMR system. A rigorous stability proof is presented and explicit computation of the finite-time is provided. For tracking objective, we demonstrate the results taking an S-shaped trajectory inclined towards collision avoidance applications. Simulation validation in real time using Gazebo-ROS on a Mecanum robot model is carried out which complies with the theoretical results.

Paper Structure

This paper contains 13 sections, 8 theorems, 47 equations, 31 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Mathematical preliminaries
  3. Mathematical model of FWMR
  4. Theoretical developments
  5. Stability Analysis
  6. Robustness Analysis
  7. Simulation, Case studies and Discussions
  8. Case 1: Point stabilization
  9. Guidelines for tuning the controller weights $K_\eta$ and $K_{z}$
  10. Factors governing the choice of finite-time parameter $\alpha$
  11. Case 2: S-shaped trajectory tracking
  12. Case 3: Robustness to external perturbations
  13. Conclusions

Key Result

Proposition 1

ref23 Let $\mathcal{O}\subseteq\mathcal{D}$ be an open neighbourhood of origin and let $\mathcal{T}(x):\mathcal{O}\backslash\{0\} \rightarrow \mathbb{R}^+$ be the finite time. Suppose the following statements hold. Then, the origin is said to be a finite-time stable equilibrium of eqn1. It will be globally finite-time stable if $\mathcal{D}=\mathcal{O}=\mathbb{R}^n$.

Figures (31)

  • Figure 1: Schematic representation of a Four Wheeled Mecanum Robot.
  • Figure 2: Schematic representation of the proposed control architecture.
  • Figure 3: Gazebo-ROS architecture
  • Figure 4: ROS computation graph
  • Figure 5: Closed loop control architecture of the system
  • ...and 26 more figures

Theorems & Definitions (15)

  • Proposition 1
  • Lemma 1: ref23
  • Lemma 2: khalil2002nonlinear Rayleigh-Ritz inequality
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • proof
  • Corollary 1
  • ...and 5 more