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Kinematic control design for wheeled mobile robots with longitudinal and lateral slip

Thiago B. Burghi, Juliano G. Iossaqui, Juan F. Camino

TL;DR

Addresses robust trajectory tracking for a nonholonomic wheeled robot under wheel slip using only pose measurements. The authors develop an adaptive kinematic control law that absorbs slip into an effective input via $\eta=\Phi(t)\xi(t)$ and updates slip estimates $\hat a_l,\hat a_r$ to handle both constant and slowly time-varying longitudinal and lateral slip. They prove exponential stability of the slip-free nominal system and uniform ultimate boundedness of the augmented error under slow slip variation and small lateral slip, supported by Lyapunov analysis and slow-time-varying system theory. Numerical simulations with realistic parameters show that the adaptive controller (AKC) tracks the reference trajectory closely under challenging slip profiles and outperforms a nonadaptive baseline (NKC). The results demonstrate practical viability for reliable high-speed trajectory tracking on slippery terrains with pose-only sensing.

Abstract

The motion control of wheeled mobile robots at high speeds under adverse ground conditions is a difficult task, since the robots' wheels may be subject to different kinds of slip. This work introduces an adaptive kinematic controller that is capable of solving the trajectory tracking problem of a nonholonomic mobile robot under longitudinal and lateral slip. While the controller can effectively compensate for the longitudinal slip, the lateral slip is a more involved problem to deal with, since nonholonomic robots cannot directly produce movement in the lateral direction. To show that the proposed controller is still able to make the mobile robot follow a reference trajectory under lateral and longitudinal time-varying slip, the solutions of the robot's position and orientation error dynamics are shown to be uniformly ultimately bounded. Numerical simulations are presented to illustrate the robot's performance using the proposed adaptive control law.

Kinematic control design for wheeled mobile robots with longitudinal and lateral slip

TL;DR

Addresses robust trajectory tracking for a nonholonomic wheeled robot under wheel slip using only pose measurements. The authors develop an adaptive kinematic control law that absorbs slip into an effective input via and updates slip estimates to handle both constant and slowly time-varying longitudinal and lateral slip. They prove exponential stability of the slip-free nominal system and uniform ultimate boundedness of the augmented error under slow slip variation and small lateral slip, supported by Lyapunov analysis and slow-time-varying system theory. Numerical simulations with realistic parameters show that the adaptive controller (AKC) tracks the reference trajectory closely under challenging slip profiles and outperforms a nonadaptive baseline (NKC). The results demonstrate practical viability for reliable high-speed trajectory tracking on slippery terrains with pose-only sensing.

Abstract

The motion control of wheeled mobile robots at high speeds under adverse ground conditions is a difficult task, since the robots' wheels may be subject to different kinds of slip. This work introduces an adaptive kinematic controller that is capable of solving the trajectory tracking problem of a nonholonomic mobile robot under longitudinal and lateral slip. While the controller can effectively compensate for the longitudinal slip, the lateral slip is a more involved problem to deal with, since nonholonomic robots cannot directly produce movement in the lateral direction. To show that the proposed controller is still able to make the mobile robot follow a reference trajectory under lateral and longitudinal time-varying slip, the solutions of the robot's position and orientation error dynamics are shown to be uniformly ultimately bounded. Numerical simulations are presented to illustrate the robot's performance using the proposed adaptive control law.

Paper Structure

This paper contains 16 sections, 7 theorems, 70 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Kinematic model of a wheeled mobile robot
  3. Adaptive kinematic control law
  4. Preliminaries
  5. Constant longitudinal slip without lateral slip
  6. Time-varying longitudinal and lateral slip
  7. Exponential stability of the nominal system
  8. Ultimate boundedness of solutions of the perturbed system
  9. Numerical results
  10. Conclusions
  11. Supporting results
  12. Ultimate boundedness
  13. Linearization
  14. Stability criterion of Liénard and Chipart
  15. Characteristic polynomial
  16. ...and 1 more sections

Key Result

Theorem 3.1

Under Assumption ass:01, the solution $e_a(t)$ of eq:nonautonomous_perturbed_system is uniformly ultimately bounded, for sufficiently small positive scalars $\gamma_1$ and $\gamma_2$. Thus, there exist positive constants $\alpha$, $u_b$, $T$ such that and

Figures (8)

  • Figure 1: Schematic model of a wheeled mobile robot.
  • Figure 2: Adaptive kinematic control strategy.
  • Figure 3: Reference trajectory $(x_{\rm{ref}}(t),y_{\rm{ref}}(t))$ generated by the reference input $\eta_{\rm{ref}}(t)={(v_{\rm{ref}}(t),\omega_{\rm{ref}}(t))}^T$.
  • Figure 4: Value of $\mathcal{F}$ for $k_1$ and $k_3$ for the fixed value $k_2=10$.
  • Figure 5: Longitudinal slip parameters $a_l(t)$ and $a_r(t)$ and lateral slip parameter $\sigma(t)$.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Remark 1
  • Theorem 3.1
  • Remark 2
  • Proposition 3.2
  • Lemma A.1: Lemma 9.1 from Khalil:2002:NS
  • Lemma A.2: Lemma 9.2 from Khalil:2002:NS
  • Theorem A.3: Theorem 4.15 from Khalil:2002:NS
  • Theorem A.4: Theorem 1 of Rosenbrock:1963:SLT
  • Theorem B.1: Theorem 11 from Gantmacher:1959:TM
  • Remark 3