Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Adaptive Robust Controller for handling Unknown Uncertainty of Robotic Manipulators

Mohamed Abdelwahab, Giulio Giacomuzzo, Alberto Dalla Libera, Ruggero Carli

TL;DR

The paper tackles accurate trajectory tracking for robotic manipulators under unknown model uncertainties. It proposes Adaptive Robust Feedback Linearization (ARFBL), a Lyapunov-guided, unsupervised update mechanism that adapts a robust term to compensate for mismatches without prior bounds. Theoretical guarantees show convergence to a boundary region or steady-state error under mild assumptions, with an enhanced update rule to ensure convergence to the desired boundary. Empirical results on a 2-DOF RR planar arm—using both perturbed nominal dynamics and a Gaussian Process black-box model—demonstrate ARFBL achieves robust, smooth tracking comparable to uncertainty-aware methods and effective even when uncertainty bounds are unavailable.

Abstract

The ability to achieve precise and smooth trajectory tracking is crucial for ensuring the successful execution of various tasks involving robotic manipulators. State-of-the-art techniques require accurate mathematical models of the robot dynamics, and robustness to model uncertainties is achieved by relying on precise bounds on the model mismatch. In this paper, we propose a novel adaptive robust feedback linearization scheme able to compensate for model uncertainties without any a-priori knowledge on them, and we provide a theoretical proof of convergence under mild assumptions. We evaluate the method on a simulated RR robot. First, we consider a nominal model with known model mismatch, which allows us to compare our strategy with state-of-the-art uncertainty-aware methods. Second, we implement the proposed control law in combination with a learned model, for which uncertainty bounds are not available. Results show that our method leads to performance comparable to uncertainty-aware methods while requiring less prior knowledge.

Adaptive Robust Controller for handling Unknown Uncertainty of Robotic Manipulators

TL;DR

The paper tackles accurate trajectory tracking for robotic manipulators under unknown model uncertainties. It proposes Adaptive Robust Feedback Linearization (ARFBL), a Lyapunov-guided, unsupervised update mechanism that adapts a robust term to compensate for mismatches without prior bounds. Theoretical guarantees show convergence to a boundary region or steady-state error under mild assumptions, with an enhanced update rule to ensure convergence to the desired boundary. Empirical results on a 2-DOF RR planar arm—using both perturbed nominal dynamics and a Gaussian Process black-box model—demonstrate ARFBL achieves robust, smooth tracking comparable to uncertainty-aware methods and effective even when uncertainty bounds are unavailable.

Abstract

The ability to achieve precise and smooth trajectory tracking is crucial for ensuring the successful execution of various tasks involving robotic manipulators. State-of-the-art techniques require accurate mathematical models of the robot dynamics, and robustness to model uncertainties is achieved by relying on precise bounds on the model mismatch. In this paper, we propose a novel adaptive robust feedback linearization scheme able to compensate for model uncertainties without any a-priori knowledge on them, and we provide a theoretical proof of convergence under mild assumptions. We evaluate the method on a simulated RR robot. First, we consider a nominal model with known model mismatch, which allows us to compare our strategy with state-of-the-art uncertainty-aware methods. Second, we implement the proposed control law in combination with a learned model, for which uncertainty bounds are not available. Results show that our method leads to performance comparable to uncertainty-aware methods while requiring less prior knowledge.
Paper Structure (8 sections, 3 theorems, 31 equations, 5 figures, 1 table)

This paper contains 8 sections, 3 theorems, 31 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Adaptive robust feedback linearization control
  4. Black-Box Dynamics Identification
  5. Numerical results
  6. First Experiment: Perturbed dynamics
  7. Second Experiment: black-box dynamics
  8. Conclusions

Key Result

Lemma 4

Assume Assumptions ass:Int-law1, ass:Int-law2 and ass:Int-law3 hold true. Then, there exists $\bar{\rho}>0$ such that if we implement eq:Fed_Lin_Scheme_robust with $w=\rho \,z/\|z\|$ where $\rho \geq \bar{\rho}$ then $\dot{V}(\xi)<0$ for all $\xi \neq 0$.

Figures (5)

  • Figure 1: Controller scheme of the proposed Adaptive Robust Feedback Linearization (ARFBL)
  • Figure 2: Implementation results of ARFBL compared to RFBL
  • Figure 3: $\rho$ evolution of the proposed update method Vs True $\rho$ from RFBL
  • Figure 4: Feedback linearization Vs. Adaptive robust feedback linearization using GP estimated dynamics
  • Figure 5: $\rho$ evolution using ARFBL when modeling dynamics using GPR

Theorems & Definitions (5)

  • Lemma 4
  • proof
  • Proposition 5
  • proof
  • Corollary 6