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Adaptive Control of Euler-Lagrange Systems under Time-varying State Constraints without a Priori Bounded Uncertainty

Viswa Narayanan Sankaranarayanan, Sumeet Gajanan Satpute, Spandan Roy, George Nikolakopoulos

Abstract

In this article, a novel adaptive controller is designed for Euler-Lagrangian systems under predefined time-varying state constraints. The proposed controller could achieve this objective without a priori knowledge of system parameters and, crucially, of state-dependent uncertainties. The closed-loop stability is verified using the Lyapunov method, while the overall efficacy of the proposed scheme is verified using a simulated robotic arm compared to the state of the art.

Adaptive Control of Euler-Lagrange Systems under Time-varying State Constraints without a Priori Bounded Uncertainty

Abstract

In this article, a novel adaptive controller is designed for Euler-Lagrangian systems under predefined time-varying state constraints. The proposed controller could achieve this objective without a priori knowledge of system parameters and, crucially, of state-dependent uncertainties. The closed-loop stability is verified using the Lyapunov method, while the overall efficacy of the proposed scheme is verified using a simulated robotic arm compared to the state of the art.
Paper Structure (8 sections, 1 theorem, 22 equations, 6 figures, 1 table)

This paper contains 8 sections, 1 theorem, 22 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Dynamics and Problem Formulation
  3. Proposed Control Solution
  4. Closed-Loop Stability analysis
  5. Simulation Results and Analysis
  6. Simulation Scenario
  7. Results
  8. Conclusions

Key Result

Theorem 1

Under Properties pro:mass_inertia - pro:skew_sym, Assumptions 1-2, and using the control law (eq:control_law) and the adaptive law (eq:adap_law), the trajectory of the closed-loop system (eq:ms_dot_3)) remains Uniformly Ultimately Bounded (UUB), and the error trajectories $\mathbf{e}, \dot{\mathbf{e

Figures (6)

  • Figure 1: A schematic of the manipulator with its coordinate frame.
  • Figure 2: The sequence of operation of the manipulator. (1) From any initial point, the manipulator settles at the initial position. (2) From the initial position, the end-effector is moved to region A, where it picks the payloads from conveyor 1. (3) To avoid collision, the end-effector is moved to an intermediate location in region B. (4) The end-effector is moved to region C, where it can drop the payloads in converyor 2. (5) The manipulator returns after dropping the payload via region B. (6) The end-effector picks up a new payload.
  • Figure 3: Trajectory of the angles $\theta_{1},\theta_{2}$ obtained by different controllers along with the desired trajectory.
  • Figure 4: Errors in angles $\theta_{1},\theta_{2}$. The proposed controller ensures that the errors stay within bounds.
  • Figure 5: Errors in angular velocities $\dot{\theta}_{1},\dot{\theta}_{2}$. The proposed controller ensures that the errors stay within the bounds.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • Remark 4: Continuity in control law