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Dedicated Nonlinear Control of Robot Manipulators in the Presence of External Vibration and Uncertain Payload

Mustafa M. Mustafa, Carl D. Crane, Ibrahim Hamarash

TL;DR

This work tackles joint-space tracking for robot manipulators operating in environments with external vibration and uncertain payloads. It presents two Lyapunov-based control designs: a bounded-disturbance approach that guarantees uniform ultimate boundedness of the tracking error, and a bounded-differentiable-disturbance approach that achieves asymptotic convergence under semi-global conditions. Both controllers are validated via two-link manipulator simulations, demonstrating substantial improvements in tracking accuracy over a standard PD controller, albeit with higher computation times for the nonlinear schemes. The methods require no prior knowledge of vibration or payload frequencies and offer practically meaningful guarantees for robust manipulation in uncertain, vibratory environments.

Abstract

Robot manipulators are often tasked with working in environments with vibrations and are subject to load uncertainty. Providing an accurate tracking control design with implementable torque input for these robots is a complex topic. This paper presents two approaches to solve this problem. The approaches consider joint space tracking control design in the presence of nonlinear uncertain torques caused by external vibration and payload variation. The properties of the uncertain torques are used in both approaches. The first approach is based on the boundedness property, while the second approach considers the differentiability and boundedness together. The controllers derived from each approach differ from the perspectives of accuracy, control effort, and disturbance properties. A Lyapunov-based analysis is utilized to guarantee the stability of the control design in each case. Simulation results validate the approaches and demonstrate the performance of the controllers. The derived controllers show stable results at the cost of the mentioned properties.

Dedicated Nonlinear Control of Robot Manipulators in the Presence of External Vibration and Uncertain Payload

TL;DR

This work tackles joint-space tracking for robot manipulators operating in environments with external vibration and uncertain payloads. It presents two Lyapunov-based control designs: a bounded-disturbance approach that guarantees uniform ultimate boundedness of the tracking error, and a bounded-differentiable-disturbance approach that achieves asymptotic convergence under semi-global conditions. Both controllers are validated via two-link manipulator simulations, demonstrating substantial improvements in tracking accuracy over a standard PD controller, albeit with higher computation times for the nonlinear schemes. The methods require no prior knowledge of vibration or payload frequencies and offer practically meaningful guarantees for robust manipulation in uncertain, vibratory environments.

Abstract

Robot manipulators are often tasked with working in environments with vibrations and are subject to load uncertainty. Providing an accurate tracking control design with implementable torque input for these robots is a complex topic. This paper presents two approaches to solve this problem. The approaches consider joint space tracking control design in the presence of nonlinear uncertain torques caused by external vibration and payload variation. The properties of the uncertain torques are used in both approaches. The first approach is based on the boundedness property, while the second approach considers the differentiability and boundedness together. The controllers derived from each approach differ from the perspectives of accuracy, control effort, and disturbance properties. A Lyapunov-based analysis is utilized to guarantee the stability of the control design in each case. Simulation results validate the approaches and demonstrate the performance of the controllers. The derived controllers show stable results at the cost of the mentioned properties.
Paper Structure (11 sections, 52 equations, 6 figures, 5 tables)

This paper contains 11 sections, 52 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Specified Dynamic Model and Preliminaries
  3. Problem Formulation and Control Approaches
  4. Problem Formulation
  5. Control Approach Based on the Bounded-Disturbance: First Control Approach
  6. Control Approach Based on the Bounded-Differentiable-Disturbance: Second Control Approach
  7. Simulation Results
  8. Simulation Results for the Control Approach Based on the Bounded Disturbance
  9. Simulation Results for the Second Control Approach Based on the Bounded-Differentiable-Disturbance
  10. Quantitative Analysis
  11. Conclusion

Figures (6)

  • Figure S1: Scheme of the simulated robot and the first controller.
  • Figure S2: Disturbance torques due to vibration and payload variation for the first approach: (a,b) vibration effect; (c,d) payload variation effect; and (e,f) effect of combination on joint 1 and joint 2, respectively.
  • Figure S3: Tracking errors and control inputs for the first proposed approach compared with the proportional derivative (PD) approach: (a,b) angular displacement errors of joint 1 and joint 2, respectively; (c,d) input torques of joint 1 and joint 2, respectively.
  • Figure S4: Performance in terms of drifts and systematic errors for the first proposed approach compared with the PD approach: (a,b) desired and actual displacements of joint 1 and joint 2, respectively; (c,d) angular displacement errors of joint 1 and joint 2, respectively.
  • Figure S5: Tracking errors and control inputs for the second proposed approach compared with the PD approach: (a,b) angular displacement errors of joint 1 and joint 2, respectively; (c,d) input torques of joint 1 and joint 2, respectively.
  • ...and 1 more figures