Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation
TL;DR: In this paper, a robust task-space control of electrically driven robot manipulators using voltage control strategy is proposed. But, the complexity of the robust control law is high, and it requires some feedbacks of the system states which providing them may be expensive.
Abstract: This paper deals with the robust task-space control of electrically driven robot manipulators using voltage control strategy. In conventional robust control approaches, the uncertainty bound is needed to design the control law. Usually, this bound is proposed conservatively which may increase the amplitude of the control signal and damage the system. Moreover, calculation of this bound requires some feedbacks of the system states which providing them may be expensive. The novelty of this paper is proposing a robust control law in which the uncertainty bound is calculated by Legendre polynomials. Compared to conventional robust controllers, the proposed controller is simpler, less computational and requires less feedbacks. Simulation results and comparisons verify the effectiveness of the proposed control approach applied on a SCARA robot manipulator driven by permanent magnet DC motors.
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TL;DR: In this article, a robust adaptive controller for electrically driven robots, without any need for velocity measurements, has been presented, which is based on universal approximation theory and using Stone-Weierstrass theorem.
Abstract: Recently, regressor-free control approach has been presented in which uncertainties are estimated using function approximation techniques (FAT) such as the Fourier series expansion or Legendre polynomials. However, FAT-based observer design remains as an open problem. With this in mind, this paper presents a robust adaptive controller for electrically driven robots, without any need for velocity measurements. The mixed observer/control design procedure is based on universal approximation theory and using Stone–Weierstrass theorem. To highlight the contribution of the paper, it should be emphasized that in comparison with previous related FAT-based controllers, the proposed controller is simpler and less computational. In addition, the number of required Fourier series expansions, control laws, and also adaptation rules has been reduced. Moreover, the observer design is free of model. Simulation results of the controller on a 6-DOF industrial robot manipulator have been presented which proves robustness of the proposed controller against various uncertainties. The results are also compared to those obtained from Chebyshev neural network.
59 citations
TL;DR: This paper intuitively shows that in order to perform repetitive tasks; the least common multiple (LCM) of fundamental period durations of the desired trajectories of the joints is a proper value for the fundamental period duration of the Fourier series expansion.
Abstract: This paper presents a novel control algorithm for electrically driven robot manipulators. The proposed control law is simple and model-free based on the voltage control strategy with the decentralized structure and only joint position feedback. It works for both repetitive and non-repetitive tasks. Recently, some control approaches based on the uncertainty estimation using the Fourier series have been presented. However, the proper value for the fundamental period duration has been left as an open problem. This paper addresses this issue and intuitively shows that in order to perform repetitive tasks; the least common multiple (LCM) of fundamental period durations of the desired trajectories of the joints is a proper value for the fundamental period duration of the Fourier series expansion. Selecting the LCM results in the least tracking error. Moreover, the truncation error is compensated by the proposed control law to make the tracking error as small as possible. Adaptation laws for determining the Fourier series coefficients are derived according to the stability analysis. The case study is an SCARA robot manipulator driven by permanent magnet DC motors. Simulation results and comparisons with a voltage-based controller using adaptive neuro-fuzzy systems show the effectiveness of the proposed control approach in tracking various periodic trajectories. Moreover, the experimental results on a real SCARA robot manipulator verify the successful practical implementation of the proposed controller.
58 citations
Additional excerpts
...Using (17) and (27), the closed loop system is given by qd + Kpq̃ + F̂(t) + Fr(t) = q̇ + F(t) (28) Using (20) and (26), (28) can be simplified as ̇̃ q + Kpq̃ = ξ P̃ + ε − Fr (29) where P̃ = P ∗ − P̂ ....
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TL;DR: A robust control scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator kinematic and dynamics, actuator dynamics and nor computing inverse kinematics.
Abstract: SUMMARY Most control algorithms for rigid-link electrically driven robots are given in joint coordinates. However, since the task to be accomplished is expressed in Cartesian coordinates, inverse kinematics has to be computed in order to implement the control law. Alternatively, one can develop the necessary theory directly in workspace coordinates. This has the disadvantage of a more complex robot model. In this paper, a robust control scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator kinematics and dynamics, actuator dynamics and nor computing inverse kinematics. The control design procedure is based on a new form of universal approximation theory and using Stone–Weierstrass theorem, to mitigate structured and unstructured uncertainties associated with external disturbances and actuated manipulator dynamics. It has been assumed that the lumped uncertainty can be modeled by linear differential equations. As the method is Model-Free, a broad range of manipulators can be controlled. Numerical case studies are developed for an industrial robot manipulator.
44 citations
TL;DR: A new method for secure communication based on chaos synchronization is proposed, consisted of a state feedback controller and a robust control term using the Fourier series expansion for compensation of uncertainties.
Abstract: In this paper, a new method for secure communication based on chaos synchronization is proposed. It is consisted of a state feedback controller and a robust control term using the Fourier series expansion for compensation of uncertainties. In comparison with other uncertainty estimators such as neural networks and fuzzy systems, Fourier series are more efficient, since they have fewer tuning. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Fourier series coefficients are estimated online using the adaptation rule obtained from stability analysis. The case study is the Duffing–Holmes oscillator. Also, observer-based secure communication using the Fourier series expansion has been proposed. Simulation results and comparisons, reveal the superiority of the proposed approach.
37 citations
TL;DR: This paper presents a novel robust control for electrically driven robot manipulators by designing an adaptive uncertainty estimator based on the first order Taylor series that is simpler, less computational, and more efficient.
33 citations
References
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Book•
01 Jan 1965
TL;DR: This book discusses ODEs, Partial Differential Equations, Fourier Series, Integrals, and Transforms, and Numerics for ODE's and PDE's, as well as numerical analysis and potential theory, and more.
Abstract: PART A: ORDINARY DIFFERENTIAL EQUATIONS (ODE'S). Chapter 1. First-Order ODE's. Chapter 2. Second Order Linear ODE's. Chapter 3. Higher Order Linear ODE's. Chapter 4. Systems of ODE's Phase Plane, Qualitative Methods. Chapter 5. Series Solutions of ODE's Special Functions. Chapter 6. Laplace Transforms. PART B: LINEAR ALGEBRA, VECTOR CALCULUS. Chapter 7. Linear Algebra: Matrices, Vectors, Determinants: Linear Systems. Chapter 8. Linear Algebra: Matrix Eigenvalue Problems. Chapter 9. Vector Differential Calculus: Grad, Div, Curl. Chapter 10. Vector Integral Calculus: Integral Theorems. PART C: FOURIER ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS. Chapter 11. Fourier Series, Integrals, and Transforms. Chapter 12. Partial Differential Equations (PDE's). Chapter 13. Complex Numbers and Functions. Chapter 14. Complex Integration. Chapter 15. Power Series, Taylor Series. Chapter 16. Laurent Series: Residue Integration. Chapter 17. Conformal Mapping. Chapter 18. Complex Analysis and Potential Theory. PART E: NUMERICAL ANALYSIS SOFTWARE. Chapter 19. Numerics in General. Chapter 20. Numerical Linear Algebra. Chapter 21. Numerics for ODE's and PDE's. PART F: OPTIMIZATION, GRAPHS. Chapter 22. Unconstrained Optimization: Linear Programming. Chapter 23. Graphs, Combinatorial Optimization. PART G: PROBABILITY STATISTICS. Chapter 24. Data Analysis: Probability Theory. Chapter 25. Mathematical Statistics. Appendix 1: References. Appendix 2: Answers to Odd-Numbered Problems. Appendix 3: Auxiliary Material. Appendix 4: Additional Proofs. Appendix 5: Tables. Index.
3,643 citations
Book•
20 Aug 19962,938 citations
2,314 citations
TL;DR: The global exponential stability of the proposed disturbance observer (DO) is guaranteed by selecting design parameters, which depend on the maximum velocity and physical parameters of robotic manipulators.
Abstract: A new nonlinear disturbance observer (NDO) for robotic manipulators is derived in this paper. The global exponential stability of the proposed disturbance observer (DO) is guaranteed by selecting design parameters, which depend on the maximum velocity and physical parameters of robotic manipulators. This new observer overcomes the disadvantages of existing DOs, which are designed or analyzed by linear system techniques. It can be applied in robotic manipulators for various purposes such as friction compensation, independent joint control, sensorless torque control and fault diagnosis. The performance of the proposed observer is demonstrated by the friction estimation and compensation for a two-link robotic manipulator. Both simulation and experimental results show the NDO works well.
1,424 citations
TL;DR: A feedback linearization (FL)-based control law made implementable using an extended state observer (ESO) is proposed for the trajectory tracking control of a flexible-joint robotic system and the closed-loop stability of the system under the proposed observer-controller structure is established.
Abstract: In this paper, a feedback linearization (FL)-based control law made implementable using an extended state observer (ESO) is proposed for the trajectory tracking control of a flexible-joint robotic system. The FL-based controller cannot be implemented unless the full transformed state vector is available. The design also requires exact knowledge of the system model making the controller performance sensitive to uncertainties. To address these issues, an ESO is designed, which estimates the state vector, as well as the uncertainties in an integrated manner. The FL controller uses the states estimated by ESO, and the effect of uncertainties is compensated by augmenting the FL controller with the ESO-estimated uncertainties. The closed-loop stability of the system under the proposed observer-controller structure is established. The effectiveness of the ESO in the estimation of the states and uncertainties and the effectiveness of the FL + ESO controller in tracking are demonstrated through simulations. Lastly, the efficacy of the proposed approach is validated through experimentation on Quanser's flexible-joint module.
424 citations