Tracking Control of Electrically Driven Robots Using a Model-free Observer

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 729-755 ◽  
Author(s):  
Alireza Izadbakhsh ◽  
Saeed Khorashadizadeh ◽  
Payam Kheirkhahan
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Tracking Error ◽  
Weierstrass Theorem ◽  
Approximation Techniques ◽  
Model Free ◽  
Electrically Driven Robots ◽  
Permanent Magnet Dc Motors ◽  
Linear Differential

SummaryThis paper presents a robust tracking controller for electrically driven robots, without the need for velocity measurements of joint variables. Many observers require the system dynamics or nominal models, while a model-free observer is presented in this paper. The novelty of this paper is presenting a new observer–controller structure based on function approximation techniques and Stone–Weierstrass theorem using differential equations. In fact, it is assumed that the lumped uncertainty can be modeled by linear differential equations. Then, using Stone–Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of proposed approach in comparison with previous related works is simplicity and reducing the dimensions of regressor matrices without the need for any information of the systems’ dynamic. Simulation results on a 6-degrees of freedom robot manipulator driven by geared permanent magnet DC motors indicate the satisfactory performance of the proposed method in overcoming uncertainties and reducing the tracking error. To evaluate the performance of proposed controller in practical implementations, experimental results on an SCARA manipulator are presented.

Robust task-space control of robot manipulators using differential equations for uncertainty estimation

Robotica ◽  
2016 ◽  
Vol 35 (9) ◽  
pp. 1923-1938 ◽  
Author(s):  
Alireza Izadbakhsh ◽  
Saeed Khorashadizadeh
Keyword(s):  
Differential Equations ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Industrial Robot ◽  
Design Procedure ◽  
Weierstrass Theorem ◽  
Actuator Dynamics ◽  
Model Free ◽  
Electrically Driven Robots ◽  
Linear Differential

SUMMARYMost 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.

A Note on a Reduced-Order Observer Based Controller for a Class of Lipschitz Nonlinear Systems

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Mohamadreza Homayounzade ◽  
Mehdi Keshmiri
Keyword(s):  
Nonlinear Systems ◽  
Global Exponential Stability ◽  
Degrees Of Freedom ◽  
Large Range ◽  
Robot Manipulator ◽  
Tracking Error ◽  
Control Law ◽  
Reduced Order ◽  
Lipschitz Nonlinear Systems ◽  
Reduced Order Observer

This paper presents a novel reduced-order observer based controller for a class of Lipschitz nonlinear systems, described by a set of second order ordinary differential equations. The control law is designed based on the measured output and estimated states. The main features are: (1) The computation cost is reduced noticeably, since the observer is a reduced-order one; (2) The controller guarantees semi-global exponential stability for both estimation and tracking error; and (3) The proposed method can be used in a large range of applications, especially in mechanical systems. The effectiveness of the proposed method is investigated through the numerical simulation for a two-degrees-of-freedom robot manipulator acting on a horizontal worktable.

Direct Adaptive Function Approximation Techniques Based Control of Robot Manipulators

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Majid Moradi Zirkohi
Keyword(s):  
Function Approximation ◽  
Fuzzy Systems ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Approximation Error ◽  
Point Of View ◽  
Orthogonal Functions ◽  
Approximation Techniques ◽  
Control Approach ◽  
Model Free

In this paper, a simple model-free controller for electrically driven robot manipulators is presented using function approximation techniques (FAT) such as Legendre polynomials (LP) and Fourier series (FS). According to the orthogonal functions theorem, LP and FS can approximate nonlinear functions with an arbitrary small approximation error. From this point of view, they are similar to fuzzy systems and can be used as controller to approximate the ideal control law. In comparison with fuzzy systems and neural networks, LP and FS are simpler and less computational. Moreover, there are very few tuning parameters in LP and FS. Consequently, the proposed controller is less computational in comparison with fuzzy and neural controllers. The case study is an articulated robot manipulator driven by permanent magnet direct current (DC) motors. Simulation results verify the effectiveness of the proposed control approach and its superiority over neuro-fuzzy controllers.

Relativistic Wave Equations

2021 ◽  
pp. 167-190
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Wave Equations ◽  
Plane Waves ◽  
Canonical Formalism ◽  
Real Field ◽  
Klein Gordon ◽  
Linear Differential ◽  
Propagation Properties

We derive the most general relativistically covariant linear differential equations, having at most two derivatives, for scalar, spinor and vector fields. We introduce the corresponding Lagrangian and Hamiltonian formalisms and present the expansion of the solutions in terms of plane waves. In each case, we study the propagation properties of the corresponding Green functions. We start with the simplest example of the Klein–Gordon equation for a real field and generalise it to that of N real, or complex fields. As a next step we derive the Weyl, Majorana and Dirac equations for spinor fields. They are first order differential equations and we show how to adapt to them the canonical formalism. We end with the Proca and Maxwell equations for massive and massless spin-one fields and, in each case, we determine the physical degrees of freedom.

scholarly journals Bertolino-Baksa stability at nonlinear vibrations of motor vehicles

2017 ◽  
Vol 44 (2) ◽  
pp. 271-291 ◽  
Author(s):  
Ljudmila Kudrjavceva ◽  
Milan Micunovic ◽  
Danijela Miloradovic ◽  
Aleksandar Obradovic
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Motor Vehicles ◽  
Numerical Code ◽  
Parameter Method ◽  
Spatial Stability ◽  
Linear Vibrations ◽  
Linear Differential

Research of vehicle response to road roughness is particularly important when solving problems related to dynamic vehicle stability. In this paper, unevenness of roads is considered as the source of non-linear vibrations of motor vehicles. The vehicle is represented by an equivalent spatial model with seven degrees of freedom. In addition to solving the response by simulating it within a numerical code, quasi-linearization of nonlinear differential equations of motion is carried out. Solutions of quasi-linear differential equations of forced vibrations are determined using the small parameter method and are indispensable for the study of spatial stability of the vehicle. An optimal stabilization for a simplified two-dimensional model was performed. Spatial stability and internal resonance are considered briefly.

Analytical and Experimental Decentralized Adaptive Control of a High-Degrees-of-Freedom Robot Manipulator

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
Alexander Bertino ◽  
Peiman Naseradinmousavi ◽  
Atul Kelkar
Keyword(s):  
Adaptive Control ◽  
Computational Efficiency ◽  
Tracking Control ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Problem Formulation ◽  
Experimental Results ◽  
Model Free ◽  
Trajectory Simulation ◽  
Adaptive Control Strategy

Abstract In this paper, we study the analytical and experimental control of a seven degrees-of-freedom (7DOF) robot manipulator. A model-free decentralized adaptive control strategy is presented for the tracking control of the manipulator. The problem formulation and experimental results demonstrate the computational efficiency and simplicity of the proposed method. The results presented here are one of the first known experiments on a redundant 7DOF robot. The efficacy of the adaptive decentralized controller is demonstrated experimentally by using the Baxter robot to track a desired trajectory. Simulation and experimental results clearly demonstrate the versatility, tracking performance, and computational efficiency of this method.

scholarly journals A model-based velocity controller for chaotization of flexible joint robot manipulators

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880252 ◽  
Author(s):  
Roger Miranda-Colorado ◽  
Luis T Aguilar ◽  
J Moreno-Valenzuela
Keyword(s):  
Vector Field ◽  
Asymptotic Stability ◽  
Chaotic Motion ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Tracking Error ◽  
Reference Vector ◽  
Flexible Joint ◽  
Model Based

This article presents a model-based velocity controller able to induce a chaotic motion on n-degrees of freedom flexible joint robot manipulators. The proposed controller allows the velocity link vector of a robot manipulator to track an arbitrary, chaotic reference vector field. A rigorous theoretical analysis based on Lyapunov’s theory is used to prove the asymptotic stability of the tracking error signals when using the proposed controller, which implies that a chaotic motion is induced to the robotic system. Experimental results are provided using a flexible joint robot manipulator of two degrees of freedom. Finally, by using Poincaré maps and Lyapunov exponents, it is shown that the behavior exhibited by the robot joint positions is chaotic.

A robotic motion controller using a self-organizing fuzzy logic algorithm with grey prediction

1998 ◽  
Vol 212 (4) ◽  
pp. 293-304 ◽  
Author(s):  
S-J Huang ◽  
J-S Lee
Keyword(s):  
Fuzzy Logic ◽  
Degrees Of Freedom ◽  
Fuzzy Controller ◽  
Tracking Error ◽  
Learning Ability ◽  
Grey Prediction ◽  
Fuzzy Logic Algorithm ◽  
Model Free ◽  
Fuzzy Parameter ◽  
Self Organizing

It is well known that robotic manipulators are highly non-linear coupled dynamic systems. It is difficult to establish an appropriate mathematical model for the design of a model-based controller. Although fuzzy logic control has model-free features, it still needs time-consuming work for rule bank and fuzzy parameter adjustment. Hence the self-organizing fuzzy controller is proposed to manipulate the motion trajectory of robots with multiple degrees of freedom. This approach has learning ability for responding to the time-varying characteristic of a robot. Its control rule bank can be established and modified continuously by on-line learning with zero initial fuzzy rules. However, this control strategy has larger oscillatory behaviour during initial learning. Here a self-organizing fuzzy controller with grey prediction is proposed to improve this behaviour. The experimental results show that this intelligent controller can reduce significantly the oscillatory amplitude of the output trajectory and tracking error.

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