An Adaptive Regressor-Free Fourier Series-Based Tracking Controller for Robot Manipulators: Theory and Experimental Evaluation

Robotica ◽  
2021 ◽  
pp. 1-16
Author(s):  
Jorge Villalobos-Chin ◽  
Víctor Santibáñez
Keyword(s):  
Fourier Series ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Transient Behavior ◽  
Asymptotic Convergence ◽  
Discontinuous Systems ◽  
Varying Coefficients ◽  
Formal Stability ◽  
Tracking Controller ◽  
Error Dynamics

SUMMARY In this article, we propose a nonlinear Proportional+Derivative (PD) tracking controller with adaptive Fourier series compensation. The proposed controller uses a regressor-free adaptive scheme that relies on a trigonometric polynomial with varying coefficients to solve the control problem. Asymptotic convergence of the position and velocity errors is proven via a formal stability analysis based on Lyapunov and LaSalle theory for discontinuous systems. The proposed controller is validated on a 2-degrees of freedom robot manipulator. The experimental results validate the theoretically obtained results and reflect the effect of certain parameters in the transient behavior of the error dynamics. Certain robustness properties are also observed.

scholarly journals Software Sensor to Enhance Online Parametric Identification for Nonlinear Closed-Loop Systems for Robotic Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3653
Author(s):  
Lilia Sidhom ◽  
Ines Chihi ◽  
Ernest Nlandu Kamavuako
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Parametric Identification ◽  
Recursive Least Squares ◽  
Unknown Parameters ◽  
Closed Loop Identification ◽  
Input Variables ◽  
Robotic Applications

This paper proposes an online direct closed-loop identification method based on a new dynamic sliding mode technique for robotic applications. The estimated parameters are obtained by minimizing the prediction error with respect to the vector of unknown parameters. The estimation step requires knowledge of the actual input and output of the system, as well as the successive estimate of the output derivatives. Therefore, a special robust differentiator based on higher-order sliding modes with a dynamic gain is defined. A proof of convergence is given for the robust differentiator. The dynamic parameters are estimated using the recursive least squares algorithm by the solution of a system model that is obtained from sampled positions along the closed-loop trajectory. An experimental validation is given for a 2 Degrees Of Freedom (2-DOF) robot manipulator, where direct and cross-validations are carried out. A comparative analysis is detailed to evaluate the algorithm’s effectiveness and reliability. Its performance is demonstrated by a better-quality torque prediction compared to other differentiators recently proposed in the literature. The experimental results highlight that the differentiator design strongly influences the online parametric identification and, thus, the prediction of system input variables.

Feedback control framework for car-like robots using the unicycle controllers

Robotica ◽  
2011 ◽  
Vol 30 (4) ◽  
pp. 517-535 ◽  
Author(s):  
Maciej Michałek ◽  
Krzysztof Kozłowski
Keyword(s):  
Stability Analysis ◽  
Feedback Control ◽  
Closed Loop ◽  
Path Following ◽  
Rear Wheel ◽  
Front Wheel ◽  
Steering Angle ◽  
Formal Stability ◽  
Control Framework ◽  
Error Dynamics

SUMMARYThe paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots—limited and unlimited ones—are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

Theoretical and Experimental Study of the Nonlinearly Coupled Heave, Pitch, and Roll Motions of a Ship in Longitudinal Waves

1993 ◽  
Author(s):  
I. G. Oh ◽  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Force Response ◽  
Governing Equations ◽  
Response Curves ◽  
Varying Coefficients ◽  
Jump Phenomena ◽  
Time Varying Coefficients ◽  
Three Degrees Of Freedom

Abstract The loss of dynamic stability and the resulting large-amplitude roll of a vessel in a head or following sea were studied theoretically and experimentally. A ship model with three degrees of freedom (roll, pitch, heave) was considered. The governing equations for the heave and pitch modes were linearized and their harmonic solutions were coupled with the nonlinear equation governing roll. The resulting equation, which has time-varying coefficients, was used to predict the response in roll. The principal parametric resonance was considered in which the excitation frequency is twice the natural frequency in roll. Force-response curves were obtained. The existence of jump phenomena and multiple stable solutions for the case of subcritical instability was observed in the experiments and found to be in good qualitative agreement with the results predicted by the theory. The experiments also revealed that the large-amplitude roll is dependent on the location of the model in the standing waves.

Trajectory Synthesis and Redundancy Resolution for High Speed Point to Point Motions of Redundant Robot Manipulators

1997 ◽  
Author(s):  
W. Kim ◽  
J. Rastegar
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Dynamic Performance ◽  
High Harmonic ◽  
Harmonic Excitation ◽  
Redundancy Resolution ◽  
Tracking Accuracy ◽  
Point To Point

Abstract Trajectory synthesis for robot manipulators with redundant kinematic degrees-of-freedom has been studied by numerous investigators. Redundant manipulators are of interest since the redundant degrees-of-freedom can be used to improve the local and global kinematic and dynamic performance of a system. As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Noting that manipulators with revolute joints have nonlinear dynamics, high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. In this paper, a redundancy resolution method is developed based on the Trajectory Pattern Method (TPM) to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. As an example, optimal trajectories are synthesized for point to point motions of a plane 3R manipulator.

Application of non-linear H∞ control to the Tetrabot robot manipulator

1998 ◽  
Vol 212 (6) ◽  
pp. 459-465 ◽  
Author(s):  
I Postlethwaite ◽  
A Bartoszewicz
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Industrial Robot ◽  
External Disturbances ◽  
Six Degrees Of Freedom ◽  
Control Scheme ◽  
Non Linear ◽  
Modelling Uncertainties ◽  
Real Robot ◽  
Robotic Application

In this paper, an application of a non-linear H∞ control law for an industrial robot manipulator is presented. Control of the manipulator motion is formulated into a non-linear H∞ optimization problem, namely optimal tracking performance in the presence of modelling uncertainties and external disturbances. Analytical solutions for this problem are implemented on a real robot. The robot under consideration is the six-degrees-of-freedom GEC Tetrabot. Investigations are made into the selection of weights for the H∞ controller and it is shown how different selections of weights affect the Tetrabot performance. The authors believe this to be the first robotic application of nonlinear H∞ control. Comparisons of the proposed control strategy with conventional proportional-derivative and proportional-integral-derivative controllers show favourable performance of the Tetrabot under the new non-linear H∞ control scheme.

scholarly journals Model tracking controller design of robot manipulator system with disturbances

2015 ◽  
Vol 7 (7) ◽  
pp. 168781401559236
Author(s):  
Dazhong Wang ◽  
Shujing Wu ◽  
Guoqiang Wang ◽  
Shigenori Okubo
Keyword(s):  
Controller Design ◽  
Robot Manipulator ◽  
Tracking Controller

Optimizing Fourier Series Based Gaits for Modular Robots Using an Evolutionary Algorithm

2013 ◽  
Author(s):  
David Ko ◽  
Harry H. Cheng
Keyword(s):  
Genetic Algorithm ◽  
Fourier Series ◽  
Evolutionary Algorithm ◽  
Periodic Motion ◽  
Degrees Of Freedom ◽  
Series Representation ◽  
Robotic System ◽  
Experimental Results ◽  
New Method ◽  
Modular Robots

A new method of controlling and optimizing robotic gaits for a modular robotic system is presented in this paper. A robotic gait is implemented on a robotic system consisting of three Mobot modules for a total of twelve degrees of freedom using a Fourier series representation for the periodic motion of each joint. The gait implementation allows robotic modules to perform synchronized gaits with little or no communication with each other making it scalable to increasing numbers of modules. The coefficients of the Fourier series are optimized by a genetic algorithm to find gaits which move the robot cluster quickly and efficiently across flat terrain. Simulated and experimental results show that the optimized gaits can have over twice as much speed as randomly generated gaits.

Singularity Analysis of Serial Robot-Manipulators

1996 ◽  
Vol 118 (4) ◽  
pp. 520-525 ◽  
Author(s):  
A. Karger
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Singularity Analysis ◽  
Singular Set ◽  
Singular Configurations ◽  
Special Cases ◽  
Serial Robot ◽  
Singular Configuration ◽  
Actual Configuration

This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.

scholarly journals Analysis and Synthesis of Global Nonlinear H∞ Controller for Robot Manipulators

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Carlos Alberto Chavez Guzmán ◽  
Luis Tupak Aguilar Bustos ◽  
Jován Oseas Mérida Rubio
Keyword(s):  
Lyapunov Function ◽  
Degrees Of Freedom ◽  
Gravitational Force ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Global Asymptotical Stability ◽  
Simulation Studies ◽  
External Disturbances ◽  
Analysis And Synthesis ◽  
Force Compensation

The H∞ regulation problem for robot manipulators using gravitational force compensation or precompensation has been solved locally while global asymptotical stability (or global stability) has been demonstrated using other methodologies. A solution to the global nonlinear H∞ regulation problem for l-degrees-of-freedom (l-DOF) robot manipulators, affected by external disturbances, is presented. We showed that the Hamilton-Jacobi-Isaacs (HJI) inequality, inherited in the solution of the H∞ control problem, is satisfied by defining a strict Lyapunov function. The performance issues of the nonlinear H∞ regulator are illustrated in experimental and simulation studies made for a 3-DOF rigid links robot manipulator.

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