A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators

1990 ◽  
Vol 112 (4) ◽  
pp. 618-629 ◽  
Author(s):  
Nader Sadegh ◽  
Roberto Horowitz ◽  
Wei-Wen Kao ◽  
Masayoshi Tomizuka
Keyword(s):  
Lyapunov Theory ◽  
Control Input ◽  
Robot Arm ◽  
Unified Approach ◽  
Parameter Adaptation ◽  
Control Laws ◽  
Position Errors ◽  
Adaptive Compensator ◽  
Mechanical Manipulators ◽  
Repetitive Controller

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley/NSK SCARA type robot arm.

Modelling of a logarithmic parameter adaptation law for adaptive control of mechanical manipulators

Robotica ◽  
2006 ◽  
Vol 24 (4) ◽  
pp. 523-525 ◽  
Author(s):  
Recep Burkan
Keyword(s):  
Parameter Estimation ◽  
Adaptive Control ◽  
Tracking Error ◽  
Lyapunov Theory ◽  
Control Law ◽  
Trigonometric Functions ◽  
Parameter Adaptation ◽  
Mechanical Manipulators ◽  
Adaptation Law ◽  
Adaptive Control Law

In the paper, a new adaptive control law for controlling robot manipulators is derived based on the Lyapunov theory; trigonometric functions are used for the derivation of the parameter estimation law. In this note, we have derived a logarithmic parameter estimation law based on a previous paper, and the boundedness of tracking error has been shown.

Model-Independent Control of a Flexible-Joint Robot Manipulator

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Withit Chatlatanagulchai ◽  
Peter H. Meckl
Keyword(s):  
Neural Networks ◽  
Open Problem ◽  
High Performance ◽  
Robot Manipulator ◽  
Intrinsic Property ◽  
Variable Structure ◽  
System Model ◽  
Control Input ◽  
Control Laws ◽  
Flexible Joint

Flexibility at the joint of a manipulator is an intrinsic property. Even “rigid-joint” robots, in fact, possess a certain amount of flexibility. Previous experiments confirmed that joint flexibility should be explicitly included in the model when designing a high-performance controller for a manipulator because the flexibility, if not dealt with, can excite system natural frequencies and cause severe damage. However, control design for a flexible-joint robot manipulator is still an open problem. Besides being described by a complicated system model for which the passivity property does not hold, the manipulator is also underactuated, that is, the control input does not drive the link directly, but through the flexible dynamics. Our work offers another possible solution to this open problem. We use three-layer neural networks to represent the system model. Their weights are adapted in real time and from scratch, which means we do not need the mathematical model of the robot in our control algorithm. All uncertainties are handled by variable-structure control. Backstepping structure allows input efforts to be applied to each subsystem where they are needed. Control laws to adjust all adjustable parameters are devised using Lyapunov’s second method to ensure that error trajectories are globally uniformly ultimately bounded. We present two state-feedback schemes: first, when neural networks are used to represent the unknown plant, and second, when neural networks are used to represent the unknown parts of the control laws. In the former case, we also design an observer to enable us to design a control law using only output signals—the link positions. We use simulations to compare our algorithms with some other well-known techniques. We use experiments to demonstrate the practicality of our algorithms.

scholarly journals Sliding Mode Robot Control with Friction and Payload Estimation

2004 ◽  
Vol 8 (5) ◽  
pp. 553-561 ◽  
Author(s):  
Lörinc Márton ◽  
◽  
Béla Lantos ◽  
Keyword(s):  
Robot Control ◽  
Control Algorithm ◽  
Lyapunov Method ◽  
Sliding Mode ◽  
Robot Arm ◽  
Tracking Accuracy ◽  
Parameter Adaptation ◽  
Robust Parameter ◽  
Payload Mass ◽  
Friction Parameters

The paper deals with robust motion control of robotic systems with unknown friction parameters and payload mass. The parameters of the robot arm were considered known with a given precision. To solve the control of the robot with unknown payload mass and friction parameters, sliding mode control algorithm was proposed combined with robust parameter adaptation techniques. Using Lyapunov method it was shown that the resulting controller achieves a guaranteed final tracking accuracy. Simulation results are presented to illustrate the effectiveness and achievable control performance of the proposed scheme.

Extended state observer-based back-stepping control for hypersonic reentry vehicle with input constraints

2018 ◽  
Vol 36 (3) ◽  
pp. 921-947 ◽  
Author(s):  
Chen Chen ◽  
Guangfu Ma ◽  
Yueyong Lyu ◽  
Yanning Guo
Keyword(s):  
State Observer ◽  
Lyapunov Theory ◽  
Extended State Observer ◽  
Control Technique ◽  
Control Input ◽  
Sigmoid Function ◽  
Input Constraints ◽  
Extended State ◽  
Reentry Vehicle ◽  
Back Stepping Control

Abstract This paper investigates the attitude-tracking control problem of hypersonic reentry vehicle in cases of multiple uncertainties, external disturbances and input constraints. The controller design is based on synthesizing the extended state observer (ESO) into a back-stepping control technique. This control-oriented model is formulated with mismatched and matched uncertainties. They reflect the total disturbances that group different types of aerodynamic uncertainties and external moment disturbances. In order to improve the system robustness, a sigmoid function-based ESO is first proposed. This will estimate the total disturbance and is equipped with a controller. The sigmoid smooth function is also introduced for the purpose of handling the input constraints. This will approximate saturation and guarantee that the control input is bounded. Error states between the actual control input and the desired control input are integrated to compensate for the saturation effect. Following this, the stability of the closed-loop system is proved within the Lyapunov theory framework. Several simulations are then investigated to illustrate the effectiveness of the proposed constrained attitude control scheme.

scholarly journals Finite-Horizon Optimal Control of Discrete-Time Switched Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qixin Zhu ◽  
Guangming Xie
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Discrete Time ◽  
Finite Horizon ◽  
Linear Control ◽  
Linear Control Systems ◽  
Control Input ◽  
Optimal Switching ◽  
Control Laws ◽  
Control Factors

Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.

scholarly journals A neural network combined with sliding mode controller for the two-wheel self-balancing robot

2021 ◽  
Vol 10 (3) ◽  
pp. 592
Author(s):  
Duc-Minh Nguyen ◽  
Van-Tiem Nguyen ◽  
Trong-Thang Nguyen
Keyword(s):  
Neural Network ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Sliding Mode Controller ◽  
Control Laws ◽  
Noise Compensation ◽  
Simulation Results ◽  
Balancing Robot ◽  
The Stability

This article presents the sliding control method combined with the selfadjusting neural network to compensate for noise to improve the control system's quality for the two-wheel self-balancing robot. Firstly, the dynamic equations of the two-wheel self-balancing robot built by Euler–Lagrange is the basis for offering control laws with a neural network of noise compensation. After disturbance-compensating, the sliding mode controller is applied to control quickly the two-wheel self-balancing robot reached the desired position. The stability of the proposed system is proved based on the Lyapunov theory. Finally, the simulation results will confirm the effectiveness and correctness of the control method suggested by the authors.

scholarly journals Cooperative Visual-SLAM System for UAV-Based Target Tracking in GPS-Denied Environments: A Target-Centric Approach

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 813 ◽  
Author(s):  
Juan-Carlos Trujillo ◽  
Rodrigo Munguia ◽  
Sarquis Urzua ◽  
Antoni Grau
Keyword(s):  
Position Estimation ◽  
Lyapunov Theory ◽  
Fundamental Aspect ◽  
Control Laws ◽  
Position Information ◽  
Practical Applications ◽  
Aerial Robots ◽  
Localization And Mapping ◽  
Flight Formation ◽  
The Stability

Autonomous tracking of dynamic targets by the use of Unmanned Aerial Vehicles (UAVs) is a challenging problem that has practical applications in many scenarios. In this context, a fundamental aspect that must be addressed has to do with the position estimation of aerial robots and a target to control the flight formation. For non-cooperative targets, their position must be estimated using the on-board sensors. Moreover, for estimating the position of UAVs, global position information may not always be available (GPS-denied environments). This work presents a cooperative visual-based SLAM (Simultaneous Localization and Mapping) system that allows a team of aerial robots to autonomously follow a non-cooperative target moving freely in a GPS-denied environment. One of the contributions of this work is to propose and investigate the use of a target-centric SLAM configuration to solve the estimation problem that differs from the well-known World-centric and Robot-centric SLAM configurations. In this sense, the proposed approach is supported by theoretical results obtained from an extensive nonlinear observability analysis. Additionally, a control system is proposed for maintaining a stable UAV flight formation with respect to the target as well. In this case, the stability of control laws is proved using the Lyapunov theory. Employing an extensive set of computer simulations, the proposed system demonstrated potentially to outperform other related approaches.

Payload Pendulation Reduction Using a Variable-Geometry-Truss Architecture with LQR and Fuzzy Controls

2003 ◽  
Vol 9 (7) ◽  
pp. 805-837 ◽  
Author(s):  
Paolo Dadone ◽  
Walter Lacarbonara ◽  
Ali H. Nayfeh ◽  
Hugh F. Vanlandingham
Keyword(s):  
Control Point ◽  
Broad Band ◽  
Ship Motions ◽  
Control Input ◽  
Variable Geometry ◽  
Linear Quadratic ◽  
Control Laws ◽  
Band Frequency ◽  
Input Acceleration ◽  
Variable Geometry Truss

We investigate the feasibility of a variable-geometry truss (VGT) based architecture for suppressing payload pendulations in ship-mounted cranes. The VGT assembly is conceived to be retrofitted onto the boom tip of ship-mounted cranes. A simplified planar model is developed. A control point along the cable hoisting the payload is constrained to move along a straight path with a given control input (acceleration) imparted via the actuators embedded in the VGT assembly. Control laws based on either linear quadratic or fuzzy control methodologies are developed in order to minimize an assigned cost functional. Their effectiveness is compared through extensive numerical simulations. The performance of the VGT architecture and associated control laws is analyzed when the crane is subject to the most severe combination of resonant excitations: a primary resonant roll excitation at the natural frequency of the controlled system, and a principal-parametric resonant heave excitation, both corresponding to sea state three and higher. The proposed strategy exhibits enough control authority over the system dynamics, greatly reducing the severe and undesirable resonant pendulations caused by the ship motions in a broad-band frequency range. Moreover, its disturbance-rejection capabilities are exerted with feasible control efforts, which are localized in the segment of the crane where they are needed.

Multibody modelling of N DOF robot arm assigned to milling manufacturing. Dynamic analysis and position errors evaluation

2016 ◽  
Vol 30 (1) ◽  
pp. 405-420 ◽  
Author(s):  
Stefano Baglioni ◽  
Filippo Cianetti ◽  
Claudio Braccesi ◽  
Denis Mattia De Micheli
Keyword(s):  
Dynamic Analysis ◽  
Robot Arm ◽  
Position Errors

Robust Trajectory Following Control of Robotic Systems

1985 ◽  
Vol 107 (4) ◽  
pp. 308-315 ◽  
Author(s):  
S. N. Singh ◽  
A. A. Schy
Keyword(s):  
Degrees Of Freedom ◽  
Digital Simulation ◽  
Robotic Systems ◽  
Control Law ◽  
Robot Arm ◽  
Control Laws ◽  
Payload Uncertainty ◽  
Trajectory Following ◽  
And Control ◽  
Three Degrees Of Freedom

Using an inversion approach we derive a control law for trajectory following of robotic systems. A servocompensator is used around the inner decoupled loop for robustness to uncertainty in the system. These results are applied to trajectory control of a three-degrees-of-freedom robot arm and control laws Cθ and CH for joint angle and position trajectory following, respectively, are derived. Digital simulation results are presented to show the rapid trajectory following capability of the controller in spite of payload uncertainty.

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