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.

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.

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.

Linearized Dynamic Models for Robot Manipulators With Varying Link Parameters

1991 ◽  
Author(s):  
Chang-Jin Li ◽  
T. S. Sankar ◽  
A. Hemami
Keyword(s):  
Computational Complexity ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Mechanical Systems ◽  
Computational Algorithms ◽  
Inverse Dynamic ◽  
Dynamic Link

Abstract In this paper, two fast computational algorithms are developed for effective formulation for the linearized dynamic robot models with varying (kinematic and dynamic) link parameters. The proposed algorithms can generate complete linearized (inverse) dynamic models for robot manipulators, taking variations (e.g., inexactness, inconstancy, or uncertainty) of the kinematic and dynamic link parameters into account. They can be applied to any robot manipulator with rotational and/or translational joints, and can be utilized, also, for sensivitity analysis of similar mechanical systems. The computational complexity of these algorithms is only of order O(n), where n is the number of degrees-of-freedom of the robot manipulator.

A New Lagrangian Formulation of Dynamics for Robot Manipulators

1989 ◽  
Vol 111 (4) ◽  
pp. 559-566 ◽  
Author(s):  
Chang-Jin Li
Keyword(s):  
Control System ◽  
Dynamic Simulation ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Lagrangian Formulation ◽  
Lagrangian Dynamics ◽  
Highly Nonlinear ◽  
Mathematical Operations

In this paper, a new Lagrangian formulation of dynamics for robot manipulators is developed. The formulation results in well structured form equations of motion for robot manipulators. The equations are an explicit set of closed form second order highly nonlinear and coupling differential equations, which can be used for both the design of the control system (or dynamic simulation) and the computation of the joint generalized forces/torques. The mathematical operations of the formulation are so few that it is possible to realize the computation of the Lagrangian dynamics for robot manipulators in real-time on a micro/mini-computer. For a robot manipulator with n degrees-of-freedom, the number of operations of the formulation is at most (6n2 + 107n − 81) multiplications and (4n2 + 102n − 86) additions; for n = 6, about 780 multiplications and 670 additions.

scholarly journals Nonlinear pd controllers with gravity compensation for robot manipulators

2014 ◽  
Vol 14 (1) ◽  
pp. 141-150 ◽  
Author(s):  
Jianfeng Huang ◽  
Chengying Yang ◽  
Jun Ye
Keyword(s):  
Degrees Of Freedom ◽  
Position Control ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Nonlinear Function ◽  
Step Response ◽  
Robot Dynamics ◽  
Gravity Compensation ◽  
Pd Controller ◽  
Globally Asymptotically Stable

Abstract A Nonlinear Proportional-Derivative (NPD) controller with gravity compensation is proposed and applied to robot manipulators in this paper. The proportional and derivative gains are changed by the nonlinear function of errors in the NPD controller. The closed-loop system, composed of nonlinear robot dynamics and NPD controllers, is globally asymptotically stable in position control of robot manipulators. The comparison of the simulation experiments in the position control (the step response) of a robot manipulator with two degrees of freedom is also presented to illustrate that the NPD controller is superior to the conventional PD controller in a position control system. The experimental results show that the NPD controller can obtain a faster response velocity and higher position accuracy than the conventional PD controller in the position control of robot manipulators because the proportional and derivative gains of the NPD controller can be changed by the nonlinear function of errors. The NPD controller provides a novel approach for robot control systems.

A new tuning procedure for nonlinear PID global regulators with bounded torques for rigid robots

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1926-1947 ◽  
Author(s):  
Jorge Orrante-Sakanassi ◽  
Víctor Santibánez ◽  
Víctor M. Hernández-Guzmán
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Experimental Tests ◽  
Pid Controllers ◽  
Stability Conditions ◽  
Proportional Integral Derivative ◽  
Global Regulators ◽  
The Stability ◽  
First Time

SUMMARYIn this paper we propose new tuning conditions for three saturated nonlinear proportional-integral-derivative (PID) global regulators with bounded torques for robot manipulators, which have been presented previously in the literature. The motivation of this work relies on the fact that the tuning conditions presented previously in the literature for assuring global asymptotic stability are so restrictive that it had been impossible, until now, to carry out experimental tests. New tuning criteria of unsaturated PID controllers for robot manipulators with stability conditions more relaxed than those presented previously in the literature have been proposed recently in some works by the authors. This was achieved by setting the stability conditions as expressions that have to be satisfied at each joint instead of general conditions for the whole robot. Based on this idea, we now obtain stability conditions for saturated global PID controllers which are so relaxed that they have allowed to perform, by the first time, experimental tests using controller gains which completely satisfy the proposed stability conditions. The results of such experiments are presented in this paper, where we have used a two-degrees-of-freedom robot manipulator.

A proof of the Ge–Lee statement on the inertia regressor of robot manipulators

Robotica ◽  
2012 ◽  
Vol 31 (1) ◽  
pp. 55-59 ◽  
Author(s):  
Juan Ignacio Mulero-Martínez
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Formal Proof ◽  
Nonlinear Functions ◽  
Inertia Matrix

SUMMARYThis paper delivers a proof of a statement due to Ge and Lee. Specifically, these authors stated, without proof, that the entries of the inertia matrix may be completely parameterized by stacking elements of a regressor superset. This superset has the advantage of avoiding to derive the complete dynamics of a robot manipulator. On the basis of both mechanics and combinatorial arguments, we deliver a formal proof. In addition, we improve the estimations by sorting joint variables and partitioning the inertia matrix that results into the reduction of the regressor superset. The number of nonlinear functions in the regressor is also quantified. A 2 degrees of freedom revolute robot is presented to illustrate these ideas.

Design and Application of Chattering-Free Sliding Mode Controller to Cable-Driven Parallel Robot Manipulator: Theory and Experiment

2010 ◽  
Author(s):  
Meysar Zeinali ◽  
Amir Khajepour
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Parallel Robot ◽  
Industrial Applications ◽  
Fast Time ◽  
Chattering Free

High-performance robust controller design for nonlinear uncertain dynamical systems such as cable-driven parallel robot manipulators is a challenging work. In this paper, a new and systematic approach to combine sliding mode control, adaptive control design techniques and PID control for tracking control of cable-driven parallel robot manipulators, in the presence of model uncertainties is presented. In the proposed method, structured (parametric) and unstructured (un-modeled) uncertainties are lumped into one term and one uncertain parameter (term) is considered corresponding to each degrees of freedom of robot manipulator. Therefore, the problem of computation burden and large number of parameters, which are not addressed in the literature, is solved to a large extent. The global uniform ultimate boundedness stability is obtained in the presence of fast time-varying uncertainties. The simulation and experimental results revealed that the proposed method is robust against uncertainties and its simplicity makes the approach attractive for industrial applications.

Uncertainty and Disturbance Estimator-Based Robust Region Tracking Control for Multiple Quadrotors

2020 ◽  
Author(s):  
Qi Lu ◽  
Beibei Ren ◽  
Yuan-dong Ji
Keyword(s):  
Tracking Control ◽  
Degrees Of Freedom ◽  
Moving Target ◽  
Simulation Studies ◽  
Model Uncertainties ◽  
External Disturbances ◽  
Target Region ◽  
Control Framework ◽  
Uncertainty And Disturbance Estimator ◽  
Disturbance Estimator

Abstract In this paper, the decentralized uncertainty and disturbance estimator (UDE)-based robust region reaching controller is developed to drive a swarm of quadrotors with the full degrees-of-freedom, nonlinear, coupled and underactuated dynamics to track the trajectory of a moving target region while avoiding collisions among themselves. The backstepping technique is utilized to seamlessly fuse the UDE into the region reaching control framework with the function of estimating and compensating the model uncertainties and external disturbances. Simulation studies are carried out to demonstrate the effectiveness of the proposed method for achieving the moving target trajectory tracking even in the presence of external disturbances.

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