H/sub ∞/ tuning for task-space feedback control of robot with uncertain Jacobian matrix

2001 ◽  
Vol 46 (8) ◽  
pp. 1313-1318 ◽  
Author(s):  
C.C. Cheah ◽  
S. Kawamura ◽  
S. Arimoto ◽  
K. Lee
Keyword(s):  
Feedback Control ◽  
Jacobian Matrix ◽  
Task Space

IMPLICIT CRITERIA OF EIGENVALUE ASSIGNMENT AND TRANSVERSALITY FOR BIFURCATION CONTROL IN FOUR-DIMENSIONAL MAPS

2004 ◽  
Vol 14 (10) ◽  
pp. 3489-3503 ◽  
Author(s):  
GUILIN WEN ◽  
DAOLIN XU
Keyword(s):  
Feedback Control ◽  
Unit Circle ◽  
Jacobian Matrix ◽  
Transversality Condition ◽  
Delayed Feedback Control ◽  
High Dimensional ◽  
Control Parameters ◽  
Washout Filter ◽  
New Criteria ◽  
Eigenvalue Assignment

In anti-control of bifurcations, it is common to create different types of bifurcations by adjusting the control parameters. For maps, the type of bifurcation is determined by the eigenvalue assignment on the unit circle at the bifurcation parameter point. Thus, an unavoidable problem in the creation of bifurcations is to desirably assign some eigenvalues at the specified locations on the unit circle, and the others inside the unit circle. However, for relatively complicated and high dimensional maps, the explicit expressions of eigenvalues are usually not available so that the implementation of the eigenvalue assignment becomes very difficult. To solve this problem, we proposed the new criteria of eigenvalue assignment without using eigenvalues. The criteria give implicit conditions to specify the eigenvalue assignments in terms of some simple algebraic equalities and inequalities associated with the elements of Jacobian matrix, i.e. eventually associated with the control parameters. Bifurcation occurs with another critical condition, the transversality condition. The computation of the transversality condition is usually nontrivial in high dimensional maps because it is related to the partial differentiation of the eigenvalues on the unit circle. We also present the implicit expression of the transversality condition in the form of the derivative of the Jacobian matrix and its eigenvectors that are computable at the bifurcation point. The proposed criteria cover most known types of bifurcations in four-dimensional maps and serve as the preferable methods for designing the critical bifurcation conditions in anti-control of bifurcations. The application to a modified Hénon map is illustrated in conjunction with the use of the delayed-feedback control and the washout-filter-aided feedback control.

Analysis of Active Joint Failure in Parallel Robot Manipulators

2004 ◽  
Vol 126 (6) ◽  
pp. 959-968 ◽  
Author(s):  
Mahir Hassan ◽  
Leila Notash
Keyword(s):  
Jacobian Matrix ◽  
Null Space ◽  
Robot Manipulators ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Task Space ◽  
Active Joint ◽  
Joint Failure ◽  
Space Vectors ◽  
Six Degree Of Freedom

In this study, the effect of active joint failure on the mobility, velocity, and static force of parallel robot manipulators is investigated. Two catastrophic active joint failure types are considered: joint jam and actuator force loss. To investigate the effect of failure on mobility, the Gru¨bler’s mobility equation is modified to take into account the kinematic constraints imposed by various branches in the manipulator. In the case of joint jam, the manipulator loses the ability to move and apply force in a specific portion of its task space; while in the case of actuator force loss, the manipulator gains an unconstrained motion in a specific portion of the task space in which an externally applied force cannot be resisted by the actuator forces. The effect of joint jam and actuator force loss on the velocity and on the force capabilities of parallel manipulators is investigated by examining the change in the Jacobian matrix, its inverse, and transposes. It is shown that the reduced velocity and force capabilities after joint jam and loss of actuator force could be determined using the null space vectors of the transpose of the Jacobian matrix and its inverse. Computer simulation is conducted to demonstrate the application of the developed methodology in determining the post-failure trajectory of a 3-3 six-degree-of-freedom Stewart-Gough manipulator, when encountering active joint jam and actuator force loss.

Task-Space Control Design and Performance Evaluation for a 6DOF Stewart Nanoscale Platform

2008 ◽  
Author(s):  
Chun-Chung Li ◽  
Yung Ting ◽  
Yi-Hung Liu ◽  
Yi-Da Lee ◽  
Chun-Wei Chiu
Keyword(s):  
Feedback Control ◽  
Hybrid Control ◽  
Feedforward Control ◽  
Feedback Controller ◽  
Test Method ◽  
Computation Method ◽  
Task Space ◽  
Force Output ◽  
End Effector ◽  
Control Scheme

A 6DOF Stewart platform using piezoelectric actuators for nanoscale positioning objective is designed. A measurement method that can directly measure the pose (position and orientation) of the end-effector is developed so that task-space on-line control is practicable. The design of a sensor holder for sensor employment, a cuboid with referenced measure points, and the computation method for obtaining the end-effector parameters is introduced. A control scheme combining feedforward and feedback is proposed. The inverse model of a hysteresis model derived by using a dynamic Preisach method is used for the feedforward control. Hybrid control to maintain both the positioning and force output for nano-cutting and nano-assembly applications is designed for the feedback controller. The optimal gain of the feedback controller is searched by using relay feedback test method and genetic algorithm. In experiment, conditions with/without external load employed with feedforward, feedback, and feedforward with feedback control schemes respectively are carried out. Performance of each control scheme verifies the capability of achieving nanoscale precision. The combined feedforward and feedback control scheme is superior to the others for gaining better precision.

A Synergy-Based Motor Control Framework for the Fast Feedback Control of Musculoskeletal Systems

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Reza Sharif Razavian ◽  
Borna Ghannadi ◽  
John McPhee
Keyword(s):  
Motor Control ◽  
Feedback Control ◽  
Real Time ◽  
Three Dimensional ◽  
Muscle Synergies ◽  
Task Space ◽  
Computationally Efficient ◽  
Control Framework ◽  
Muscle Activations ◽  
Musculoskeletal Systems

This paper presents a computational framework for the fast feedback control of musculoskeletal systems using muscle synergies. The proposed motor control framework has a hierarchical structure. A feedback controller at the higher level of hierarchy handles the trajectory planning and error compensation in the task space. This high-level task space controller only deals with the task-related kinematic variables, and thus is computationally efficient. The output of the task space controller is a force vector in the task space, which is fed to the low-level controller to be translated into muscle activity commands. Muscle synergies are employed to make this force-to-activation (F2A) mapping computationally efficient. The explicit relationship between the muscle synergies and task space forces allows for the fast estimation of muscle activations that result in the reference force. The synergy-enabled F2A mapping replaces a computationally heavy nonlinear optimization process by a vector decomposition problem that is solvable in real time. The estimation performance of the F2A mapping is evaluated by comparing the F2A-estimated muscle activities against the measured electromyography (EMG) data. The results show that the F2A algorithm can estimate the muscle activations using only the task-related kinematics/dynamics information with ∼70% accuracy. An example predictive simulation is also presented, and the results show that this feedback motor control framework can control arbitrary movements of a three-dimensional (3D) musculoskeletal arm model quickly and near optimally. It is two orders-of-magnitude faster than the optimal controller, with only 12% increase in muscle activities compared to the optimal. The developed motor control model can be used for real-time near-optimal predictive control of musculoskeletal system dynamics.

Base invariance of the manipulability index

Robotica ◽  
2004 ◽  
Vol 22 (4) ◽  
pp. 455-462 ◽  
Author(s):  
Karl Gotlih ◽  
Inge Troch
Keyword(s):  
Configuration Space ◽  
Jacobian Matrix ◽  
Quantitative Measure ◽  
Performance Measure ◽  
Control Algorithms ◽  
Design Phase ◽  
Task Space ◽  
Or Groups ◽  
Insight Into ◽  
Base Invariance

The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.

Postural Balance of an Underactuated Biped Robot With a Reaction Wheel

2017 ◽  
Author(s):  
Chris M. Maurice ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Feedback Control ◽  
Postural Balance ◽  
Biped Robot ◽  
Zero Dynamics ◽  
Total System ◽  
Task Space ◽  
Reaction Wheel ◽  
Control Laws ◽  
Biped Robots ◽  
Nonlinear Control Theory

Practical and effective biped robots are trending toward reality with increasing interest in the technology and recent major innovations in nonlinear control theory. The development of underactuated techniques transitioned biped robot walking to a more elegant human-like motion. When disturbances are encountered, maintaining postural balance becomes a proven challenge that limits the practicality of these machines. This paper offers a solution to this issue by showing that an underactuated five-link reaction wheel-equipped planar biped robot can be posturally balanced successfully and efficiently with feedback control laws derived from the system’s zero dynamics and through task space optimization. The zero dynamics controller is shown to exhibit better performance compared to the task space controller in terms of settling time and total system work.

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