State Estimation Observability Based on the Null Space of the Measurement Jacobian Matrix

2005 ◽  
Vol 20 (3) ◽  
pp. 1656-1658 ◽  
Author(s):  
E. Castillo ◽  
A.J. Conejo ◽  
R.E. Pruneda ◽  
C. Solares
Keyword(s):  
State Estimation ◽  
Jacobian Matrix ◽  
Null Space

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.

Mixed Measurement State Estimation of the Equivalent Current Transformation Based on Generalized Tellegen's Theorem

2013 ◽  
Vol 373-375 ◽  
pp. 970-975
Author(s):  
Gui Hua Lin ◽  
Tao Wang ◽  
Yu Ying Wang ◽  
Li Guo Zheng
Keyword(s):  
State Estimation ◽  
Numerical Stability ◽  
Stability Problem ◽  
Jacobian Matrix ◽  
Estimation Method ◽  
Constant Matrix ◽  
Equivalent Current ◽  
Scada System ◽  
Current State ◽  
Secondary Factor

One of the most important ways to enhance the speed of state estimation is to establish the constant matrix Jacobian. This essay puts forward the state estimation method of the equivalent current transformation based on the Generalized Tellegens Theorem. This estimation method establishes the constant Jacobian matrix without neglecting the secondary factor making use of the Generalized Tellegens Theorem, solves the numerical stability problem caused by the establishment of the constant Jacobian matrix in the current state estimation, and has the advantages of a relatively rapid computing rate, making advantage of measuremnt of WAMS and SCADA system, and an unparalleled astringency. The method put forward in this essay has been verified through IEEE-30 Node System, and the efficiency of it has been fully proved by the example results.

scholarly journals Compliant behaviour of redundant robot arm - experiments with null-space

2015 ◽  
Vol 12 (1) ◽  
pp. 81-98
Author(s):  
Petar Petrovic ◽  
Nikola Lukic ◽  
Ivan Danilov
Keyword(s):  
Stiffness Matrix ◽  
Jacobian Matrix ◽  
Null Space ◽  
Joint Space ◽  
Robot Arm ◽  
Kinematic Redundancy ◽  
Redundant Robot ◽  
Redundant Robots ◽  
Compliant Behavior ◽  
Congruent Transformation

This paper presents theoretical and experimental aspects of Jacobian nullspace use in kinematically redundant robots for achieving kinetostatically consistent control of their compliant behavior. When the stiffness of the robot endpoint is dominantly influenced by the compliance of the robot joints, generalized stiffness matrix can be mapped into joint space using appropriate congruent transformation. Actuation stiffness matrix achieved by this transformation is generally nondiagonal. Off-diagonal elements of the actuation matrix can be generated by redundant actuation only (polyarticular actuators), but such kind of actuation is very difficult to realize practically in technical systems. The approach of solving this problem which is proposed in this paper is based on the use of kinematic redundancy and nullspace of the Jacobian matrix. Evaluation of the developed analytical model was done numerically by a minimal redundant robot with one redundant d.o.f. and experimentally by a 7 d.o.f. Yaskawa SIA 10F robot arm.

scholarly journals Constraint Analysis and Redundancy of Planar Closed Loop Double Chain Linkages

2014 ◽  
Vol 6 ◽  
pp. 635423 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Yixiang Xu ◽  
Jian Feng
Keyword(s):  
Boundary Conditions ◽  
Closed Loop ◽  
Jacobian Matrix ◽  
Null Space ◽  
Degree Of Freedom ◽  
Double Chain ◽  
Constraint Equations ◽  
System Constraint ◽  
Natural Coordinate ◽  
Planar Linkages

This paper studies the kinematics of planar closed double chain linkages using the natural coordinate method. Different constraints including the rigid bar, pin joint, generalized angulated element (GAE) joint, and the boundary conditions of linkages were firstly used to form the system constraint equations. Then the degree of freedom of the linkages was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints can also be given by this method. Many types of planar linkages, such as the Hoberman linkage, Types I and II GAEs, nonintersecting GAEs, and linkages with the loop parallelogram condition, were investigated in this paper. It is found that when three boundary conditions are added to the system, the global motion of the system is lost. The results show that these linkages have only one degree of freedom. Moreover, the last two GAE constraints of the numerical examples given in this paper are redundant.

A Robust Null Space Method for Linear Equality Constrained State Estimation

2010 ◽  
Vol 58 (8) ◽  
pp. 3961-3971 ◽  
Author(s):  
Russell J. Hewett ◽  
Michael T. Heath ◽  
Mark D. Butala ◽  
Farzad Kamalabadi
Keyword(s):  
State Estimation ◽  
Null Space ◽  
Linear Equality ◽  
Space Method

Mobility and Kinematic Analysis of Foldable Plate Structures Based on Rigid Origami

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jianguo Cai ◽  
Zelun Qian ◽  
Chao Jiang ◽  
Jian Feng ◽  
Yixiang Xu
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Null Space ◽  
Building Structures ◽  
Rigid Plate ◽  
Deployable Structures ◽  
Plate Structures ◽  
Constraint Equations ◽  
New Type ◽  
System Constraint

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

MOTION RECOVERY AFTER JOINT FAILURE IN PARALLEL MANIPULATORS

2011 ◽  
Vol 35 (4) ◽  
pp. 559-571 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Jacobian Matrix ◽  
Null Space ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Partial Recovery ◽  
Joint Failure ◽  
Motion Recovery ◽  
Motion Performance ◽  
Planar Parallel Manipulators

In this paper, the failure of parallel manipulators is investigated. Failure modes of parallel manipulators and their causes and effects from the kinematics point of view are discussed. Methodologies for investigating the effect of failures, due to joint failure or singularity, on the motion performance of manipulators are presented, and the criteria for full and partial recovery from these failures are established. The proposed methodologies are based on the projection of the lost motion onto the orthogonal complement of the null space of the Jacobian matrix after failure. The procedure is simulated for planar parallel manipulators to examine if after joint failure the required motion of manipulator could be fully recovered; as well as to calculate the corrections to the motion of remaining joints for recovering the lost motion.

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