Redundant Robot Kinematics Error Analysis for Neurosurgical Procedures

SummaryFor redundant robot kinematics with a degree of redundancy 1 a self-motion vector field is examined whose equilibrium points lie at singular configurations of the kinematics, and whose orbits determine the self-motion manifolds. It is proved that the self-motion vector field is divergence-free. Locally, around singular configurations of corank 1, the self-motion vector field defines a 2-dimensional Hamiltonian dynamical system. An analysis of the phase portrait of this system in a neighbourhood of a singular configuration solves completely the question of avoidability or unavoidability of this configuration. Complementarily, sufficient conditions for avoidability and unavoidability are proposed in an analytic form involving the self-motion Hamilton function. The approach is illustrated with examples. A connection with normal forms of kinematics is established.

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Redundant Robot Kinematics Control with HCMAC Neural Network Manipulability Enhancement

IFAC Proceedings Volumes ◽

10.3182/20080706-5-kr-1001.00919 ◽

2008 ◽

Vol 41 (2) ◽

pp. 5450-5455

Author(s):

V. Řikovský ◽

Š. Kozák

Keyword(s):

Neural Network ◽

Robot Kinematics ◽

Redundant Robot

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Quadratic normal forms of redundant robot kinematics with application to singularity avoidance

IEEE Transactions on Robotics and Automation ◽

10.1109/70.720360 ◽

1998 ◽

Vol 14 (5) ◽

pp. 834-837 ◽

Cited By ~ 4

Author(s):

K. Tchon

Keyword(s):

Normal Forms ◽

Robot Kinematics ◽

Redundant Robot ◽

Singularity Avoidance

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Error Analysis in Solving the Inverse Problem of the Cable-driven Parallel Underactuated Robot Kinematics and Methods for their Elimination

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2019.11.352 ◽

2019 ◽

Vol 52 (13) ◽

pp. 1156-1161

Author(s):

Alexander V. Maloletov ◽

Mikhail Y. Fadeev ◽

Alexandr S. Klimchik

Keyword(s):

Inverse Problem ◽

Error Analysis ◽

Robot Kinematics ◽

Underactuated Robot

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Performance Analysis of Numerical Integration Methods in the Trajectory Tracking Application of Redundant Robot Manipulators

International Journal of Advanced Robotic Systems ◽

10.5772/45682 ◽

2011 ◽

Vol 8 (5) ◽

pp. 63 ◽

Cited By ~ 5

Author(s):

Emre Sariyildiz ◽

Hakan Temeltas

Keyword(s):

Numerical Integration ◽

Trajectory Tracking ◽

Robot Manipulator ◽

Robot Manipulators ◽

Inverse Kinematic ◽

Robot Kinematics ◽

Integration Methods ◽

Redundant Robot ◽

Kinematic Method ◽

Numerical Integration Methods

Differential kinematic is one of the most important solution methods in robot kinematics. The main advantage of the differential kinematic method is that it can be easily implemented any kind of mechanisms. Also, an accurate and efficient kinematic based trajectory tracking application can be easily implemented by using this method. In differential kinematic method, we use Jacobian as a mapping operator in the velocity space. Inversion of Jacobian matrix transforms the desired trajectory velocities, which are the linear and angular velocities of the end effector, into the joint velocities. The joint velocities are required to be integrated to obtain the pose of the robot manipulator. This integration can be evaluated by using numerical integration methods, since the inverse kinematic equations are highly complex and nonlinear. Therefore, the performance of the trajectory tracking application of the robot manipulator is directly affected by the chosen numerical integration method. This paper compares the performances of numerical integration methods in the trajectory tracking application of redundant robot manipulators. Several widely used numerical integration methods are implemented into the trajectory tracking application of the 7-DOF redundant robot manipulator named PA-10 and simulation results are given.

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The O–C diagrams of minor planets − a new approach to modelling the rotation

International Astronomical Union Colloquium ◽

10.1017/s0252921100031407 ◽

1999 ◽

Vol 173 ◽

pp. 185-188

Author(s):

Gy. Szabó ◽

K. Sárneczky ◽

L.L. Kiss

Keyword(s):

Error Analysis ◽

Time Dependence ◽

Theoretical Work ◽

Minor Planet ◽

Minor Planets ◽

New Approach ◽

Preliminary Results ◽

Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

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Error Analysis in Neuropsychological Assessment of Verbal Memory and Learning

European Journal of Psychological Assessment ◽

10.1027/1015-5759.11.1.21 ◽

1995 ◽

Vol 11 (1) ◽

pp. 21-28 ◽

Cited By ~ 5

Author(s):

Dietmar Heubrock

Keyword(s):

Error Analysis ◽

Verbal Memory ◽

Verbal Learning ◽

Learning Disorders ◽

Memory And Learning ◽

Auditory Verbal Learning Test ◽

Additional Information ◽

Auditory Verbal Learning ◽

Accurate Picture ◽

Learning Test

Performance on a German version of the Rey Auditory-Verbal Learning Test (AVLT) was investigated for 64 juvenile patients who were subdivided in 6 clinical groups. In addition to standard evaluation of AVLT protocols which is usually confined to items recalled correctly, an error analysis was performed. Differentiating between total errors (TE), repetition errors (RE), and misnamings (ME), substantial differences between clinical groups could be demonstrated. It is argued that error analysis of verbal memory and learning enriches the understanding of neuropsychological syndromes, and provides additional information for diagnostic and clinical use. Thus, it is possible to gain a more accurate picture so that patients can be appropriately retrained, and research into the functional causes of memory and learning disorders can be intensified.

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