Singularities of Holonomic and Non-holonomic Robotic Systems: A Normal Form Approach

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Joanna Ratajczak
Keyword(s):  
Normal Form ◽  
Robotic Systems ◽  
Form Approach

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

A New Mechanical Algorithm for Calculating the Amplitude Equation of the Reaction-Diffusion Systems

2011 ◽  
pp. 205-213
Author(s):  
Houye Liu ◽  
Weiming Wang
Keyword(s):  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Normal Form ◽  
Reaction Diffusion ◽  
Amplitude Equation ◽  
Diffusion Reaction ◽  
Future Studies ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Form Approach

Amplitude equation may be used to study pattern formatio. In this chapter, we establish a new mechanical algorithm AE_Hopf for calculating the amplitude equation near Hopf bifurcation based on the method of normal form approach in Maple. The normal form approach needs a large number of variables and intricate calculations. As a result, deriving the amplitude equation from diffusion-reaction is a difficult task. Making use of our mechanical algorithm, we derived the amplitude equations from several biology and physics models. The results indicate that the algorithm is easy to apply and effective. This algorithm may be useful for learning the dynamics of pattern formation of reaction-diffusion systems in future studies.

scholarly journals A Closed-Form Approach to Determine the Base Inertial Parameters of Complex Structured Robotic Systems

2015 ◽  
Vol 48 (1) ◽  
pp. 316-321 ◽  
Author(s):  
J. Klodmann ◽  
D. Lakatos ◽  
C. Ott ◽  
A. Albu-Schäffer
Keyword(s):  
Closed Form ◽  
Robotic Systems ◽  
Inertial Parameters ◽  
Base Inertial Parameters ◽  
Form Approach

CODIMENSION ONE BIFURCATION OF EQUIVARIANT NEURAL NETWORK MODEL WITH DELAY

2010 ◽  
Vol 20 (04) ◽  
pp. 1255-1259
Author(s):  
CHUNRUI ZHANG ◽  
BAODONG ZHENG
Keyword(s):  
Neural Network ◽  
Normal Form ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Double Zero ◽  
Codimension One ◽  
Bam Neural Network ◽  
Manifold Theory ◽  
Form Approach

In this paper, we consider double zero singularity of a symmetric BAM neural network model with a time delay. Based on the normal form approach and the center manifold theory, we obtain the normal form on the centre manifold with double zero singularity. Some numerical simulations support our analysis results.

scholarly journals Controllability and local accessibility - A normal form approach

2003 ◽  
Vol 48 (10) ◽  
pp. 1724-1736 ◽  
Author(s):  
Wei Kang ◽  
Mingqing Xiao ◽  
I.A. Tall
Keyword(s):  
Normal Form ◽  
Form Approach
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