Homogenization of the Jacobian Matrix of Manipulators by Using Inertial Parameters

2018 ◽  
pp. 219-226
Author(s):  
J. A. Pamanes ◽  
H. A. Moreno
Keyword(s):  
Jacobian Matrix ◽  
Inertial Parameters

The Robust Adaptive Control of Free-Floating Space Manipulator Systems

2001 ◽  
Author(s):  
Chen Li ◽  
Liu Yanzhu
Keyword(s):  
Adaptive Control ◽  
Jacobian Matrix ◽  
Robust Adaptive Control ◽  
Dynamic Equations ◽  
Generalized Jacobian ◽  
Space Manipulator ◽  
Floating Base ◽  
Inertial Parameters ◽  
Control Scheme ◽  
Robust Adaptive

Abstract In this paper, the kinematics and dynamics of free-floating space manipulator systems are analyzed, and it is shown that the Jacobian matrix and the dynamic equations of the system are nonlinearly dependent on inertial parameters. In order to overcome the above problems, the system is modeled as under-actuated robot system, and the idea of augmentation approach is adopted. It is demonstrate that the augmented generalized Jacobian matrix and the dynamic equations of the system can be linearly dependent on a group of inertial parameters. Based on the results, the robust adaptive control scheme for free-floating space manipulator with uncertain inertial parameters to track the desired trajectory in workspace is proposed, and a two-link planar space manipulator system is simulated to verify the proposed control scheme. The proposed control scheme is computationally simple, because we choose to make the controller robust to the uncertain inertial parameters rather than explicitly estimating them online. In particular, it require neither measuring the position, velocity and acceleration of the floating base with respect to the orbit nor controlling the position and attitude angle of the floating base.

The Composite Adaptive Control of Free-Floating Space Robot System With Prismatic Joint

2001 ◽  
Author(s):  
Li Chen ◽  
Yanzhu Liu
Keyword(s):  
Adaptive Control ◽  
Jacobian Matrix ◽  
Jacobi Matrix ◽  
Space Robot ◽  
Robot System ◽  
Prismatic Joint ◽  
Inertial Parameters ◽  
Control Scheme ◽  
Generalized Jacobi Matrix ◽  
Composite Adaptive Control

Abstract In this paper, the kinematics and dynamics of a free-floating space robot system with prismatic joint are analyzed, and it is shown that the Jacobian matrix and the dynamic equations of the system cannot be linearly parameterized. With the augmentation approach, we demonstrate that the augmented generalized Jacobi matrix and the dynamic equation of the system can be linearly dependent on inertial parameters. Based on the results, the composite adaptive control scheme for a free-floating space robot with unknown inertial parameters to track the desired trajectory in workspace is proposed, and a two-link planar space robot system with prismatic joint is simulated to verify the proposed control scheme.

Improved Cubature Kalman Filtering-Based Estimation of the Jacobian Matrix for Environment Mutation

2019 ◽  
Author(s):  
Xiuqian Jia ◽  
Haixia Wang ◽  
Chunyang Sheng ◽  
Zhiguo Zhang ◽  
Wei Cui ◽  
...  
Keyword(s):  
Kalman Filtering ◽  
Jacobian Matrix

scholarly journals The dynamics of a Leslie type predator–prey model with fear and Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan ◽  
Bundit Unyong ◽  
Grienggrai Rajchakit ◽  
...  
Keyword(s):  
Local Stability ◽  
Allee Effect ◽  
Jacobian Matrix ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Lyapunov Coefficient ◽  
Points Of View ◽  
Two Parameter

AbstractIn this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.

Parameter Normalization in Multibody Dynamics

2008 ◽  
Author(s):  
Saeed Ebrahimi ◽  
Jo´zsef Ko¨vecses
Keyword(s):  
Parameter Estimation ◽  
Multibody Dynamics ◽  
Eigenvalue Problems ◽  
Physical Structure ◽  
Control Problems ◽  
Inertial Parameters ◽  
Parametric Studies ◽  
Novel Concept ◽  
And Control

In this paper, we introduce a novel concept for parametric studies in multibody dynamics. This is based on a technique that makes it possible to perform a natural normalization of the dynamics in terms of inertial parameters. This normalization technique rises out from the underlying physical structure of the system, which is mathematically expressed in the form of eigenvalue problems. It leads to the introduction of the concept of dimensionless inertial parameters. This, in turn, makes the decomposition of the array of parameters possible for studying design and control problems where parameter estimation and sensitivity is of importance.

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
M. F. Ruiz-Torres ◽  
E. Castillo-Castaneda ◽  
J. A. Briones-Leon
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Geometric Analysis ◽  
Vector Equation ◽  
Prismatic Joints ◽  
Hollow Cylinders ◽  
Moving Platform ◽  
Direct Kinematics

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

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