Mobile manipulator modeling with Kane's approach

Robotica ◽  
2001 ◽  
Vol 19 (6) ◽  
pp. 675-690 ◽  
Author(s):  
Herbert G. Tanner ◽  
Kostas J. Kyriakopoulos
Keyword(s):  
Control Strategies ◽  
Nonholonomic Constraints ◽  
Dynamic Equations ◽  
Mobile Manipulator ◽  
Constraint Equations ◽  
Motion Constraints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Physical Insight ◽  
Complete Framework

A wheeled mobile manipulator system is modeled using Kane's dynamic equations. Kane's equations are constructed with minimum effort, are control oriented and provide both physical insight and fast simulations. The powerful tools of Kane's approach for incorporating nonholonomic motion constraints and bringing noncontributing forces into evidence are exploited. Both nonholonomic constraints associated with slipping and skidding as well as conditions for avoiding tipping over are included. The resulting equations, along with the set of constraint equations provide a safe and complete framework for developing control strategies for mobile manipulator systems.

A Recursive Approach for Analysis of Snake Robots Using Kane’s Equations

2005 ◽  
Author(s):  
Hadi Tavakoli Nia ◽  
Hossein Nejat Pishkenari ◽  
Ali Meghdari
Keyword(s):  
Nonholonomic Constraints ◽  
Dynamic Equations ◽  
Snake Robot ◽  
Euler’S Method ◽  
Cpu Time ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Link Model ◽  
Computational Procedures ◽  
Snake Robots

This paper presents a recursive approach for solving kinematic and dynamic problem in snake-like robots using Kane’s equations. An n-link model with n-nonholonomic constraints is used as the snake robot model in our analysis. The proposed algorithm which is used to derive kinematic and dynamic equations recursively enhances the computational efficiency of our analysis. Using this method we can determine the number of additions and multiplications as a function of n. The proposed method is compared with the Lagrange and Newton-Euler’s method in three different aspects: Number of operations, CPU time and error in the computational procedures.

Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach

1988 ◽  
Vol 55 (4) ◽  
pp. 899-904 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Null Space ◽  
Computationally Efficient ◽  
New Approach ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Linearly Independent ◽  
Kane's Equations ◽  
Constrained Dynamical Systems ◽  
Coordinate Reduction ◽  
Algebraic Constraint

In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

Dynamics of Large Constrained Flexible Structures

1988 ◽  
Vol 110 (1) ◽  
pp. 78-83 ◽  
Author(s):  
F. M. L. Amirouche ◽  
R. L. Huston
Keyword(s):  
Structure Analysis ◽  
Flexible Structures ◽  
Orthogonal Complement ◽  
Space Structures ◽  
Governing Equations ◽  
Finite Segment ◽  
Closed Loops ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Kane's Equations

This paper presents an automated procedure useful in the study of large constrained flexible structures, undergoing large specified motions. The structure is looked upon as a “partially open tree” system, containing closed loops in some of the branches. The governing equations are developed using Kane’s equations as formulated by Huston et al. The accommodation of the constraint equations is based on the use of orthogonal complement arrays. The flexibility and oscillations of the bodies is modelled using finite segment modelling, structure analysis, and scaling techniques. The procedures developed are expected to be useful in applications including robotics, space structures, and biosystems.

A fresh insight into Kane's equations of motion

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 498-510 ◽  
Author(s):  
H. Nejat Pishkenari ◽  
S. A. Yousefsani ◽  
A. L. Gaskarimahalle ◽  
S. B. G. Oskouei
Keyword(s):  
Dynamic Systems ◽  
Rapid Development ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
The Matrix ◽  
Impulsive Forces ◽  
Multi Body ◽  
Fresh Insight

SUMMARYWith rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.

A Conservation Theorem for Constrained Multibody Systems

1993 ◽  
Vol 60 (4) ◽  
pp. 962-969
Author(s):  
J. T. Wang
Keyword(s):  
Multibody Systems ◽  
Nonholonomic Constraints ◽  
First Integral ◽  
Integral Of Motion ◽  
Power Equation ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Power And Energy ◽  
Conservation Theorem ◽  
General Conservation

This paper presents a general conservation theorem for multibody systems subject to simple nonholonomic constraints. It is applicable to both conservative and nonconservative systems. The derivation of this theorem is based on Kane’s equations with undetermined multipliers. A power equation and a first integral of motion have been derived. They emerge in physically meaningful forms and include expressions for evaluating the power and energy flowing into the system. Like Kane’s equations, the power equation and the first integral of motion are derived in matrix form. This makes them particularly useful for the computer formulation and solution of multibody system dynamics.

A recursive approach for the analysis of snake robots using Kane's equations

Robotica ◽  
2006 ◽  
Vol 24 (2) ◽  
pp. 251-256 ◽  
Author(s):  
H. Tavakoli Nia ◽  
H. N. Pishkenari ◽  
A. Meghdari
Keyword(s):  
Nonholonomic Constraints ◽  
Dynamic Problems ◽  
Snake Robot ◽  
Euler’S Method ◽  
Cpu Time ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Link Model ◽  
Computational Procedures ◽  
Snake Robots

This paper presents a recursive approach for solving kinematic and dynamic problems in snake-like robots using Kane's equations. An n-link model with n-nonholonomic constraints is used as the snake robot model in our analysis. The proposed algorithm which is used to derive kinematic and dynamic equations recursively, enhances the computational efficiency of our analysis. Using this method we can determine the number of additions and multiplications as a function of n. The proposed method is compared with the Lagrange and Newton-Euler's method in three different aspects: Number of operations, CPU time and error in the computational procedures.

scholarly journals On path following control of nonholonomic mobile manipulators

2009 ◽  
Vol 19 (4) ◽  
pp. 561-574 ◽  
Author(s):  
Alicja Mazur ◽  
Dawid Szakiel
Keyword(s):  
Control Algorithm ◽  
Dynamic Control ◽  
Path Following ◽  
Mobile Manipulator ◽  
Mobile Manipulators ◽  
Control Laws ◽  
Kinematic Control ◽  
Motion Constraints ◽  
Path Following Control ◽  
Cascade Structure

On path following control of nonholonomic mobile manipulatorsThis paper describes the problem of designing control laws for path following robots, including two types of nonholonomic mobile manipulators. Due to a cascade structure of the motion equation, a backstepping procedure is used to achieve motion along a desired path. The control algorithm consists of two simultaneously working controllers: the kinematic controller, solving motion constraints, and the dynamic controller, preserving an appropriate coordination between both subsystems of a mobile manipulator, i.e. the mobile platform and the manipulating arm. A description of the nonholonomic subsystem relative to the desired path using the Frenet parametrization is the basis for formulating the path following problem and designing a kinematic control algorithm. In turn, the dynamic control algorithm is a modification of a passivity-based controller. Theoretical deliberations are illustrated with simulations.

scholarly journals Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Coupled System ◽  
Weak Form ◽  
Integration Scheme ◽  
Motion Constraints ◽  
Multibody Dynamic ◽  
Time Integration Scheme

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

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