Redundancy Resolution of Robotic Manipulators Using Normalized Generalized Inverses

1995 ◽  
Vol 117 (3) ◽  
pp. 454-459 ◽  
Author(s):  
J. T. Wang
Keyword(s):  
Generalized Inverse ◽  
Robotic Manipulators ◽  
Redundancy Resolution ◽  
Objective Functions ◽  
Dynamical Equations ◽  
Kinematic Constraint ◽  
Joint Torques ◽  
Constraint Equations ◽  
Force Method ◽  
Inverse Form

A dynamical formulation based upon the undetermined force method is presented for analyzing redundant robotic manipulators. The equivalence between this dynamical formulation and the general solution of kinematic constraint equations is then obtained through use of a normalized generalized inverse. This leads to a special form of the dynamical equations, called the N-inverse form of the dynamical equations. A class of problems, associated with the optimization of quadratic objective functions, are then studied. We find that the N-inverse form of the dynamical equations is the solution of this class of problems. Examples, including local minimization of joint torques and global minimization of kinetic energy, are presented.

Comparison of Different Methods to Control Constraints Violation in Forward Multibody Dynamics

2013 ◽  
Author(s):  
Paulo Flores ◽  
Parviz E. Nikravesh
Keyword(s):  
Multibody Dynamics ◽  
Multibody Systems ◽  
Generalized Inverse ◽  
Jacobian Matrix ◽  
Equations Of Motion ◽  
Control Constraints ◽  
Algebraic Equations ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Velocity Constraint

The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

Efficient Dynamic Analysis Method for Multibody Systems With Constraint Violation Stabilization Method

1999 ◽  
Author(s):  
Apiwat Reungwetwattana ◽  
Shigeki Toyama
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Analysis Method ◽  
Stabilization Method ◽  
Kinematic Constraint ◽  
Constraint Violation ◽  
Closed Loops ◽  
Constraint Stabilization ◽  
Constraint Equations ◽  
Crank Mechanism

Abstract This paper presents an efficient extension of Rosenthal’s order-n algorithm for multibody systems containing closed loops. Closed topological loops are handled by cut joint technique. Violation of the kinematic constraint equations of cut joints is corrected by Baumgarte’s constraint violation stabilization method. A reliable approach for selecting the parameters used in the constraint stabilization method is proposed. Dynamic analysis of a slider crank mechanism is carried out to demonstrate efficiency of the proposed method.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

scholarly journals Path planning optimization of six-degree-of-freedom robotic manipulators using evolutionary algorithms

2020 ◽  
Vol 17 (2) ◽  
pp. 172988142090807
Author(s):  
Sandi Baressi Šegota ◽  
Nikola Anđelić ◽  
Ivan Lorencin ◽  
Milan Saga ◽  
Zlatan Car
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Differential Evolution ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Degree Of Freedom ◽  
Joint Torques ◽  
Point To Point ◽  
Computation Algorithms ◽  
Six Degree Of Freedom

Lowering joint torques of a robotic manipulator enables lowering the energy it uses as well as increase in the longevity of the robotic manipulator. This article proposes the use of evolutionary computation algorithms for optimizing the paths of the robotic manipulator with the goal of lowering the joint torques. The robotic manipulator used for optimization is modelled after a realistic six-degree-of-freedom robotic manipulator. Two cases are observed and these are a single robotic manipulator carrying a weight in a point-to-point trajectory and two robotic manipulators cooperating and moving the same weight along a calculated point-to-point trajectory. The article describes the process used for determining the kinematic properties using Denavit–Hartenberg method and the dynamic equations of the robotic manipulator using Lagrange–Euler and Newton–Euler algorithms. Then, the description of used artificial intelligence optimization algorithms is given – genetic algorithm using random and average recombination, simulated annealing using linear and geometric cooling strategy and differential evolution. The methods are compared and the results show that the genetic algorithm provides best results in regard to torque minimization, with differential evolution also providing comparatively good results and simulated annealing giving the comparatively weakest results while providing smoother torque curves.

Dynamics of Constrained Multibody Systems

1984 ◽  
Vol 51 (4) ◽  
pp. 899-903 ◽  
Author(s):  
J. W. Kamman ◽  
R. L. Huston
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Closed Loops ◽  
Constrained Multibody Systems ◽  
Constraint Equations ◽  
Cable Dynamics ◽  
Hanging Chain ◽  
A Chain

A new automated procedure for obtaining and solving the governing equations of motion of constrained multibody systems is presented. The procedure is applicable when the constraints are either (a) geometrical (for example, “closed-loops”) or (b) kinematical (for example, specified motion). The procedure is based on a “zero eigenvalues theorem,” which provides an “orthogonal complement” array which in turn is used to contract the dynamical equations. This contraction, together with the constraint equations, forms a consistent set of governing equations. An advantage of this formulation is that constraining forces are automatically eliminated from the analysis. The method is applied with Kane’s equations—an especially convenient set of dynamical equations for multibody systems. Examples of a constrained hanging chain and a chain whose end has a prescribed motion are presented. Applications in robotics, cable dynamics, and biomechanics are suggested.

The influence of manufacturing tolerances on the kinematic performance of mechanisms

1998 ◽  
Vol 212 (1) ◽  
pp. 35-47 ◽  
Author(s):  
A A Fogarasy ◽  
M R Smith
Keyword(s):  
Linear Systems ◽  
Linear Dimension ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Non Linear ◽  
Manufacturing Tolerances ◽  
Kinematic Performance ◽  
Non Linear Systems

The well-established theory of linear dimension and tolerance chains has been extended to include non-linear systems, such as linkage mechanisms, employing a technique based on the use of kinematic constraint equations. The results are interpreted with reference to production and assembly technologies and two examples are analysed to demonstrate the application of the technique.

Sign in / Sign up

Export Citation Format

Share Document