Natural Dynamics of Robot Manipulators in the Presence of Obstacles

1991 ◽  
Vol 113 (1) ◽  
pp. 170-174
Author(s):  
T. Jia ◽  
F. M. L. Amirouche
Keyword(s):  
Collision Detection ◽  
Jacobian Matrix ◽  
Null Space ◽  
Robot Manipulators ◽  
Dynamic Control ◽  
Inequality Constraints ◽  
Dimensional Problem ◽  
Constraint Equations ◽  
Natural Dynamics ◽  
Natural Dynamic

This paper presents the natural dynamic control problem of robot manipulators and its application to collision avoidance and path planning. A set of moving convex obstacles (or polyhedron) are modeled to achieve the desired conditions for collision detection and avoidance. The conditions represent a set of inequality constraints which are automatically incorporated to assure collision free motion. A minimum dimensional problem is achieved through the use of the null space of the Jacobian matrix associated with the constraint equations. A simple example to illustrate the procedures developed above is given.

Analysis of Active Joint Failure in Parallel Robot Manipulators

2004 ◽  
Vol 126 (6) ◽  
pp. 959-968 ◽  
Author(s):  
Mahir Hassan ◽  
Leila Notash
Keyword(s):  
Jacobian Matrix ◽  
Null Space ◽  
Robot Manipulators ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Task Space ◽  
Active Joint ◽  
Joint Failure ◽  
Space Vectors ◽  
Six Degree Of Freedom

In this study, the effect of active joint failure on the mobility, velocity, and static force of parallel robot manipulators is investigated. Two catastrophic active joint failure types are considered: joint jam and actuator force loss. To investigate the effect of failure on mobility, the Gru¨bler’s mobility equation is modified to take into account the kinematic constraints imposed by various branches in the manipulator. In the case of joint jam, the manipulator loses the ability to move and apply force in a specific portion of its task space; while in the case of actuator force loss, the manipulator gains an unconstrained motion in a specific portion of the task space in which an externally applied force cannot be resisted by the actuator forces. The effect of joint jam and actuator force loss on the velocity and on the force capabilities of parallel manipulators is investigated by examining the change in the Jacobian matrix, its inverse, and transposes. It is shown that the reduced velocity and force capabilities after joint jam and loss of actuator force could be determined using the null space vectors of the transpose of the Jacobian matrix and its inverse. Computer simulation is conducted to demonstrate the application of the developed methodology in determining the post-failure trajectory of a 3-3 six-degree-of-freedom Stewart-Gough manipulator, when encountering active joint jam and actuator force loss.

scholarly journals Constraint Analysis and Redundancy of Planar Closed Loop Double Chain Linkages

2014 ◽  
Vol 6 ◽  
pp. 635423 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Yixiang Xu ◽  
Jian Feng
Keyword(s):  
Boundary Conditions ◽  
Closed Loop ◽  
Jacobian Matrix ◽  
Null Space ◽  
Degree Of Freedom ◽  
Double Chain ◽  
Constraint Equations ◽  
System Constraint ◽  
Natural Coordinate ◽  
Planar Linkages

This paper studies the kinematics of planar closed double chain linkages using the natural coordinate method. Different constraints including the rigid bar, pin joint, generalized angulated element (GAE) joint, and the boundary conditions of linkages were firstly used to form the system constraint equations. Then the degree of freedom of the linkages was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints can also be given by this method. Many types of planar linkages, such as the Hoberman linkage, Types I and II GAEs, nonintersecting GAEs, and linkages with the loop parallelogram condition, were investigated in this paper. It is found that when three boundary conditions are added to the system, the global motion of the system is lost. The results show that these linkages have only one degree of freedom. Moreover, the last two GAE constraints of the numerical examples given in this paper are redundant.

Mobility and Kinematic Analysis of Foldable Plate Structures Based on Rigid Origami

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jianguo Cai ◽  
Zelun Qian ◽  
Chao Jiang ◽  
Jian Feng ◽  
Yixiang Xu
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Null Space ◽  
Building Structures ◽  
Rigid Plate ◽  
Deployable Structures ◽  
Plate Structures ◽  
Constraint Equations ◽  
New Type ◽  
System Constraint

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

Mobility and Kinematic Paths of Foldable Origami Structures

2016 ◽  
Author(s):  
Jianguo Cai ◽  
Zelun Qian ◽  
Jian Feng ◽  
Chao Jiang ◽  
Yixiang Xu
Keyword(s):  
Jacobian Matrix ◽  
Null Space ◽  
Degree Of Freedom ◽  
Building Structures ◽  
Deployable Structures ◽  
Plate Structures ◽  
Constraint Equations ◽  
All Solutions ◽  
New Type ◽  
System Constraint

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, pin joints and the boundary conditions of linkages were firstly used to generate the system constraint equations. Then the degree of freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method and multiple kinematic paths existing in origami structures were studied by obtaining all solutions of constraint equations. Different solutions represent different kinematic configurations. The degree of freedom and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in details.

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.

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.

Development of Driving Training Simulator of a Caterpillar Vehicle

2013 ◽  
Vol 380-384 ◽  
pp. 2653-2657
Author(s):  
Jing Tao Zhou ◽  
Huai Guang Wang ◽  
Liang Zhou
Keyword(s):  
Collision Detection ◽  
Dynamic Control ◽  
Scene Modeling ◽  
Training Simulator ◽  
Special Effects ◽  
Technical Problems ◽  
Sound Control ◽  
3D Scene ◽  
Communication Control ◽  
And Training

Driving training simulator of a caterpillar vehicle is a simulation system which can simulate all kinds of training course and has the evaluation function, this system using VC++ 6.0 and Direct X software, which has solved the 3D modeling, model introduction, 3D scene modeling, view dynamic control, collision detection, communication control, special effects, sound control, and other key technical problems, it has meted effectively the new equipment teaching and training needs.

ON THE COLLISION DETECTION PROBLEM FOR ROBOT MANIPULATORS

1995 ◽  
Vol 26 (2) ◽  
pp. 189-210 ◽  
Author(s):  
Mark Gill ◽  
Albert Zomaya
Keyword(s):  
Collision Detection ◽  
Robot Manipulators ◽  
Detection Problem

scholarly journals Compliant behaviour of redundant robot arm - experiments with null-space

2015 ◽  
Vol 12 (1) ◽  
pp. 81-98
Author(s):  
Petar Petrovic ◽  
Nikola Lukic ◽  
Ivan Danilov
Keyword(s):  
Stiffness Matrix ◽  
Jacobian Matrix ◽  
Null Space ◽  
Joint Space ◽  
Robot Arm ◽  
Kinematic Redundancy ◽  
Redundant Robot ◽  
Redundant Robots ◽  
Compliant Behavior ◽  
Congruent Transformation

This paper presents theoretical and experimental aspects of Jacobian nullspace use in kinematically redundant robots for achieving kinetostatically consistent control of their compliant behavior. When the stiffness of the robot endpoint is dominantly influenced by the compliance of the robot joints, generalized stiffness matrix can be mapped into joint space using appropriate congruent transformation. Actuation stiffness matrix achieved by this transformation is generally nondiagonal. Off-diagonal elements of the actuation matrix can be generated by redundant actuation only (polyarticular actuators), but such kind of actuation is very difficult to realize practically in technical systems. The approach of solving this problem which is proposed in this paper is based on the use of kinematic redundancy and nullspace of the Jacobian matrix. Evaluation of the developed analytical model was done numerically by a minimal redundant robot with one redundant d.o.f. and experimentally by a 7 d.o.f. Yaskawa SIA 10F robot arm.

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