Rational Motion Interpolation Under Kinematic Constraints of Spherical 6R Closed Chains

2007 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Iterative Algorithm ◽  
Ordered Set ◽  
Extreme Points ◽  
Rational Curves ◽  
Geometric Constraints ◽  
Constrained Motion ◽  
Kinematic Constraints ◽  
Cartesian Space ◽  
Rational Spline ◽  
Closed Chain

The work reported in this paper brings together the kinematics of spherical closed chains and the recently developed freeform rational motions to study the problem of synthesizing rational interpolating motions under the kinematic constraints of spherical 6R closed chains. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational spherical motions for spherical open chains. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of spherical closed chains in the Cartesian space. Quaternions are used to represent spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions. The kinematic constraints are transformed into geometric constraints for the design of quaternion curves. An iterative algorithm for constrained motion interpolation is presented that detects the violation of the kinematic constraints by searching for those extreme points of the quaternion curve that do not satisfy the constraints. Such extreme points are modified so that the constraints are satisfied and the resulting new points are added to the ordered set of the initial positions to be interpolated. An example is presented to show how this algorithm produces smooth spherical rational spline motions that satisfy the kinematic constraints of a spherical 6R closed chain. The algorithm can also be used for the synthesis of rational interpolating motions that approximate the kinematic constraints of spherical 5R and 4R closed chains within a user-defined tolerance.

Rational Motion Interpolation Under Kinematic Constraints of Spherical 6R Closed Chains

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Ordered Set ◽  
Extreme Points ◽  
Rational Curves ◽  
Geometric Constraints ◽  
Free Form ◽  
Constrained Motion ◽  
Kinematic Constraints ◽  
Cartesian Space ◽  
Rational Spline ◽  
Closed Chain

The work reported in this paper brings together the kinematics of spherical closed chains and the recently developed free-form rational motions to study the problem of synthesizing rational interpolating motions under the kinematic constraints of spherical 6R closed chains. The results presented in this paper are an extension of our previous work on the synthesis of piecewise rational spherical motions for spherical open chains. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of spherical closed chains in the Cartesian space. Quaternions are used to represent spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions. The kinematic constraints are transformed into geometric constraints for the design of quaternion curves. An iterative algorithm for constrained motion interpolation is presented. It detects the violation of the kinematic constraints by searching for those extreme points of the quaternion curve that do not satisfy the constraints. Such extreme points are modified so that the constraints are satisfied, and the resulting new points are added to the ordered set of the initial positions to be interpolated. An example is presented to show how this algorithm produces smooth spherical rational spline motions that satisfy the kinematic constraints of a spherical 6R closed chain. The algorithm can also be used for the synthesis of rational interpolating motions that approximate the kinematic constraints of spherical 5R and 4R closed chains within a user-defined tolerance.

Dimensional Synthesis and Constrained Motion Interpolation for Planar and Spherical 6R Closed Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Qiaode Jeffrey Ge
Keyword(s):  
Rational Curve ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Initial Attempt ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Cartesian Space ◽  
Closed Chain ◽  
Kinematic Mapping ◽  
The Given

In the recent past, we have studied the problem of synthesizing rational interpolating motions under the kinematic constraints of any given planar and spherical 6R closed chain. This work presents some preliminary results on our initial attempt to solve the inverse problem, that is to determine the link lengths of planar and spherical 6R closed chains that follow a given smooth piecewise rational motion under the kinematic constraints. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. By using kinematic mapping and a quaternions based approach to represent displacements of the coupler of the closed chains, the given smooth piecewise rational motion is mapped to a smooth piecewise rational curve in the space of quaternions. In this space, the aforementioned workspace constraints on the coupler of the closed chains define a constraint manifold representing all the positions available to the coupler. Thus the problem of dimensional synthesis may be solved by modifying the size, shape and location of the constraint manifolds such that the mapped rational curve is contained entirely inside the constraint manifolds. In this paper, two simple examples with preselected moving pivots on the coupler as well as fixed pivots are presented to illustrate the feasibility of this approach.

Rational Motion Interpolation Under Kinematic Constraints of Planar 6R Closed Chain

2007 ◽  
Author(s):  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Rational Interpolation ◽  
Geometric Constraints ◽  
Rational Curve ◽  
Constrained Motion ◽  
Extreme Position ◽  
Kinematic Constraints ◽  
Closed Chain ◽  
Curve Interpolation

This paper deals with the problem of synthesizing planar rational motions under the kinematic constraints of planar 6R closed chain. It follows our previous work on the synthesis of rational motions under the kinematic constraints of planar open chains. Planar quaternions are used to represent planar displacements. In this way, the problem of rational motion interpolation is transformed into that of rational curve interpolation, and the kinematic constraints of a planar 6R closed chain are transformed into geometric constraints for the rational interpolation. An algorithm for the constrained motion interpolation is developed that detects an extreme position on the rational motion that violates the kinematic constraints. This position is then modified so that it is in compliance with the kinematic constraints and is added to the list of positions to be interpolated. By restricting the kinematic constraints to 5R and 4R closed chains, the algorithm is also applicable to the problem of synthesizing planar rational motions for 5R and 4R closed chains.

Constraint-Based Virtual Environment for Supporting Assembly and Maintainability Tasks

1999 ◽  
Author(s):  
Terrence Fernando ◽  
Prasad Wimalaratne ◽  
Kevin Tan
Keyword(s):  
Virtual Environment ◽  
Current System ◽  
Research Programme ◽  
Geometric Constraints ◽  
Simulation Environment ◽  
Constrained Motion ◽  
Constraint Management ◽  
Interactive Product ◽  
Assembly Operations ◽  
The University

Abstract This paper presents the design and implementation of a constraint-based virtual environment for supporting interactive assembly and maintenance tasks. The system architecture of the constraint-based virtual environment is based on the integration of components such as OpenGL Optimizer, Parasolid geometric kernel, a Constraint Engine and an Assembly Relationship Graph (ARG). The approach presented in this paper is based on pure geometric constraints. Techniques such as automatic constraint recognition, constraint satisfaction, constraint management and constrained motion are employed to support interactive assembly operations and realistic behaviour of assembly parts. The current system has been evaluated using two industrial case studies. This work is being carried out as a part of a research programme referred to as IPSEAM (Interactive Product Simulation Environment for Assessing Assembly and Maintainability), at the University of Salford.

Dynamic modeling and simulation of two cooperating structurally-flexible robotic manipulators

Robotica ◽  
1995 ◽  
Vol 13 (4) ◽  
pp. 375-384 ◽  
Author(s):  
K. Krishnamurthy ◽  
L. Yang
Keyword(s):  
Modeling And Simulation ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Geometric Constraints ◽  
Flexible Manipulators ◽  
Order Model ◽  
Closed Chain ◽  
Extended Hamilton’S Principle

SummaryA dynamic model for two three-link cooperating structurally-flexible robotic manipulators is presented in this study. The equations of motion are derived using the extended Hamilton's principle and Galerkin's method, and must satisfy certain geometric constraints due to the closed chain formed by the two manipulators and the object. The dynamic model presented here is for the purpose of designing controllers. Therefore, a low-order model which captures all the major effects is of interest. Computer simulated results are presented for the case of moving an object along an elliptical path using the two cooperating flexible manipulators.

scholarly journals Analysis of Geometric Obstacles Avoidance in Assembling Complex Products as a Decision-making Problem

2018 ◽  
pp. 17-34
Author(s):  
A. N. Bozhko
Keyword(s):  
Obstacle Avoidance ◽  
Information Technologies ◽  
Computational Experiment ◽  
Ordered Set ◽  
Geometric Constraints ◽  
Assembly Planning ◽  
Ordered Sets ◽  
Complex Products ◽  
Minimum Number ◽  
Person Game

Computer aided assembly planning (CAAP) of complex products is an important and urgent problem of state-of-the-art information technologies. A configuration of the technical system imposes fundamental restrictions on the design solutions of the assembly process. The CAAP studies offer various methods for modelling geometric constraints. The most accurate results are obtained from the studies of geometric obstacles, which prohibit the part movement to the appropriate position in the product, by the collision analysis methods. An assembly of complex technical systems by this approach requires very high computational costs, since the analysis should be performed for each part and in several directions.The article describes a method for minimizing the number of direct checks for geometric obstacle avoidance. Introduces a concept of the geometric situation to formalize such fragments of a structure, which require checking for geometric obstacle avoidance. Formulates two statements about geometric heredity during the assembly. Poses the task of minimizing the number of direct checks as a non-antagonistic two-person game on two-colour painting of an ordered set. Presents the main decision criteria under uncertainty. To determine the best criterion, a computational experiment was carried out on painting the ordered sets with radically different structural properties. All the connected ordered sets are divided into 13 subclasses, each of which includes structurally similar instances. To implement the experiment, a special program has been developed that creates a random ordered set in the selected subclass, implements a game session on its coloration, and also collects and processes statistical data on a group of the homogeneous experiments.The computational experiment has shown that in all subclasses of the partial orders, the Hurwitz criterion with a confidence coefficient of 2/3 and that of Bayes-Laplace demonstrate the best results. The Wald and Savage criteria have demonstrated the worst results. In the experiment, a difference between the best and worst results reached 70%. With increasing height (maximum number of levels) of an ordered set, this difference tends to grow rapidly. In the subclass of pseudo-chains, all criteria showed approximately equal results.The game model of geometric obstacles avoidance allows formalizing data on geometric heredity and obtaining data on the composition and the minimum number of configurations, the test of which objectifies all existing-in-the-product geometric constraints on the movements of parts during assembly.

Task constrained motion planning for 7-degree of freedom manipulators with parameterized submanifolds

2018 ◽  
Vol 45 (3) ◽  
pp. 363-370 ◽  
Author(s):  
Qiang Qiu ◽  
Qixin Cao
Keyword(s):  
Motion Planning ◽  
Explicit Expression ◽  
Collision Detection ◽  
Tool Path ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Constrained Motion ◽  
Content Type ◽  
Planning Methods ◽  
Two Parameters

PurposeThis paper aims to use the redundancy of a 7-DOF (degree of freedom) serial manipulator to solve motion planning problems along a given 6D Cartesian tool path, in the presence of geometric constraints, namely, obstacles and joint limits.Design/methodology/approachThis paper describes an explicit expression of the task submanifolds for a 7-DOF redundant robot, and the submanifolds can be parameterized by two parameters with this explicit expression. Therefore, the global search method can find the feasible path on this parameterized graph.FindingsThe proposed planning algorithm is resolution complete and resolution optimal for 7-DOF manipulators, and the planned path can satisfy task constraint as well as avoiding singularity and collision. The experiments on Motoman SDA robot are reported to show the effectiveness.Research limitations/implicationsThis algorithm is still time-consuming, and it can be improved by applying parallel collision detection method or lazy collision detection, adopting new constraints and implementing more effective graph search algorithms.Originality/valueCompared with other task constrained planning methods, the proposed algorithm archives better performance. This method finds the explicit expression of the two-dimensional task sub-manifolds, so it’s resolution complete and resolution optimal.

Path-Constrained Motion Planning for Robotics Based on Kinematic Constraints

2007 ◽  
Author(s):  
N. J. M. van Dijk ◽  
N. van de Wouw ◽  
H. Nijmeijer ◽  
W. C. M. Pancras
Keyword(s):  
Optimal Path ◽  
Robot Kinematics ◽  
Constrained Motion ◽  
Complex Dynamic ◽  
Kinematic Constraints ◽  
Tracking Tasks ◽  
Dynamic Constraint ◽  
Time Optimal ◽  
Actuator Constraints ◽  
Constraint Approach

Common robotic tracking tasks consist of motions along predefined paths. The design of time-optimal path-constrained trajectories for robotic applications is discussed in this paper. To increase industrial applicability, the proposed method accounts for robot kinematics together with actuator velocity, acceleration and jerk limits instead of accounting for the generally more complex dynamic equations of a manipulator with actuator torque and torque-rate limits. Besides actuator constraints also constraints acting on process level are accounted for. The resulting non-convex optimization problem is solved using a cascade of genetic algorithms and Nelder-Mead’s method. Simulations performed on a Puma 560 manipulator model show that for a proper choice of the kinematic constraints results can be obtained that match the quality of those obtained using the more complex dynamic constraint approach.

Kinematic Acquisition of Geometric Constraints for Task Centered Mechanism Design

2010 ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Hai-Jun Su ◽  
Feng Gao
Keyword(s):  
Mechanism Design ◽  
Motion Analysis ◽  
Geometric Constraints ◽  
Planar Motion ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Analysis Problem ◽  
Geometric Means ◽  
New Type ◽  
Mechanical Linkage

A motion task can be given in various ways. It may be defined parametrically or discretely in terms of an ordered sequence of displacements or in geometric means. This paper studies a new type of motion analysis problem in planar kinematics that seeks to acquire geometric constraints associated with a planar motion task which is given either parametrically or discretely. The resulting geometric constraints can be used directly for type as well as dimensional synthesis of a physical device such as mechanical linkage that generates the constrained motion task. Methods for kinematic acquisition of geometric constraints bridge the gap between type and dimensional synthesis and provide the foundation for task centered mechanism design.

A QP-Based Approach to Kinematic Motion Planning of Multibody Systems

2015 ◽  
Author(s):  
Junggon Kim ◽  
Rudranarayan Mukherjee
Keyword(s):  
Motion Planning ◽  
Multibody Systems ◽  
Linear Constraints ◽  
Software Implementation ◽  
Robotic Systems ◽  
Time Step ◽  
Kinematic Constraints ◽  
Cartesian Space ◽  
Kinematic Motion ◽  
Dual Arm

This article presents a quadratic programming (QP) based approach to local kinematic motion planning of general multibody robotic systems. Given kinematic constraints and targets such as desired positions and orientations in Cartesian space, we find locally optimal joint velocities toward the targets at every time step by formulating the problem into a constrained optimization with a quadratic objective function and linear constraints in terms of the joint velocities. The solution is integrated to obtain the joint displacements at the next time step, and this process is repeated until reaching the targets or converging to a certain configuration. Our formulation based on relative Jacobian is particularly useful in handling constraints on relative motions, which arises in many practical problems such as dual-arm manipulation and self-collision avoidance, in a concise manner. A brief overview of our software implementation and its applications to manipulation and mobility planning of a simulated multi-limbed robot are also presented.

Sign in / Sign up

Export Citation Format

Share Document