ARTTR

EEKS

A KIN

EMATIC

SYN

THESIS

SOLVER F

OR TREE

TOPO

LOGIE

S.

PR

ES

EN

TE

D B

Y A

LI

TA

MI M

I

OUTLINE• ARCHITECTURE

• INSTALLATION

• INPUT

• FORWARD KINEMATHIC

• SOLVABILITY

ARCHITECTUREInput File: Contains the tree topology and the task

positions, velocities and accelerations.

Solvability Library: Functions to calculate tree solvability.

Solvability output: Results of solvability calculations.

Generator File: Functions to check solvability, assemble forward kinematics equations and assign initial values.

Synthesis File: output file with design equations.

Synthesis Library: Library of functions to communicate solver and Synthesis file.

Solvers: Genetic algorithm and Minpack C++ code to generate candidate solutions and perform minimization.

Synthesis output: output file containing the result of the synthesis.

ARCHITECTURE

InputFile

Solvability

Library

Generator

File

Solvability

Output

Synthesis

File

Synthesis

Library

Synthesis

Output

Solvers

INSTALLATION DEPENDENCY• libdq :library for using and manipulating unit dual

quaternions

• cminpack:C++ library for solving nonlinear equations and nonlinear least squares problems .

• Ptheread:defines an API for creating and manipulating threads.

• Lua: a powerful, fast, lightweight, embeddable scripting language.

• SDL(Simple Direct Media Layer): a library designed to provide a low level hardware abstraction layer to computer hardware components.

• libpng: a platform-independent library that contains C functions for handling PNG images.

• Gl: Graphics Library

• Glu: The OpenGL Utility Library (GLU) is a computer graphics library for OpenGL.

• Nlopt: a free/open-source library for nonlinear optimization.

• Minpack: library for solving nonlinear equations and nonlinear least squares problems .

INPUT (TYPE)

Previous Version

• Example: 2-(2,1-(3,3,3),2)

New Version:

• ppt=(0,1,1,1,3,3,3)

• Joints=(2,2,1,2,3,3,3)

INPUT

Forward Kinematics

• Topology of Tree

• Position, Velocity, Acceleration of End Effectors

Solvability

• Topology of Tree

FORWARD KINEMATICS• Make Synthesis FileChain (access)TCP (Contact Point)Splitter

• Send to Synthesis.C

• Use Solvers

• Generate output Files

FORWARD KINEMATICS

SOLVABILITY• Send to Solvability Library

• Notes: Tc ,Bee

SOLVABILITY(BUILD SUBGRAPHS)

SOLVABILITY(BUILD SUB GRAPHS)

ppt={0,1,1,1,3,3,3}Joints={2,2,1,2,3,3,3}

ppt(1)={-1,0,2,2,3,3,3}Joints(1)={-1,2,1,2,3,3,3}

ppt(2)={-1,-1,5,3,0,5,5}Joints(2)={-1,-1,1,2,3,3,3}

ppt(3)={-1,-1,6,3,-1,0,6}Joints(3)={-1,-1,1,2,-1,3,3}

ppt(4)={-1,-1,7,3,-1,-1,0}Joints(4)={-1,-1,1,2,-1,-1,3}

DEMO

Demo Time