workspace analysis in multirobot manipulation international symposium on robotics stockholm, sweden....

International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002

Workspace Analysis in Multirobot Manipulation

Ramon Costa-Castelló, Luis Basañez

CONTENTS

Introduction Basic Definitions Multirobot System Analysis

Dexterous Workspace Reachable Workspace

Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction

Two RX-90 cell Conclusions

INTRODUCTION

Multirobot Cell

INTRODUCTION

Multirobot Manipulation Advantages Load Capacity Increase

Dexterity Improvement

Flexible Objects

Multirobot Manipulation Drawbacks Coordination Needed

Workspace Reduction

INTRODUCTION

Workspace Approaches Analytical Methods

• Singularity Analysis• Exact approach

Volumetric Methods• Workspace discretization• Approximation• Obstacles

Intersection Approach • Intersection of several geometric figures• Quicker approach• Work cell Design capabilities

CONTENTS

Introduction

Basic Definitions Multirobot System Analysis

The kinematics f of a mechanism is the relation between the configuration space C and the operational space O

Workspace: elements of O in which the robot end-effector can be placed in

Reachable Workspace: set of positions reachable by the robot end-effector in at least one orientation

Dexterous workspace: set of positions reachable by the robot in all orientations

BASIC DEFINITIONS

|W x O C x f

| ( )nRW p R x R p W R SO n

| ( )nDW p R x W x R p R SO n

CONTENTS

Introduction Basic Definitions

Multirobot System Analysis Dexterous Workspace Reachable Workspace

MULTIROBOT SYSTEMS ANALYSIS

0 0 0 0 1c i i i iC C C i N

i i i iB f O Individual kinematics

Multirobot System Configuration Space

i i i i i i

f B f i O B f i B

f B f i O

p R R p R p p

R R R R

Position and Orientation Constraining Equations

MULTIROBOT SYSTEMS ANALYSISDexterous Workspace

0 0| ( )

1i i ii i

nD i i

O B Bf

W x R R SO n C C

Rp R p p x i N

Dexterous Workspace Definition

Expression Manipulation

WpRpxRR

WRpRpxR

pWRpRxR

TB WppxRsph

Workspace

Dexterous Figure

Dexterous Figure definition

Dexterous Workspace from Dexterous Figure

iDOBTB

iD WppxRsphWxW

iii ,|ˆ

DiDD WWW

MULTIROBOT SYSTEMS ANALYSISReachable Workspace

i oR R RW W W

Reachable Space Approximation

Reachable Figure Definition

Reachable Workspace from Reachable Figure

ReachableFigure

Workspace

MULTIROBOT SYSTEMS ANALYSISReachable Figure

0| , i i i i

n T iR R O O B R BW x R x W R x RR p R W p

| i i i i

i n T iR O O B R BW x R R x RR p R W p

CONTENTS

RX-90 robot

APPLICATION TO RX-90 ROBOT

RX-90 Configuration Space section

RX-90 Work Space section1 ctt

RX-90 3D WorkspaceRX-90 selected sections

RX-90 Dexterous Figure Construction Scheme

APPLICATION TO RX-90 ROBOTDexterous Workspace

Reachable figure for

APPLICATION TO RX-90 ROBOTReachable Figure

Reachable figure for mmpiO

CONTENTS

1 0 0 500

0 1 0 0

0 0 1 461

0 0 0 1

Cell Picture

TWO RX-90 CELL

1 0 0 846

0 1 0 1306

0 0 1 0

0 0 0 1

08.680

Reference Robot Workspace and Reachable Figure

TWO RX-90 CELL

31 193534m 46 36%

TWO RX-90 CELLReachable Workspace

CONTENTS

Two RX-90 cell

Conclusions

• A new method to analyze multirobot workspace has been presented. The method is based in computing the intersection of the reference manipulator workspace and the reachable/dexterous figure of the other robots.

• The method has been applied to PUMA like manipulators.

• Further work : Introduction of orientation kinematics.

CONCLUSIONS

Robots in the same Position and different Orientation

Orientation Range Analysis

Further Works

Orientation Range Analysis through Analytic Methods

Automatic Work Cell Design (Position and Orientation)

workspace analysis in multirobot manipulation international symposium on robotics stockholm, sweden....

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