ROBOT VISION LABORATORY

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Robot Applications-

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Direct KinematicsDirect Kinematics

Where is my hand?

Direct Kinematics:HERE!

Serial and Parallel Serial and Parallel ManipulatorsManipulators

Serial and Parallel Serial and Parallel ManipulatorsManipulators

PUMA560

Hexapod

Links and JointsLinks and Joints

Joints:

Links

End Effector

Robot Basis

2 DOF’s

Link Length and TwistLink Length and TwistAxis i

Axis i-1

a i-1

i-1

Denavit-Hartenberg Denavit-Hartenberg ParametersParameters

Axis i-1

a i-1

i-1

Axis i

Link i

di

i

Example: PUMA560Example: PUMA560

Inverse KinematicsInverse Kinematics

How do I put my hand here?

IK: Choose these angles!

What is the reachable space? Take l1, l2 fixed and vary 3

Example: Planar 3-link robotExample: Planar 3-link robot

l2

l3

l1

1

2

3

321321

321

321321211

321321211

, Take

sinsinsin

coscoscos

llllll

llly

lllx

Now vary 1

Finally, vary 2

Existence of SolutionsExistence of Solutions A solution to the IKP exists if the target belongs to

the workspace Workspace computation may be hard. In practice

is made easy by special design of the robot The IKP may have more than one solution. How

to choose the appropriate one?

2 solutions!

An Example:An Example:

L1

L2

X

YV3

1

2

Joint Velocity and the JacobianJoint Velocity and the Jacobian

Look! I’m moving!

Introduction to Robot Motion Introduction to Robot Motion PlanningPlanning

Robotics meet Computer Science

ExampleExampleA robot arm is to build an assembly from a set of

parts.

Tasks for the robot: Grasping: position gripper on object

design a path to this position Trasferring: determine geometry path for arm

avoide obstacles + clearance Positioning

Information requiredInformation required

Knowledge of spatial arrangement of wkspace. E.g., location of obstacles

Full knowledge full motion planning Partial knowledge combine planning and

execution

motion planning = collection of problems

Basic ProblemBasic Problem

A simplified version of the problem assumes Robot is the only moving object in the wkspace No dynamics, no temporal issues Only non-contact motions

MP = pure “geometrical” problem

Components of BMPP Components of BMPP (cont.)(cont.) The Problem: Given an initial position and orientation POinit

Given a goal position and orientation POgoal

Generate: continuous path t from POinit to POgoal

t is a continuous sequence of Pos’

Mathematic Notion of PathMathematic Notion of Path Need a notion of continuity Define a distance function d : C x C -> R+

Example: d(q,q’) = maxa in A ||a(q) - a(q’)||

y

x

q

'

'

'

'

y

x

qd

Connect Start and Connect Start and Goal to RoadmapGoal to RoadmapStart Goal

Find the Path from Find the Path from Start to GoalStart to Goal

Start Goal