ROBOT VISION LABORATORY 김 형 석
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Transcript of ROBOT VISION LABORATORY 김 형 석
ROBOT VISION LABORATORY
김 형 석
Robot Applications-
Bhttp://world.honda.com/run/mov-run-60.html
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