Robotic Motion Planning: Configuration Space

[Pages:71]Robotic Motion Planning: Configuration Space

Robotics Institute 16-735

Howie Choset

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

What if the robot is not a point?

The Scout should probably not be modeled as a point...

Nor should robots with extended linkages that may contact obstacles...

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

What is the position of the robot?

Expand obstacle(s)

Reduce robot

16-735, Howie Choset with slides fnroomt qGui.tDe. rHigahgte.r.,.Z. Dodds, and Dinesh Mocha

Configuration Space

? A key concept for motion planning is a configuration:

? a complete specification of the position of every point in the system

? A simple example: a robot that translates but does not rotate in the plane:

? what is a sufficient representation of its configuration?

? The space of all configurations is the configuration space or Cspace.

C-space formalism:

Lozano-Perez `79

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

Robot Manipulators

What are this arm's forward kinematics?

(x,y)

(How does its position depend on its joint angles?)

L2

y

L1

x

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

Robot Manipulators

What are this arm's forward kinematics?

(x,y)

Find (x,y) in terms of and ...

L2

y

L1

x

Keeping it "simple" c = cos() , s = sin() c = cos() , s = sin() c+= cos(+) , s+= sin(+)

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

Manipulator kinematics

(x,y)

L2

y

L1

x

x =

L1c +

L2c+

y

L1s

L2s+

Position

Keeping it "simple" c = cos() , s = sin() c = cos() , s = sin() c+= cos(+) , s+= sin(+)

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

Inverse Kinematics

Inverse kinematics -- finding joint angles from Cartesian coordinates

via a geometric or algebraic approach...

L2

(x,y)

L1

Given (x,y) and L1 and L2 , what are the values of , , ?

16-735, Howie Choset with slides from G.D. Hager, Z. Dodds, and Dinesh Mocha

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