CarLike Robot: How to Park a Car Nonholonomic Planning

1
Car-Like RobotHow to Park a Car? (Nonholonomic
Planning)
2
Car-Like Robot
f
L
q
f
y
x
Configuration space is 3-dimensional q (x, y,
q)
3
Motion Constraints
f
L
q
f
y
x
Configuration space is 3-dimensional q (x, y,
q) The control space is 2-dimensional (v, f)
4
Motion Constraints
5
Motion Constraints
6
Type 1 Maneuver
q
r
dq
dq
r

• ? Allows sidewise motion

7
Type 2 Maneuver

• ? Allows pure rotation

8
Combination
9
Combination
10
Coverage of a Path by Cylinders
q
y
x
Path created ignoring the car constraints
11
Path Transform
Path created ignoring the car constraints
y
x
12
Path Examples
13
Drawbacks

• Final path can be far from optimal
• Not applicable to car that can only move forward
  (e.g., think of an airplane)

14
Other Technique Control-Based Sampling

• 1. Select a node m
• 2. Pick v, f, and dt
• 3. Integrate motion from m
• new configuration

15
Computed Paths
Tractor-trailer
Car That Can Only Turn Left
jmax45o, jmin22.5o
jmax45o
16
Application
17
Architectural Design Verification of Building
Code
C. Han
18
Other Similar Robots/Moving Objects
(Nonholonomic)

• Rolling-with-no-sliding contact (friction),
  e.g. car, bicycle, roller skate
• Submarine, airplane
• Conservation of angular momentum satellite
  robot, under-actuated robot, catWhy is it
  useful?
• - Fewer actuators design simplicity, less weight
• - Convenience (think about driving a car with 3
  controls!)

19
Other Similar Robots/Moving Objects
(Nonholonomic)

• Rolling-with-no-sliding contact (friction),
  e.g. car, bicycle, roller skate
• Submarine, airplane
• Conservation of angular momentum satellite
  robot, under-actuated robot, catWhy is it
  useful?
• - Fewer actuators design simplicity, less weight
• - Convenience (think about driving a car with 3
  controls!)