1. An Extension to the Dynamic Window Approach
for arbitrarily shaped Robots
Christian Mandel A1[RoboMap], 09/17/04

2. Overview Rolland: new hardware platform Motivation
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Overview
Rolland: new hardware platform
Motivation
Basic principles of the Dynamic Window Approach
DWA & the problem with non circular shaped robots
Implementation issues: Curve Segments Table, Collision Table
Computing the Trajectory
Computing the Velocity Profile
What remains to do
Preliminary Experiments
SFB/IQN-Kolloquium 09/17/04
- 0 -

3. Meyra Champ wheelchair
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Meyra Champ wheelchair
omnidirectional camera system
controlling laptop connected via single usb cable
emergency stop button
2 laser range finder
2 incremental encoders
Rolland: hardware platform
SFB/IQN-Kolloquium 09/17/04
- 1 -

4. Motivation Wheelchair in its environment
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Motivation
decision points
voronoi edges
What is it all about?
Wheelchair set up as an experimental platform for spatial navigation tasks driven by Human-Computer-Interaction
Wheelchair equipped with Laser Range Finders -> Scans are integrated into local obstacle map.
Evidence Grid as the metrical representation of the environment -> the more often we scan an obstacle the higher the evidence in ist representing cell
Voronoi-Graph as the topological representation of the environment -> consists of edges and decision points
To allow spatial navigation tasks: The basic question is how to navigate between decision points, while taking care of dynamic obstacles
the dynamic aspects of driving on a computed path and taking care of non-static obstacles requires reactive algorithm that runs frequently
Wheelchair in its environment
Metrical & topological representation.
How to navigate between decision points while taking care of dynamic obstacles?
SFB/IQN-Kolloquium 09/17/04
- 2 -

5. Basic principles of the Dynamic Window Approach1
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Basic principles of the Dynamic Window Approach1
Local navigation combined with reactive collision avoidance.
DWA assumes: Robot velocity is a piecewise constant function in time.
DWA considers: Robot has initial velocity and limited accelerations.
DWA computes optimal circular arc in every time step.
DWA looks one curve ahead.
1 [Fox, Burgard, Thrun] „The Dynamic Window Approach To Collision Avoidance“
SFB/IQN-Kolloquium 09/17/04
- 3 -

6. DWA & the problem with non circular shaped robots
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
DWA & the problem with non circular shaped robots
computed arc
current pose
headed pose
current pose
computed arc1
computed arc2
current pose
computed arc
collision
SFB/IQN-Kolloquium 09/17/04
- 4 -

7. An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Curve Segments Table
start curvature
curvature prime
direction
poses
+ MAX
backwards
- MAX
forwards
...
Motivation of a Curve Segments Table:
precompute nearly every path one can want to drive given a startCurvature, CurvaturePrime and a direction
startCurvature == Radius of Arc wheelchair is currently driving on
curvaturePrime == rate of changing the curvature (its only discretized by three values!!! steer left, hold, steer rigth)
direction == driving forwards/backwards
explain some of the outer arcs because in the six examples you only showed an infinite radius
SFB/IQN-Kolloquium 09/17/04
- 5 -

8. An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Collision Table
...
{(0,-1),(1,0),(0,1),(1,0),(0,-1),(1,-1),
(0,1),(1,0),(0,-1)}
offset between occupied cells ({(x1,y1),...,(xn,yn)})
arclength (t)
...
{(-1,1),(-1,-1),(1,1),(1,-1),(2,1),(2,-1),
(3,-1),(3,-2),(4,-1),(4,-2)}
occupied cells ({(x1,y1),...,(xn,yn)})
arclength (t)
...
{(-1,1),(-1,-1),(1,1),(1,-1),(2,1),(2,-1)}
occupied cells ({(x1,y1),...,(xn,yn)})
arclength (t)
t=0
t=1
t=2
t=3
t=4
t=5
t=6
t=7
t=8
Vorteil: Jede Zelle des Collisiontables, sei sie absolut(relativ zu t=0) oder als offset zur vorher getesteten Zelle aufzufassen, wird nur einmal auf Kollision mit dem EvidenceGrid getestet und ist demnach auch nur einmal im Collisiontable vorhanden, naemlich zu dem fruehsten Zeitpunkt.
SFB/IQN-Kolloquium 09/17/04
- 6 -

9. Algorithmic Refinements 1
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Algorithmic Refinements 1
Precompute and store only paths whose first pose
has zero heading.
Goal: reduce Size of
Curve Segments Table
Test-for-Collision-Operation has to rotate CT-entries.
Collision Table
Precompute additional table which holds rotated
offsets between occupied cells.
SFB/IQN-Kolloquium 09/17/04
- 7 -

10. Score Function startPose headedPose path goalPose
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Score Function
startPose
headedPose
path
the folks does not know yet, that we want to test a huge bunch of possible paths.....
so introduce the Objective Function which will asses a single tested path
goalPose
SFB/IQN-Kolloquium 09/17/04
- 8 -

11. Odometry Pose, Goal Pose
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Computing the Optimal Path
Algorithm (basic idea)
Input
Local Evidence Grid,
Odometry Pose, Goal Pose
Curve Segments Table
Collision Table
SFB/IQN-Kolloquium 09/17/04
- 9 -

12. optimal path w.r.t. objective function
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Algorithmic Refinements 2
arc1.curvature, arc1.length, arc1.direction do
arc2.curvature, arc2.length, arc2.direction do
construct path
test for collision and prune if necessary
calc score
if (path.score < bestPath.score) set bestPath = path
Algorithm (basic idea)
arc1.curvature, arc1.length, arc1.direction do
arc2.curvature, arc2.direction do
construct path
test for collision and prune if necessary
minimise path.score
if (path.score < bestPath.score) set bestPath = path
Algorithm (with constant arc2.length)
set arc2.length = MAX_arc2.length
Goal: reduce complexity of computation
Computing the
optimal path w.r.t. objective function
SFB/IQN-Kolloquium 09/17/04
- 10 -

13. Algorithmic Refinements 3
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Algorithmic Refinements 3
pose arc2 do
calc score with goalPose = pose
store goalPose with minimal score
Algorithm
(witch constant
arc2.length)
minimise
path.score
potential goalPose
arc2 do
calc score
store goalPose with minimal score
SFB/IQN-Kolloquium 09/17/04
- 11 -

14. Computing the Velocity Profile
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Computing the Velocity Profile
Algorithm
FOR EVERY DO:
COMPUTE MAXIMUM velocity FOR WHICH HOLDS:
Input
FOR EVERY DO:
INCORPORATE LONGITUDINAL ACCELERATION LIMIT :
Solution Path
Velocities in Start & Goal
Lateral Acceleration Limit
Longitudinal Acceleration Limit
Rotational Velocity Limit
Longitudinal Velocity Limit
SFB/IQN-Kolloquium 09/17/04
- 12 -

15. An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
What remains to do
current implementation considers only binary information from the evidence grid while doing the collision test
better: collision test should also return minimal distance to obstacles for tested path
SFB/IQN-Kolloquium 09/17/04
- 13 -

16. Preliminary Experiments
An Extension to the Dynamic Window Approach for arbitrarily shaped Robots.
A1[RoboMap]
Preliminary Experiments
SFB/IQN-Kolloquium 09/17/04
- 14 -