1. The document presents a method called Finite Horizon Cubic Spline (FHCS) for smoothing and shortening rotorcraft trajectories produced by roadmap-based global path planning. 2. Simulation results show FHCS trajectories reduced time by 5-20% compared to linear paths, while maintaining motion safety. FHCS required only 4.7% additional CPU time on average. 3. Open areas of future work include improving path repair in local planning and adapting spline segments more aggressively in narrow passages.

1. Trajectory Time Reduction using Field of View-
based Smoothing of Roadmap-based Paths
Florian-Michael Adolf
German Aerospace Center (DLR)
Dept. Unmanned Aircraft
Braunschweig, Germany
Mohamed Abou-Hussein
German University in Cairo (GUC)
Faculty of Information Engineering and Technology (IET)
New Cairo City, Egypt
Chad Goerzen
San Jose State University Research Foundation
Ames Research Center, Moffett Field, CA
Session: Unmanned VTOL Aircraft & Rotorcraft I

2. Autonomous Rotorcraft Testbed for Intelligent Systems (ARTIS)
www.DLR.de • Chart 2 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Unmanned rotorcraft midiARTIS (MTOW 14 kg)
shown with stereo-based obstacle detection.
Texas City disaster April 16, 1947:
Complex docks building.
[Special Collections, University of Houston Libraries]
Earthquake, Chile 2010
Obstacle Field Navigation (OFN) problems:
 A priori unknown terrain
 3D obstacles (e.g. bridges, overhangs etc.)
 Limited obstacle sensing (range, resolution, speed)
 Limited CPU performance
 Flight endurance critical

3. www.DLR.de • Chart 3
Obstacle Detection and Mapping
> Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
[Andert et al., 2009 / Krause 2010]

4. Roadmap-based Global Path Planner
www.DLR.de • Chart 4 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
B
A GoalStart

5. DLR’s test site “Rosenkrug”: Flight test obstacle data fed into the roadmap
-Test site “Rosenkrug”
www.DLR.de • Chart 5
Roadmap Updates for Online Planning
> Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

6. Roadmap-based Path (Re-)Planning
www.DLR.de • Chart 6 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
B
A
Initial path
Online
Polygon
Updates
Non-traversable
roadmap edges
B
A
Replanned path
*) Results presented at AHS-Forum 68, 2012
Problem:
Linear free-space representation
is not an ideal path geometry for
fast(er) navigation*

7. Linear Connection Strategy
www.DLR.de • Chart 7 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

8. Approach: Finite Horizon Cubic Spline (FHCS)
1) Revise connection
strategy:
Case dependent steering
of vertex in front of the
rotorcraft
2) Generate collision free
and smooth geometry
within field of view
3) Consider sensor FOV and
hover capability: Special
cases for multiple goal
waypoints
www.DLR.de • Chart 8 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
UAV
dstop
Linear extrapolated q‘
UAV
dstop
Heuristic
extrapolation(s)
B
A
B
A
B
A

9. FHCS: Steered Vertex
www.DLR.de • Chart 9 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

10. FHCS Collision Avoidance
www.DLR.de • Chart 10 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
After limit of N
iterations is
reached,
switch to linear
segment

11. Simulation Setup
www.DLR.de • Chart 11 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
3-D LIDAR Model
50 m detection range
180 degree
scan plane 360 degree rotation @1Hz
of 2-D scan plane
Vehicle state update
ARTIS Closed Loop Simulation
Laser beam
collision detection
A Priori ‘Unknown’ Polygons
Extracted Terrain Polygons
Velocity Command
Roadmap-Based Planner
Closed Loop Flights in “Unknown” Terrain

12. OFN Benchmark: Simple and Urban Scenarios
www.DLR.de • Chart 12 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
OFN Benchmark Files from [Mettler et.al., AHS 2010], s.a. http://aem.umn.edu/people/mettler/projects/AFDD/AFFDwebpage.htm
San Diego, CA

13. Parameters:
vmax = 3 m/s
vvert = 1.5 m/s
amax = 0.5 m/s/s
rmax = 90 deg/s
dclear = 8 m
dsample = 20 m
dsense = 50 m
freplan = 2 Hz
fsense = 5 Hz
Urban Scenario A1 to A: Runtime Example
www.DLR.de • Chart 13 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Sensor FOV
Model
Linear Roadmap Path
FHCS Path
UAV

14. Trajectories for Simple Cases
www.DLR.de • Chart 14 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Baseline
FHCS
Linear

15. Timeline for “Wall Baffle”
www.DLR.de • Chart 15 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Baseline FHCS Linear
SpeedSmoothnessSafetyDifficulty

16. Statistics for “Wall Baffle”
www.DLR.de • Chart 16 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
FHCS Linear
Baseline
Speed
Speed
Smoothness Safety

17. Trajectories for Urban Cases
www.DLR.de • Chart 17 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
A
Baseline
FHCS
Linear

18. Timeline Urban Scenario A1 to A
www.DLR.de • Chart 18 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Baseline
FHCS Linear
SpeedSmoothnessSafetyDifficulty

19. Relative Performance
www.DLR.de • Chart 19 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Scenarios FHCS [s] Linear [s] Relative
Difference
[%]
Out and back 80.1 83.8 -4.4%
Point 40.3 50.4 -20%
Wall 46.8 57.8 -19%
Cube 51.5 53.9 -4.5%
Wall Baffle 51.4 59.5 -13.6%
Cube Baffle 65.8 79.7 -17.4%
Sum 335.9 385.1 -12.8%
Scenarios FHCS [s] Linear [s] Relative
Difference
[%]
A1 93.6 100.2 -7.4%
A2 105.1 110.5 -4.7%
A3 98.6 105.8 -6.8%
A4 74.7 78.9 -5.3%
A5 117.2 140.4 -16.5%
A6 100.9 102.1 -1.2%
Sum 590.1 637.5 -7.4%
FHCS vs. Linear Path Following
Results presented
at AHS-Forum 68, 2012

20. libOFN2010 344.4 +22.6% libOFN2010 521.5 +8.6%
Performance Comparison
www.DLR.de • Chart 20 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
FHCS vs. libOFN2010 vs. Baseline
Scenarios FHCS [s] Baseline [s] Relative
Difference
[%]
Out and back 80.1 78.8 +1.6%
Point 40.3 39.3 +2.5%
Wall 46.8 39.3 +19%
Cube 51.5 42.1 +22.3%
Wall Baffle 51.4 41.7 +23.3%
Cube Baffle 65.8 39.8 +65%
Sum 335.9 281.2 +19.4%
Scenarios FHCS [s] Baseline
[s]
Relative
Difference
[%]
A1 93.6 92.7 +1%
A2 105.1 76.2 +37.9%
A3 98.6 74.6 +32.2%
A4 74.7 70.9 +5.4%
A5 117.2 87.4 +34.1%
A6 100.9 81.7 +23.5%
Sum 590.1 483.6 +22,8%
43.8 s
Online performance depends on fsense, dsense, changes in flight
direction etc
=> If FHCS planner is fully informed a priori, it is close to baseline

21. CPU Time Overhead
www.DLR.de • Chart 21 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
Urban
Scenarios
Relative Difference
of FHCS to Linear
Mode [%]
A1 5.2%
A2 5.8%
A3 6.7%
A4 3.3%
A5 4.1%
A6 3%
Mean +4.7%
FHCS vs. Linear Path Following
1) Smoothing and velocity
profiling uses 4.7% of CPU
usage time during mission
2) CPU time for collision
detection less than 0.1%
Note:
Smoothing over a longer distance that dstop would
increase the percentage and is not required

22. Summary
1. Trajectory Time Reduction Approach:
a. FHCS, a finite horizon spline-based smoothing technique
b. Heuristics for rotorcraft w.r.t. sensor FOV
c. Feasible connection strategy for online roadmap-based path re-
planning
2. Benchmark-based Results
a. From 5% up to 20% time reduction
b. Motion safety preserved (here: obstacle clearance)
c. 5% to 7% CPU time overhead
d. FHCS reuses of roadmap’s free space tunnels
=> less than 0.1% is collision checking time
3. Open Tasks:
a. Local planner cannot repair sub-optimality of global planner
b. Adapt spline segments more aggressively in narrow passages
www.DLR.de • Chart 22 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

23. Questions?
Feedback?
Comments?
…
Thank you for your attention!
www.DLR.de • Chart 23 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

24. Urban Scenario A
Accumulated terrain over all six test cases.
www.DLR.de • Chart 24 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

25. 0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
8 m 10 m 12.5 m 15 m 17.5 m 20 m
total (avg)
replan
(avg)
max
CPU time over Planning Resolution
CPU time for different sample distances.
www.DLR.de • Chart 25 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May

26. CPU time over Planning Resolution
www.DLR.de • Chart 26 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May
FHCS2012 Rel. Perf.:
Baseline libOFN2010 Linear2012
1,65% -5,21% -4,42%
2,54% -18,09% -20,04%
19,08% -13,49% -19,03%
22,33% -1,34% -4,45%
23,26% -2,10% -13,61%
65,33% 26,78% -17,44%
19,54% -2,47% -12,78%
0,97% -4,39% -6,59%
38,11% 31,87% -4,89%
37,71% 20,69% -6,81%
5,36% -4,60% -5,32%
34,10% 18,38% -16,52%
23,50% 18,85% -1,18%
22,84% 13,15% -7,49%
- MiPlEx with FHCS outperforms
Linear version
- In simple cases, FHCS performs
similar to libOFN
- In difficult urban scenarios, spline
smoothing degrades

27. Specification of missions goals
(Waypopints, dedicated Subtasks)
obstacles
search area
Mission Planning
3D Motion Planning
3D Path Planning
Trajectory Optimization
Task Scheduling
Optimization towards missions goals
A B
C
Star
t
A B
C
Star
t
Roadmap-based 3D path planning
Fast 3D offline path smoothing
Mission Planning and Execution (MiPlEx)
www.DLR.de • Chart 27 > Trajectory Time Reduction using FOV-based Smoothing > Florian-M. Adolf • AHS Forum 69, UAV I > 22nd May