Path Planning for Fixed-Wing Unmanned Aerial Vehicles

107 Pages·2016·10.14 MB·English

ETH Library
Path Planning for Fixed-Wing
Unmanned Aerial Vehicles
Master Thesis
Author(s):
Schneider, Daniel
Publication date:
2016
Permanent link:
https://doi.org/10.3929/ethz-a-010646508
Rights / license:
In Copyright - Non-Commercial Use Permitted
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Autonomous Systems Lab
Prof. Roland Siegwart
Master Thesis
Path Planning for
Fixed-Wing Unmanned
Aerial Vehicles
Autumn Term 2016
Supervised by: Author:
Philipp Oettershagen Daniel Schneider
Enric Galceran Yebenes

Declaration of Originality
I hereby declare that the written work I have submitted entitled
Path Planning for Fixed-Wing Unmanned Aerial Vehicles
isoriginalworkwhichIalonehaveauthoredandwhichiswritteninmyownwords.1
Author(s)
Daniel Schneider
Student supervisor(s)
Philipp Oettershagen
Enric Galceran Yebenes
Supervising lecturer
Roland Siegwart
With the signature I declare that I have been informed regarding normal academic
citationrulesandthatIhavereadandunderstoodtheinformationon’Citationeti-
quette’(https://www.ethz.ch/content/dam/ethz/main/education/rechtliches-
abschluesse/leistungskontrollen/plagiarism-citationetiquette.pdf). The
citation conventions usual to the discipline in question here have been respected.
The above written work may be tested electronically for plagiarism.
9XXMKIR(cid:16)(cid:4)(cid:20)(cid:22)(cid:4)1E](cid:4)(cid:22)(cid:20)(cid:21)(cid:26)
Place and date Signature
1Co-authored work: The signatures of all authors are required. Each signature attests to the
originalityoftheentirepieceofwrittenworkinitsfinalform.
i
Contents
Abstract iv
Symbols, Notation, Terms And Definitions vi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Goal of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Background 4
2.1 Terms and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Motion planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Sampling-based motion planning . . . . . . . . . . . . . . . . 7
2.2.3 Geometric planning . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Control-based planning . . . . . . . . . . . . . . . . . . . . . 9
2.2.5 Informed sampling . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.6 Sampling-based motion planning algorithms . . . . . . . . . . 14
2.3 Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Collision checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Flexible Collision Library . . . . . . . . . . . . . . . . . . . . 21
2.4.2 Height checking . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5 System dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.1 Dubins car . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.2 Dubins airplane . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Path planning method 28
3.1 Software structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Collision checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Airplane motion model . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 Non-optimal Dubins airplane paths . . . . . . . . . . . . . . . 31
3.3.2 Dubins set classification . . . . . . . . . . . . . . . . . . . . . 32
3.3.3 Dubins airplane state space for OMPL . . . . . . . . . . . . . 32
3.4 Path planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.1 Control-based planning . . . . . . . . . . . . . . . . . . . . . 35
3.4.2 Informed sampling . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.3 Dubins airplane adapted sampling . . . . . . . . . . . . . . . 36
3.4.4 Combining the use of straight lines and non-optimal Dubins
airplane paths . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4.5 Forward propagation . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.6 Optimal fast marching tree using non-optimal Dubins air-
plane paths (D-FMT*). . . . . . . . . . . . . . . . . . . . . . 39
ii
3.5 Manual code optimization . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Experiments and results 42
4.1 Parameter tuning for planners . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Preliminary results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.1 FCL and height checking . . . . . . . . . . . . . . . . . . . . 44
4.2.2 Determine the time complexity of FMT* . . . . . . . . . . . 46
4.2.3 Non-optimal vs. optimal Dubins airplane paths . . . . . . . . 46
4.2.4 Manual code optimizations . . . . . . . . . . . . . . . . . . . 49
4.3 Final results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1 Block experiment . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.2 Gap experiment . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.3 Random map experiment . . . . . . . . . . . . . . . . . . . . 53
4.3.4 Slalom experiment . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.5 Mountain experiment . . . . . . . . . . . . . . . . . . . . . . 57
4.3.6 Kandervalley experiment . . . . . . . . . . . . . . . . . . . . 61
4.4 Summary and analysis of the experiments . . . . . . . . . . . . . . . 63
5 Conclusion and future work 69
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Bibliography 81
A Additional material 82
A.1 Proof: Eq. 3.6 is a pseudometric . . . . . . . . . . . . . . . . . . . . 82
A.2 Proof: The length of non-optimal Dubins airplane paths is a premetric 82
B More results 84
B.1 Block experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
B.2 Gap experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
B.3 Random map experiment . . . . . . . . . . . . . . . . . . . . . . . . 85
B.4 Slalom experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
B.5 Mountain experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 85
B.6 Kandervalley experiment . . . . . . . . . . . . . . . . . . . . . . . . . 93
Abstract
This thesis presents a first implementation of a real-time capable onboard path
planningframeworkcomputingshortestpathsforfixed-wingaerialvehiclesformany
start-goal configurations. The framework provides kinodynamic planning based on
the Dubins airplane motion model.
TheframeworkisimplementedasaROSnodewhatmakesitexecutableoncommon
companion-computers installed on fixed-wing aerial vehicles.
We evaluated 8 different sampling-based motion planning algorithms in theoretical
andrealexperimentalsetups. Twonewideastoreducethetimeforfindingshortest
pathsfortheDubinsairplaneareexplainedandcomparedagainstexistingplanning
methods. Ontheonehand,theinformedsubsetoftheDubinsairplaneforminimum
pathlengthisapproximatedasasubsetoftheinformedsubsetforasystemwithout
differential constraints. On the other hand, in order to find initial paths as fast as
possible,theinitialpathisplannedusingstraight-lineconnectionsbetweensamples
insteadofdynamicallyfeasiblepaths. AmodificationtotheoptimalFastMarching
Treealgorithm(FMT*)ispresented. Themodificationallowstopredicttheamount
of samples workable in the time available for planning and thereby makes FMT*
usable for real-time and onboard path planning.
Experimentshaveshownthatplanninginitialpathswithstraightlinesandapproxi-
matingtheinformedsubsetfortheDubinsairplaneforminimumpathlengthallows
findinginitialpathsinlessthan1secondandexpeditestheconvergencetotheopti-
mal path such that after 2 seconds reasonably short paths are found. Furthermore,
planners iteratively drawing one sample at a time, e.g. optimal Rapidly-exploring
Random Tree (RRT*), perform better than planners drawing batches of samples,
e.g. Batch Informed Tree (BIT*), if planning in wide open spaces. For cluttered,
narrow and twisted maps, it is the other way round. Additional experiments have
shown that computing non-optimal paths for start-goal configurations occurring
rarely in real application scenarios, speeds up the computation of the paths up
to 40 times. Further experiments have shown that using a light collision checking
algorithm reduces the time spent for collision checking more than 10 times.
iv
Acknowledgement
I would first like to thank my thesis advisors, Philipp Oettershagen and Enric
Galceran Yebenes of the Autonomous Systems Lab at ETH in Zurich, who steered
me in the right direction and supported my work with a lot of helpful answers and
bright ideas.
I also owe much to Prof. Dr. Roland Siegwart, the Autonomous Systems Lab and
all members thereof, who made this thesis possible and in some way promoted it.
Finally, I must express my profound gratitude to my parents, siblings, cousins and
friends for providing me with permanent support and continuous encouragement
throughout this thesis.
v
Symbols, Notation, Terms
And Definitions
Symbols
φ,ψ,θ Roll, pitch and yaw angle
C Configuration space
q Configuration
q Start/ initial configuration
I
q Goal configuration
G
X State space
x State
x Start/ initial state
I
x Goal state
G
x x-component of a configuration q or state x
y y-component of a configuration q or state x
z z-component of a configuration q or state x
Θ Yaw-component of a configuration q or state x
c Minimum possible cost of a path connecting start and goal in obstacle-free space
min
c Cost of current best path
best
r Minimum turning radius of the Dubins airplane
min
γ Maximum climb and sink angle of the Dubins airplane
max
Acronyms and Abbreviations
ETH Eidgen¨ossische Technische Hochschule
ASL Autonomous Systems Lab
UAV Unmanned aerial vehicle
RRT Rapidly-Exploring Random Tree
FMT Fast-Marching Tree
BIT Batch Informed Tree
KPIECE Kinodynamic Motion Planning by Interior-Exterior Cell Exploration
BVP Boundary value problem
RRT Rapidly-exploring Random Tree
RRT* Optimal Rapidly-exploring Random Tree
FMT* Optimal Fast Marching Tree
BIT* Batch Informed Tree
vi