Real-time Trajectory Planning for Ground and Aerial Vehicles in A Dynamic Environment

136 Pages·2008·3.29 MB·English

by  Jian Yang

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Electronic Theses and Dissertations, 2004-2019
2008
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Jian Yang
University of Central Florida
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Real-time Trajectory Planning for Ground
and Aerial Vehicles in A Dynamic Environment
by
Jian Yang
B.S. Central South University, China 1999
M.S. Central South University, China 2002
M.S. University of Central Florida, 2005
A dissertation submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
from the School of Electrical Engineering and Computer Science
in the College of Engineering and Computer Science
at the University of Central Florida
Orlando, Florida
Spring Term
2008
Major Professor: Zhihua Qu
c 2008 by Jian Yang
(cid:13)
Abstract
In this dissertation, a novel and generic solution of trajectory generation is developed
and evaluated for ground and aerial vehicles in a dynamic environment. By explicitly con-
sidering a kinematic model of the ground vehicles, the family of feasible trajectories and
their corresponding steering controls are derived in a closed form and are expressed in terms
of one adjustable parameter for the purpose of collision avoidance. A collision-avoidance
condition is developed for the dynamically changing environment, which consists of a time
criterion and a geometrical criterion. By imposing this condition, one can determine a family
of collision-free paths in a closed form. Then, optimization problems with respect to differ-
ent performance indices are setup to obtain optimal solutions from the feasible trajectories.
Among these solutions, one with respect to the near-shortest distance and another with re-
spect to the near-minimal control energy are analytical and simple. These properties make
them good choices for real-time trajectory planning. Such optimal paths meet all boundary
conditions, are twice differentiable, and can be updated in real time once a change in the
environment is detected. Then this novel method is extended to 3D space to find a real-time
optimal path for aerial vehicles. After that, to reflect the real applications, obstacles are
classified to two types: “hard” obstacles that must be avoided, and “soft” obstacles that can
be run over/through. Moreover, without losing generality, avoidance criteria are extended
iii
to obstacles with any geometric shapes. This dissertation also points out that the emphases
of the future work are to consider other constraints such as the bounded velocity and so on.
The proposed method is illustrated by computer simulations.
iv
To My Wife and Parents.
v
Acknowledgments
I would like to thank Dr. Zhihua Qu, my supervisor, for his many suggestions and constant
support during this research. I am also thankful to Dr. Jing Wang for his guidance through
the early years of chaos and confusion.
Ishouldalsogivethankstoallthegraduatestudentswhoworkedorworkinrobotics/conctrol
lab, they give many helps to my research.
Of course, I am grateful to my wife and parents for their patience and love. Without
them this work would never have come into existence (literally).
vi
TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
CHAPTER 2 REVIEW OF PLANNING . . . . . . . . . . . . . . . . . . . . 7
2.1 Classical Path Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Road Map Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Cell Decomposition Methods . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Potential Field Methods . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Motion Planning In A Dynamic Environment . . . . . . . . . . . . . . . . . 16
2.2.1 Velocity Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Shortest Path Satisfying The Kinematic Constraint . . . . . . . . . . . . . . 20
vii
2.3.1 Dubin’s Car . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
CHAPTER 3 REAL-TIME TRAJECTORY PLANNING FOR GROUND
VEHICLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Weakness Of The Existed Approaches . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Trajectory Planning For A Ground Vehicle . . . . . . . . . . . . . . . . . . . 29
3.3.1 Scenario for Trajectory Planning . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Optimal Solutions for Real-time Trajectory Planning . . . . . . . . . 33
3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Trajectories Comparison Without Obstacles . . . . . . . . . . . . . . 46
3.4.2 Trajectories Comparison With Obstacles . . . . . . . . . . . . . . . . 48
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
CHAPTER4 REAL-TIMETRAJECTORYPLANNINGFOR AERIALVE-
HICLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Problem Formulation In 3D Space . . . . . . . . . . . . . . . . . . . . . . . 58
viii
4.2.1 Scenario of 3D Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.2 Model of Flying Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 Optimal Real-time Trajectory For Flying Vehicles . . . . . . . . . . . . . . . 62
4.3.1 Trajectory Planning without Considering Obstacles . . . . . . . . . . 63
4.3.2 Trajectory Planning with Static and Moving Obstacles . . . . . . . . 66
4.3.3 Optimal Feasible Trajectory in 3D Space . . . . . . . . . . . . . . . . 72
4.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
CHAPTER5 TRAJECTORYPLANNINGFOR GROUNDVEHICLESWITH
CONSIDERING “HARD” AND “SOFT” OBSTACLES . . . . . . . . . . . 83
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 General Description Of Obstacles . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.1 Obstacles with Any Geometric Shapes . . . . . . . . . . . . . . . . . 85
5.2.2 Collision Avoidance Criteria for Different Type of Obstacles . . . . . 86
5.3 Optimal Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.1 Optimal Feasible Trajectory for “Hard” Obstacles . . . . . . . . . . . 90
5.3.2 Optimal Feasible Trajectory for All Obstacles . . . . . . . . . . . . . 96
5.3.3 Further Improvement of The Performance . . . . . . . . . . . . . . . 98
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