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AnIntegratedFrameworkforPlanningand ControlofSemi

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AnIntegratedFrameworkforPlanningand ControlofSemi-AutonomousVehicles By Andrew Jacob Gray ... University of California, Berkeley

An Integrated Framework for Planning and
Control of Semi Autonomous Vehicles
Andrew Jacob Gray
Doctor of Philosophy in Engineering Mechanical Engineering
University of California Berkeley
Professor J Karl Hedrick Co Chair
Professor Francesco Borrelli Co Chair
This thesis presents the design of a novel active safety system prevent
ing unintended roadway departures The proposed framework unifies threat
assessment stability and control of passenger vehicles into a single com
bined optimization problem A nonlinear Model Predictive Control NMPC
problem is formulated where the nonlinear vehicle dynamics in closed loop
with a driver model is used to optimize the steering and braking actions
needed to keep the driver safe A model of the drivers nominal behavior is
estimated based on his observed behavior The driver commands the vehicle
while the safety system corrects the drivers steering and braking action in
case theres a risk that the vehicle will unintentionally depart the road The
resulting predictive controller is always active and mode switching is not nec
essary We show simulation results detailing the behavior of the proposed
controller as well as experimental results obtained by implementing the pro
posed framework on embedded hardware in a passenger vehicle The results
demonstrate the capability of the proposed controller to detect and avoid
roadway departures while avoiding unnecessary interventions
List of Publications
1 A Gray Y Gao T Lin J K Hedrick E Tseng and F Borrelli Predic
tive Control for Agile Semi Autonomous Ground Vehicles using Motion
Primitives American Control Conference Montreal Canada June 2012
2 Gao Y A Gray J Frasch T Lin E Tseng J K Hedrick and F
Borrelli Spatial Predictive Control for Agile Semi Autonomous Ground
Vehicles International Symposium on Advanced Vehicle Control Seoul
Korea September 2012
3 A Gray M Ali Y Gao J K Hedrick and F Borrelli Integrated Threat
Assessment and Control Design for Roadway Departure Avoidance In
telligent Transportation Systems Anchorage September 2012
4 A Gray M Ali Y Gao J K Hedrick and F Borrelli Semi
Autonomous Vehicle Control for Road Departure and Obstacle Avoidance
IFAC Symposium on Control in Transportation Systems Sofia Bulgaria
September 2012
5 J V Frasch A Gray M Zanon H J Ferreau S Sager F Borrelli and
M Diehl An Auto generated Nonlinear MPC Algorithm for Real Time
Obstacle Avoidance of Ground Vehicles European Controls Conference
Zurich Switzerland July 2013
6 A Gray M Ali Y Gao J K Hedrick and F Borrelli A Unified
Framework for Semi autonomous Control and Active Safety Transactions
in Intelligent Transportation Systems 2013
7 A Hackbarth A Gray and E Kreuzer Multi Agent Motion Control of
Autonomous Vehicles in 3D Flow Fields Proceedings in Applied Math
ematics and Mechanics Hamburg Germany June 2012
8 A Hackbarth A Gray E Kreuzer and J K Hedrick Collaborative
Control of Multiple AUVs for Improving the Estimation of Flow Field
Dependent Variables IEEE Underwater Vehicles South Hampton Eng
land September 2012
9 A Gray Y Gao J K Hedrick and F Borrelli Robust Predictive
Control for Semi Autonomous Vehicles with an Uncertain Driver Model
IEEE Intelligent Vehicles Symposium Gold Coast Australia June 2013
10 A Gray M Ali Y Ga J K Hedrick and F Borrelli Multi Objective
Collision Avoidance Dynamic Systems and Controls Conference Stan
ford October 2013
11 A Gray Y Gao J K Hedrick and F Borrelli Stochastic Predictive
Control for Semi Autonomous Vehicles with an Uncertain Driver Model
Intelligent Transportation Systems Conference The Hague Netherlands
2013 Submitted
12 Y Gao A Gray J K Hedrick and F Borrelli Robust Predictive
Control of Semi autonomous Ground Vehicle Transactions in Intelligent
Transportation Systems 2013 Submitted
I would like to thank my research advisors J Karl Hedrick and Francesco
Borrelli as well as Pieter Abbeel for providing invaluable guidance and sup
port while conducting the research presented in this thesis Further I would
like to acknowledge those I worked with in the Vehicle Dynamics and Control
Lab Namely Brandon Basso Jared Wood Shih Yuan Liu Jared Garvey
Selina Pan and SangHyun Hong I would also like to acknowledge those in
the Model Predictive Control Lab Yiqi Gao Theresa Lin and Ashwin Car
valho Further this work received the invaluable support and influence from
Mohammed Ali at Volvo Car Thank you all
Table of Contents
List of Publications i
Acknowledgments iii
1 Introduction 1
1 1 Contributions 3
1 1 1 Hierarchical Model Predictive Control 3
1 1 2 A Unified Framework for Active Safety 3
1 1 3 Robust Model Predictive Control for Uncertain Driver
2 Vehicle Dynamics 5
2 1 Nonlinear Four Wheel Model 8
2 2 Tire Models 13
2 2 1 Pacjeka Tire Model 13
2 2 2 Fiala Tire Model 19
2 2 3 Linear Tire Force Model 21
2 3 Bicycle Model 23
2 4 Spatial Model 25
2 5 Linear Model 28
2 6 Safety Constraints 31
3 Driver Models 33
3 1 Nominal Driver Model 35
3 1 1 Parameter Estimation 35
3 2 Attentive Driver Model 40
3 3 Uncertain Driver Model 41
3 4 Stochastic Driver Model 42
3 5 Driver in the Loop Vehicle Model 43
4 Driver Assistance Systems 44
5 Model Predictive Control 51
5 1 Nonlinear Model Predictive Control 53
5 2 Linear Time Varying Model Predictive Control 55
5 3 Robust Model Predictive Control 58
5 3 1 Set based Robust MPC 58
5 3 2 Stochastic Robust MPC 65
6 Hierarchical Model Predictive Control 71
6 1 Motion Primitive Path Planner 75
6 1 1 High Level Motion Primitive Framework 75
6 1 2 Motion Primitives for Collision Avoidance 78
6 1 3 Planning With Motion Primitives 84
6 1 4 Low Level MPC Path Follower 85
6 1 5 Simulation And Experimental Results 86
6 2 Spatial Model Path Planner 94
6 2 1 High Level Spatial Model Framework 96
6 2 2 Low Level MPC Path Follower 97
6 2 3 Simulation and Experimental Results 98
7 Integrated Safety Framework 106
7 1 Integrated Active Safety 109
7 2 Simulation Results 111
7 2 1 Unintentional Roadway Departure 111
7 2 2 Collision Avoidance 125
7 3 Experimental Results 133
7 3 1 Test 1 Excessive Speed in a Curve 134
7 3 2 Test 2 Unintentional Drifting 137
7 4 Set based Robust Active Safety 140
7 4 1 Simulation Results 143
7 5 Stochastic Robust Active Safety 149
7 5 1 Simulation Results 150
A Experimental Vehicle Setup 154
Bibliography 158
List of Figures 169
List of Tables 178
Advances in sensing technologies have enabled the introduction and commer
cialization of several automated driving features over the last two decades
Examples of such applications are threat assessment Warning Strategies
12 Adaptive Cruise Control ACC 91 Rear end Collision Avoidance sys
tems 22 as well as Lane Keeping systems 77 In safety applications
autonomous interventions are activated automatically Over activation of
automated safety interventions might be felt as intrusive by the driver while
on the other hand a missed or delayed intervention might lead to a collision
A typical active safety system architecture is modular 3 with separate
threat assessment decision making and intervention modules In particular
the threat assessment module deals with the task of determining whether in
terventions are necessary and plays an important role in the interaction with
the driver The threat assessment module repeatedly evaluates the driver s
ability in maintaining safety in each situation and this information is used by
the decision making module in order to decide whether and how to assist the
driver It is a challenge for an active safety system to properly assess when to
intervene In the literature a large variety of threat assessment and decision
making approaches can be found 22 78 62 29 In the simplest approaches
used in production vehicles automated steering or braking interventions are
issued when simple measures like the time to collision 22 or time to line
crossing 78 pass certain thresholds
More sophisticated approaches on the other hand include the computa
tion of Bayesian collision probabilities 62 or sets of safe states from which the
vehicle can safely evolve 29 In advanced safety systems such as roadway
departure prevention the intervention module has the goal to both determine
a safe trajectory and coordinate the vehicle actuators The literature on ve
hicle path planning and control is rich see e g 32 72 104 48 Because of
its capability to systematically handle system nonlinearities and constraints
work in a wide operating region and close to the set of admissible states and
inputs Model Predictive Control MPC has been shown to be an attractive
method for solving the path planning and control problem 32 33 Previous
approaches to lane departure prevention using predictive control as in 4
make the assumption that the vehicle is traveling at a constant velocity and
can therefore not consider braking and does not use any information about
the human driver
In this thesis we design a novel active safety system for prevention of un
intended roadway departures with a human in the loop Rather than sepa
rately solving the threat assessment decision making and intervention prob
lems we reformulate them as a single combined optimization problem In
particular a predictive optimal control problem is formulated which simul
taneously uses predicted driver s behavior and determines the least intrusive
intervention that will keep the vehicle in a region of the state space where the
driver is deemed safe The proposed controller is always active which avoids
the design of switching logic or the tuning of a sliding scale In addition
since the proposed controller is designed to only apply the correcting control
action that is necessary to avoid violation of the safety constraints the in
trusiveness of the safety application is kept minimal Furthermore the full
nonlinear dynamics of the vehicle are considered in the optimization problem
and the corrective action can augment both the driver s steering and braking
The thesis is organized as follows in Chapter 2 we detail the vehicle
models that are used for control Chapter 3 introduces simplified driver
models that are estimated in real time as well as presents some extensions
to model uncertainty in the driver s future behavior Chapter 5 introduces
our Model Predictive Control approach as well as details how we handle the
uncertainty in the uncertain driver models Chapter 6 presents simulation
and experimental results from an implementation of Hierarchical MPC on an
experimental platform and Chapter 7 unifies everything into an Integrated
Safety Framework and presents simulative and experimental results
1 1 Contributions
The following describes the list of contributions made by the author The
bibliographic references refer to the List of Publications at the beginning of
this thesis
1 1 1 Hierarchical Model Predictive Control
Papers 1 2 describe an approach that decomposes the planning and con
trol problems into an upper and lower level In 1 the upper level solves the
path planning problem using motion primitives The authors are the first to
investigate the feasibility of planning using motion primitives for automotive
applications by formulating the problem and implementing the planning ar
chitecture on an experimental test vehicle The details are described in 6 1
In 2 the planning problem is made solvable in real time by utilizing a co
ordinate transformation where the contribution made is the implementation
of such a transformation within the model predictive control framework and
is discussed in 6 2 The work in 6 further reduces the computation time of
the MPC problem by using tailored algorithms
1 1 2 A Unified Framework for Active Safety
The main contribution in this thesis is on the development and implementa
tion of a novel active safety system framework for semi autonomous vehicles
presented in Chapter 7 In 3 and 4 the framework was proposed to unify
the threat assessment planning and control problem into a single combined
optimization problem that incorporates closed loop human behavior predic
tion In 6 the framework was implemented on a test vehicle and the suc
cessful results show the utility of the proposed controller In 10 we extend
the approach to include moving obstacles
1 1 3 Robust Model Predictive Control for Uncertain
Driver Models
The remaining contributions extend the unified framework to include robust
guarantees on safety by explicitly modeling the uncertainty on the driver s
behavior In 9 we use set based methods to capture the spread on all
possible future trajectories and constrain the controller to satisfy the safety
constraints for the whole invariant set as outlined in 5 3 1 In 12 we extend
this approach to the nonlinear vehicle model by reforming the dynamics and
approximating the robust invariant set and implementing the controller on
an experimental test vehicle In 11 we propose an uncertain driver model
by modeling the uncertainty using a probability distribution function and
probabilistically satisfy the safety constraints The approach is presented in
Vehicle Dynamics Models
This chapter introduces the various vehicle dynamics models useful for con
trol design The models presented capture the relevant dynamics deemed
important for our application of threat assessment planning and control
but are in general oversimplified as further dynamics are neglected Vehicle
dynamics has been well studied and we draw extensively from the literature
91 68 Consider the vehicle in Figure 2 1
Figure 2 1 A vehicle sketch depicting the body fixed coordinate frame Ob
as well as body fixed longitudinal and lateral velocities x and y forces Fx
Fy and moment M
The translational body fixed velocities are denoted as x and y for the
longitudinal and lateral axes respectively The yaw angle is denoted as
and the yaw rate about the z axis through the center of gravity is The
total longitudinal force acting on the vehicle is Fx the total lateral force
is Fy and the moment about the z axis through the center of gravity is
M Newton s law is applied to the center of gravity CoG to obtain the
general rigid body dynamics The following differential equations describe
the longitudinal lateral and yaw motion
mx Fx 2 1a
my Fy 2 1b
where m is the vehicle mass and I is the inertia about the z axis To model
the planar motion of the vehicle a coordinate transformation is needed from
the vehicle body fixed frame Ob to the inertial frame OI A simple rotation
around the z axis by the amount of the yaw angle is used to calculate the
velocities in the inertial frame
X x cos y sin 2 2a
Y y sin x cos 2 2b
where X and Y are the vehicle longitudinal and lateral velocities respectively
in the inertial frame and is the yaw rate
The sections to follow will detail the calculations of the forces acting
on the vehicle to arrive at mathematical models of varying complexity to
describe the vehicle motion The rest of the chapter is organized in the fol
lowing way in section 2 1 a Four Wheel Nonlinear Model is derived where
the forces Fx Fy and M are computed as nonlinear functions of the vehicle
state steering braking and driving at the four wheels In section 2 2 the
Pacjeka and Fiala tire models are presented A simplification from the Four
Wheel Model to a Bicycle model is derived in section 2 3 where the reduced

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