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A Practical Trajectory Planning Framework for Autonomous Ground Vehicles Driving in Urban Environments

Authors:
  • The Beijing Institute of Basic Medical Sciences

Abstract and Figures

This paper presents a practical trajectory planning framework towards fully autonomous driving in urban environments. Firstly, based on the behavioral decision commands , a reference path is extracted from the digital map using the LIDAR-based localization information. The reference path is refined and interpolated via a nonlinear optimization algorithm and a parametric algorithm, respectively. Secondly, the trajectory planning task is decomposed into spatial path planning and velocity profile planning. A closed-form algorithm is employed to generate a rich set of kinematically-feasible spatial path candidates within the curvilinear coordinate framework. At the same time, the velocity planning algorithm is performed with considering safety and smoothness constraints. The trajectory candidates are evaluated by a carefully developed objective function. Subsequently, the best collision-free and dynamically-feasible trajectory is selected and executed by the trajectory tracking controller. We implemented the proposed trajectory planning strategy on our test autonomous vehicle in the realistic urban traffic scenarios. Experimental results demonstrated its capability and efficiency to handle a variety of driving situations, such as lane keeping, lane changing, vehicle following, and static and dynamic obstacles avoiding, while respecting traffic regulations.
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A Practical Trajectory Planning Framework for Autonomous Ground
Vehicles Driving in Urban Environments
Xiaohui Li, Zhenping Sun, Zhen He, Qi Zhu, and Daxue Liu
Abstract This paper presents a practical trajectory plan-
ning framework towards fully autonomous driving in urban
environments. Firstly, based on the behavioral decision com-
mands, a reference path is extracted from the digital map
using the LIDAR-based localization information. The reference
path is refined and interpolated via a nonlinear optimization
algorithm and a parametric algorithm, respectively. Secondly,
the trajectory planning task is decomposed into spatial path
planning and velocity profile planning. A closed-form algorithm
is employed to generate a rich set of kinematically-feasible
spatial path candidates within the curvilinear coordinate frame-
work. At the same time, the velocity planning algorithm is
performed with considering safety and smoothness constraints.
The trajectory candidates are evaluated by a carefully develope-
d objective function. Subsequently, the best collision-free and
dynamically-feasible trajectory is selected and executed by the
trajectory tracking controller. We implemented the proposed
trajectory planning strategy on our test autonomous vehicle
in the realistic urban traffic scenarios. Experimental results
demonstrated its capability and efficiency to handle a variety of
driving situations, such as lane keeping, lane changing, vehicle
following, and static and dynamic obstacles avoiding, while
respecting traffic regulations.
I. INTRODUCTION
Autonomous driving technologies have great potentials
to improve driving safety, comfort and efficiency. The past
three decades have witnessed the remarkable development
of autonomous driving technologies, which have attracted
considerable interest and efforts from both academia and
industry. Particularly in the last decade, with the advent of
advances in sensing, computer technologies, artificial intel-
ligence, and so forth, the autonomous driving technologies
have become an extraordinary active research field in the
robotics community. During the DARPA Grand Challenges
(DGC) and DARPA Urban Challenge (DUC), AGVs exhib-
ited their abilities of autonomously driving in both off-road
and on-road environments [1], [2], [3], [4].
When AGVs advance towards handling realistic dynamic
urban traffic scenarios, they are required to be capable of
handling a variety of complex maneuvers, such as lane
keeping, vehicle following, lane changing, merging, while
respecting traffic rules, avoiding static and dynamic ob-
stacles, and interacting with other traffic participants [5].
To enable the vehicle to autonomously drive in realistic
*This work was supported in part by the National Natural Science
Foundation of China under Grant 61473303 and 91220301.
Xiaohui Li, Zhenping Sun, Zhen He, Qi Zhu, and Daxue Liu
are with the College of Mechatronic Engineering and Automation,
National University of Defense Technology, Changsha, P. R.
China (e-mail: xiaohui lee@outlook.com, sunzhenping@outlook.com,
hezhen.nudt@gmail.com, zhq cs@126.com).
urban environments, various state-of-the-art technologies are
required. As one of the core technologies, motion planning
plays a critical role in coping with these challenges. Based
upon amount of previous research on this topics [3], [4],
[6], this paper focuses on addressing the trajectory planning
problem for AGVs driving in realistic urban scenarios in a
practical way rather than a theoretical way.
II. RELATED WORK
A large number of motion planning algorithms have been
proposed for AGVs driving in urban environments. These
algorithms can be roughly categorized into two major groups.
One focuses on computing a long-term collision-free path
using deterministic or random graph-search algorithms [7],
[8], [9], which are capable of handling complex environmen-
tal constraints and efficiently preventing reactive motions.
Most of these powerful algorithms are especially suitable
for AGVs driving in partially or completely unknown envi-
ronments. However, the resultant paths are often comprised
of concatenated short-term motion primitives, such as stop-
and-redirect motions, which cannot meet the smooth and
relatively high-speed requirements in typical urban driving
scenarios. In addition, most of these search-based algorithms
are too computationally demanding to deal with the dynamic
traffic situations.
There has been substantial research on trajectory planning
for AGVs driving in urban environments. A well-known and
efficient strategy follows a discrete sampling and optimiza-
tion scheme. In [3], a model-predictive motion planner is
proposed using the curvature polynomials to parameterize the
control input space based on the work in [10]. A similar work
can be found in [11] and [12]. In [13], nudges and swerves
laterally shifting from the base trajectory are employed to
avoid obstacles along the reference path while being aligned
with the reference path. A similar scheme is adopted in [5],
but considering both the lateral and longitudinal movements
within the Fren´
et framework. The authors in [14] considers
both the vehicle model and closed-loop feedback control
laws to generate drivable trajectory candidates aligning with
the reference path. A similar strategy was applied in [9].
Based on the Boss work in DUC [3], a powerful trajectory
planner for highway driving is proposed using spatiotemporal
lattice conforming to the road geometry [15]. Gu et al.
proposed a two-step motion planner aiming at addressing
both urban and highway driving in one framework [16]. Most
of these approaches generate a rich set of drivable trajectory
candidates firstly. Then the best trajectory which minimizes
a specified cost function is selected for execution. Instead
2015 IEEE Intelligent Vehicles Symposium (IV)
June 28 - July 1, 2015. COEX, Seoul, Korea
978-1-4673-7266-4/15/$31.00 ©2015 IEEE 1160
of applying the discrete optimization scheme, very recent
work in [6] formulates the trajectory planning problem as a
nonlinear optimization problem with inequality constraints.
Based on a reference corridor provided by the digital map,
online perception data, and high-level decision process, the
planner explicitly considers hard constraints imposed by both
static obstacle and dynamic vehicles, as well as the maximal
steering curvature. The Newton type method is applied to
solve the optimization problem in the continuous state space.
Based upon previous work mentioned above, this paper
focuses on addressing the trajectory planning problem for
AGVs driving in urban environments. The reference path is
extracted using the digital map relying on the accurate and
robust LIDAR-based localization technology. We admit that
the trajectory planner assumes more responsibility to handle
many dynamic traffic situations in an reactive manner with
explicitly considering the constraints imposed by vehicle
motion model and dynamic environments. Even though, it
is still necessary for the trajectory planner to take advantage
of maneuver decisions from the behavioral planner. In this
way, it does not only significantly reduce the search space for
trajectory planning but also avoid over-reactive or aggressive
maneuvers in most of non-imminent traffic situations.
III. FRAMEWORK AND METHODOLOGY
An overview of the system framework is described here.
As shown in Fig. 1, the reference path is derived firstly. To
meet realtime requirements, we apply the nonlinear optimiza-
tion algorithm to refine the reference path locally rather than
globally. After that, the cubic B-spline algorithms is used
to interpolate the optimized path in order to obtain dense
waypoints. Considering the road geometry constraints as well
as handling both static and moving objects, we decompose
the trajectory planning problem into two subtasks: spatial
path planning and velocity planning. Instead of using the
optimization scheme to produce a sole optimal trajectory in
each replan cycle [6], the trajectory planner is capable of
generating a rich set of sub-optimal candidates, which could
efficiently overcome noises in the perception and localization
systems. Besides, it ensures that the vehicle could safely stop
in the imminent situations.
Reference path extraction
and smoothening
Spatial path
generation
Velocity profile
generation
Situation-ware
Trajectory
evaluation
Collision Test
Fig. 1: System framework overview.
To guarantee driving safety and improve driving comfort,
the collision test is performed to trim the trajectory collide
with static and moving objects. Then, a objective function
with a set of cost terms is carefully designed to select the
best trajectory candidate. To handle various realistic driving
situations in urban environments, a situation-aware policy is
introduced to adaptively tune the weights of the cost terms
in the objective function. The best trajectory is transformed
into actuator commands by the trajectory tracking controller
subsequently.
A. Online perception and localization for trajectory plan-
ning
Many researchers have proposed efficient trajectory plan-
ning algorithms for AGVs driving in highways and urban
environments. Most of them assume that lanes could be
obtained as prior information. To the best of the authors’
knowledge, even in urban environments, the lanes cannot be
robustly detected in many areas. Besides, the lane detection
performance is highly dependent on weather and light con-
ditions. A possible method to mitigate these issues is using
digital maps combined with GPS-based inertial navigation
System. Nevertheless, it may still suffer from the localization
noises resulting from the block and reflection effects caused
by tall buildings or forests. All of these negative effects make
it hard to obtain robust localization information of lane-level
accuracy. To overcome these problems, many researchers
take advantage of LIDAR or vision-based localization tech-
nologies [17], [18].
Fig. 2: Local trajectory planning map based on reference
information from the digital map.
In this study, the trajectory planner uses the reference
path information based on the LIDAR-based localization ap-
proach, which is similar to that proposed in [17]. Combining
the data from GPS, IMU, and Velodyne HD-LIDAR, the
high-resolution grid-map are created offline. Then we use
the online LIDAR perception data for real-time localization.
The experiments demonstrate its ability to provide reliable
localization information for realtime autonomous driving in
the urban environments with narrow roads. Based on the
localization method, we are able to use lane information
provided by the digital map. As shown in Fig. 2, the
green and blue waypoints represent the right and left lanes
respectively. The grey-scale mother map is created offline
with high resolution (20cm ×20cm per cell) using cloud
point data of the 64-beam HD-LIDAR. The grey-scale value
represents the height value of each grid. The cells with
magenta color indicates online detected obstacles, including
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dynamic and static obstacles. The rectangles represent the
detected dynamic obstacles with arrows indicating their
moving directions.
B. Reference path smoothing
Based upon the aforementioned localization approach, rich
information of the digital map can be utilized for AGVs.
For trajectory planning, the reference path could be the
centerline of the desired lane, which could be obtained
from behavioral commands. However, the centerline may
not be smoothly enough to be tracked in many situations,
e.g. when the vehicle negotiates a curvy turn. To ensure
that the desired path could be easily tracked by the vehi-
cle, the conjugate gradient method is applied to refine the
reference path. A similar method was referred in [8]. It
is able to smoothen the centerline in a continuous space.
Giving discrete waypoints of the centerline as seed vertices
xi=(xi,y
i),(i=1, ..., N ), which can be slightly tuned to
minimize the following objective function:
arg min(ω1
N1
i=1
xi+1 Δxi)2+ω2
N1
i=1
(Δθi
|Δxi|)
2
)(1)
where Δxi=xixi1,(i>=2)is the dis-
placement vector at the vertex xi=(xi,y
i);Δθi=
tan1Δyi+1
Δxi+1 tan1Δyi
Δxi
is the vector direction change at
the vertex; ω1
2are weights. The first term minimizes the
the vector change between the adjacent vectors, while the
second term minimizes the cumulative curvature along the
path.
After applying the aforementioned optimization algorith-
m, a much smoother path could be obtained. In practice,
to achieve realtime performance, the waypoints taken for
smoothing are often sparse and the distances between the
waypoints are often large. To solve this problem, we take the
sparse point as the control points and use the cubic B-spline
to interpolate the refined reference path. In the meanwhile,
four dimensional states (x, y, θ, κ)of each point along the
smooth path could be obtained in an analytical manner. The
tangent angle θ(i)and the curvature κ(i)of the waypoints
along the path are defined as
θ=tan
1(˙x
˙y)(2)
κ(t)= ˙x¨y¨x˙y
x2y2)3/2(3)
As shown in Fig.3, the green curve with equidistant way-
points is the optimized reference path. To simplify the nonlin-
ear optimization problem and achieve realtime performance,
environmental constraints are not explicitly considered dur-
ing the path smoothing process. Obstacle avoidance will
be taken into account by the trajectory planning algorithms
discussed later.
right bound
left bound
centerline
C.G. optimization result
&XELF%íVSOLQHLQWHUSRODWLQJUHVXOW
Fig. 3: Conjugate gradient algorithm is applied to smooth the
centerline. Then dense waypoints are obtained using cubic
B-spline interpolating method.
C. Spatial path generation based on the curvilinear coordi-
nate framework
When AGVs drive in urban environments, in order to
safely and friendly interact with other traffic participants
like human drivers while respecting traffic regulations, it
is necessary to generate trajectories explicitly considering
both road geometry and speed constraints. To achieve this,
instead of using the Cartesian coordinate framework, the
road geometry model is described using the curvilinear
coordinate framework. More precisely, the reference path is
parameterized as a function of the arc length. In this way,
vehicles’ movements could be naturally divided into two
dimensions: one is the lateral movement, and the other is
the longitudinal movement. Relying on this framework, the
trajectory planning are inherently decoupled into spatial path
generation and velocity profile generation. The spatial path
generation problem is solved firstly.
After using the smoothing algorithm mentioned above, the
reference path is obtained and taken as the base frame of
the curvilinear system. To ensure the consistency between
consecutive replans, the generated path is required to be
aligned with the base frame. In [3], a model-predictive
motion planner is proposed, which sampled a finite set of
terminal states laterally shifting from the base frame firstly.
Then, the path generation problem was reformulated as a
two-point boundary value problem. To reduce the solution
space while guaranteeing the representativeness of output
maneuvers, curvature polynomials were employed to param-
eterize the control input space. The approach considered
constraints imposed by the sampling terminal configurations.
However, it ignored the road geometry. As a consequence,
when the reference path is curvy, it is difficult to generate
long-term paths being aligned with the road geometry.
To overcome this disadvantage, we refer to the trajec-
tory planning strategy mentioned in [5]. The well-known
sampling-based motion planning strategy is employed to
efficiently generate a rich set of path candidates, which are
capable of avoiding static obstacles as well as being aligned
with the reference path geometry. The details are described
as follows.
Based on the curvilinear coordinate framework, the sam-
pling terminal states could be represented by two parameters,
one is the preview distance sfalong the reference path
and the other is the lateral offset lf. This is different from
the sampling method in the Cartesian coordinate [3]. The
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preview distance sfdetermines how fast the vehicle is
regulated to be aligned with the base frame. In practice, it
could be adaptively tuned according to the vehicle speed
without violating the maximal lateral acceleration limit. The
lateral offset l0is the perpendicular distance between the
vehicle current position and the corresponding point the
nearest point along the base frame.
Base on the differential flatness control theory referred
in [19], polynomial splines can be applied to represent the
smooth transition from the current lateral offset l0to the
sampling terminal lateral offset lf. To ensure the path could
be analytically solved and cubic polynomial is applied as
referred in [20], quintic polynomial could also be applied to
guarantee the continuity of the first-derivative of the lateral
offset. But in practice, we found that it is also more sensible
to the initial conditions.
l(s)=c0+c1s+c2s2+c3s3(4)
Hence, it can be obtained
l(s0)=l0,l(sf)=lf(5)
Besides, the heading difference θ(s)between the vehicle
and the base frame could be derived by the first derivative
of the later offset l(s)with respect to the arc length s.
θ(s) = arctan( dl
ds)(6)
For simplicity, the terminal heading of the generated path
is set to be same as that of the base frame at the preview
distance sf. The vehicle’s initial heading angle may be
different from the tangent direction of the base frame at the
current position, so we can obtain:
θ(s0)=θ0(sf)=0 (7)
θ0is the initial heading difference between the vehicle and
the base frame. Since the number of unknown parameter-
s is equal to that of equations, the unknown parameters
{c0,c
1,c
2,c
3}could be analytically solved.
The curvature of the generated spatial path κ(s)can be
derived from the curvature κbof the base frame [21], [20],
[5].
κ(s)= 1
Q(κb+(1 b)(d2l/ds2)+κb(dl/ds)2
Q2)(8)
with
Q=(dl/ds)2+(1b)2
To guarantee the kinematical-feasibility of the generated
path, (1 b)is required to be greater than zero. In other
words, using this method is not able to generate drivable
paths when the lateral offset lsis greaterer than the radius of
the corresponding point on the base frame. The motion plan-
ning approach referred in [3] could be applied to overcome
the issue. Since the curvature state is the invariant interme-
diate variable between the curvilinear coordinate framework
and the Cartesian coordinate framework, the spatial path in
the Cartesian coordinate could be numerically solved using
the vehicle kinematic equations as follows.
˙x(s)=Qcos(θ(s))
˙y(s)=Qsin(θ(s))
˙
θ(s)=(s))
κ(s)=max{κmin,min{κ(s)max }}
(9)
where κmin and κmax indicate steering angle constraints
imposed by the vehicle. When vehicles drive at high speed, it
is necessary for the local planner to generate long-term path
to avoid reactive maneuvers. To achieve this, d2l/ds2=0
and dl/ds =0, when (s>=sf). In this way, the generated
paths are set to be aligned with the reference path after they
reach the sampling terminal states.
As shown in Fig. 4(a), the generated spatial path candi-
dates are able to connect the current vehicle state with the
sampling terminal states. Figure 4(b) illustrates that when
the vehicle has the initial lateral deviation (curves with dark
green color) or a certain initial heading difference (curves
with red color) from the base frame. The path generation
approach is capable of generating spatial path candidates
which are aligned with the base frame.
generated path
candidates
reference path
sampling
terminal states
(a)
ǻș
ǻd
(b)
Fig. 4: Path candidates generation results. (a) l0=0and
θ0=0,(b) l0dand θ0θ
D. Velocity profile generation
Velocity planning has a significant impact on the driving
safety and comfort. Especially when vehicles drive in the
dynamic road traffic, where velocity planning is required
to be explicitly considered. In this paper, velocity profile
generation is performed considering a variety of constraints,
such as commands from the behavioral planner, maximal
allowed lateral and longitudinal accelerations. These con-
straints could considerably reduce the solution space for the
velocity planning as well as allow the velocity planner to
concentrate on the space where the optimal solution is most
likely to exist.
In this study, a hierarchical velocity profile generation
scheme is developed. The maximal speed is determined
firstly. Then, the trapezoidal profile is employed to generate
the initial velocity law assigned along the generated path.
After that, to improve smoothness of the longitudinal control,
polynomial splines are applied to smoothen the linear ve-
locity profiles and generate acceleration-continuous velocity
curves.
1163
Firstly, in order to guarantee safety and improve driving
comfort, several constraints are taken into account to deter-
mine the maximal speed as follows.
(i) The maximal allowed speed Vlimit1. It could be derived
by considering the high-level behavioral planner reasoning
about the road conditions, traffic regulations and the safe
distance of the generated path to the obstacles.
(ii) The maximal allowed lateral acceleration AccMaxLat
V2
limit2 |κ|≤AccMaxLat
To prevent lateral force acting on tires from entering into the
nonlinear or saturated zone, alleviate sideslip effects as well
as ensure the yaw stability, the AccM axLat is required to be
carefully determined considering vehicle dynamics.
(iii) The maximal longitudinal velocity acceleration limit
AccMax Lon and deceleration limit DecMax Lon.
V2
limit3 v2
0
2AccMax Lon
+V2
limit3 v2
f
2DecMax Lon
+Dsafe =S
where v0is the current velocity, vfis the terminal speed,
and Srepresents the path length. The terminal speed vf
is determined by the high-level behavioral planner, which
considers the surround moving vehicles and traffic regu-
lations. For instance, when the vehicle executes a vehicle
following maneuver, the terminal speed is set to be the same
as the front vehicle. When the vehicle approaches a stop
sign/line or meets the passing pedestrians, vfis set to be
zero. The details will not be discussed in this paper. Besides,
the safety distance Dsafe, which involves the response time
delay tdelay and imminent braking distance Dimminent. The
imminent braking distance Dimminent can be represented as
a function with respect to vf, e.g. the well-known constant
time gap law can be employed.
Dsafe =tdelayv0+Dimminent(vf)
02
v
2
f
v
01
v
t
v
max 2
v
max1
v
limit
V
s
table
t
1
f
v
Lon
Acc
Lon
D
ec
(a)
00
(, )va
O
t
v
11
(, )va
22
(, )va
33
(, )va
Ramp-up
velocity profile
Ramp-down
velocity profile
(b)
Fig. 5: Velocity profile generation results. (a) trapezoidal
velocity profile generation,(b) velocity profile smoothing
As shown in Fig. 5, the trapezoidal velocity profile is
employed to generate the initial velocity profile. For sim-
plicity, the linear velocity profile with constant acceleration
and deceleration values is used. Base on our experimental
experience gained in field tests, to avoid oscillations of
the longitudinal control, the velocity is required to be kept
at the maximal speed vmax for a certain period of time,
which is longer than tsteady. Therefore, vmax does not
necessarily reach the maximal allowed speed Vlimit, such
as the blue solid velocity curve shows in Fig. 5. Given the
initial speed v0, terminal speed vf, the path length S, the
maximal allowed speed Vlimit, and user-specified parameters
{Acclon,Dec
lon,t
stable}, the closed-form velocity profile
can be obtained.
For the smooth tracking purpose, we smoothen the ini-
tially generated trapezoidal velocity profiles to guarantee the
continuity of the longitudinal acceleration. Inspired by the
parametric velocity profile generation method in [16], the
velocity is smoothed using cubic polynomial.
v(t)=v0+at +bt2+ct3
Correspondingly, the acceleration acc(t)and path length
s(t)can be derived through the first derivative and integration
of the velocity function respectively. Given initial velocity v0
and acceleration a0, the terminal velocity vf, acceleration af,
and path length sf. The unknown parameters {a, b, c, tf}in
(10) could be analytically solved via the following equations.
acc(0) = a=a0
v(tf)=v0+atf+bt2
f+ct2
3=vf
acc(tf)=a+2btf+3ct2
f=af
s(tf)=v0tf+1
2at2
f+1
3bt3
f+1
4ct4
f=sf
(10)
As shown in Fig. 5, the acceleration-continuous S-shaped
ramp-up velocity profile (the red solid line) and ramp-down
velocity profile (the blue dash line) are solved respectively.
IV. TRAJECTORY CANDIDATES EVALUATION
The collision test is performed to trim the part of tra-
jectories colliding with obstacles instead of the entire tra-
jectory. To achieve this, the local trajectory planning map
is represented as an occupancy grid map based on the
online perception information. To reduce the computational
complexity of the collision test, the rectangular shape of the
vehicle is approximated by a set of circles with the same
radius [6].
Noticed that avoidance of the moving objects which run in
the same or opposite directions of ours are handled through
the longitudinal velocity planning using the lane information
from the digital map. To avoid the pedestrians or vehicles
runs in the traffic intersection, we conservatively consider
the prediction of the their movements within a finite time
horizon (e.g 3s). The research in [22] provides a promising
approach to handle moving obstacle avoiding in dynamic
traffic scenarios.
After the collision test, the remaining trajectories are eval-
uated via an objective function comprised of four weighted
cost terms as
i=N
argmin
i=1
(ωpJp(τi)+ωsJs(τi)+ωdJd(τi)+ωcJc(τi))
(11)
where J{p, s, d, c}are cost terms, ω{p, s, d, c}are the
corresponding weighted factors, and τi(i=1, ..., N)is the
evaluated trajectory candidate. The cost value is normalized
to be within [0, 1]. The cost term Jpprefer longer trajectory
in order to prevent over-reactive maneuvers.
Jp=(Smax S(τi))/Smax (12)
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where S(τi)is the path length of the trajectory candidate τi
along the base frame and Smax is the path length threshold.
To avoid aggressive lateral movements, smoothness criterion
is considered by the cost term Js, which is the integration
of curvature along the trajectory candidate.
Js=1
sfsf
0
κ(τi(s))
κmax
ds (13)
To ensure the vehicle track the base frame accurately, the
cost term Jdpenalizes path which deviates far from the base
frame.
Jd=1
sfsf
0
|D(τi(s))|
Dmax
ds (14)
where D(τi(s)) is the deviation distance and Dmax is the
deviation distance threshold.
The cost term Jcpenalizes the path inconsistency during
consecutive replans. The inconsistency between consecutive
replans can easily result in abrupt steering actions, control
overshoots or even control instability. To solve the problem,
we minimize the sampling terminal lateral offset variations
between consecutive replans.
Jc=|l(τi)lp(τi)|
lmax
(15)
where l(τi)is the sampling terminal lateral offset of the
current path, lp(τi)is the sampling terminal lateral offset
of the best path in the previous plan.
High Low
Cost
Fig. 6: Trajectory candidates evaluation.
As shown in Fig. 6, the color illustrates the cost of the
generated trajectory candidates, the lowest cost trajectory
candidate with green color is selected for execution. Cur-
rently, the weights are empirically determined to make a
compromise between the cost terms mentioned above, the
machine learning technique could be introduced to adaptively
tune these parameters.
V. E XPERIMENTAL RESULTS
Our test autonomous vehicle is shown in Fig.7. The low-
level steer and speed control systems have been modified to
be drive-by-wire. Field experiments have been carried out
on this platform to verify the efficiency and applicability of
the proposed trajectory planning algorithms in the realistic
urban environments.
The proposed local trajectory planning algorithms are
implemented in C++, which runs on a PC (Intel(R) Core(TM)
SICK LMS Laser
Riegl Laser
Velodyne Laser
SICK LMS
Laser
SICK LDLRS
Laser SICK LMS
Laser
IBEO
Laser
Stereo Vision
System
Fig. 7: Our test autonomous vehicle.
i7@2.70GHz, 4.0GB memory) with Linux system. The re-
plan cycle is set to 100ms. The trajectory planning consumes
around 20ms, while the time spent on path smoothing
is around 50ms. In practice, this can meet the real-time
requirements.
The maximal speed is set to 25km/h limited by the
traffic regulation of the urban area, where we carry out the
experiments. The terminal speed of the trajectory is set to
20km/h, when it does not collide with obstacles. The maxi-
mal path length is limited to 80m limited by the perception
information. The maximal lateral acceleration limit is set to
3.0 m/s2to ensure the driving comfort. The total number
of the generated trajectory candidates is 500, which could
be enhanced to cope with the complex environments. For
instance, to improve the probability of the existence of the
collision-free path candidates, sampling terminal states, such
as lateral offset and preview distance, can be sampled more
densely.
Figure 8 shows the trajectory planning results when the
AGV negotiates a smooth turn and a curvy turn, respectively.
It can be seen that vehicle is capable of generating the tra-
jectory candidates which are aligned with the road geometry
while avoid stationary obstacles.
(a) (b)
Fig. 8: Trajectory Planning results for Lane keeping. (a) a
smooth turn, (b) a curvy turn
Figure. 9 depicts the trajectory planning results when the
AGV interacts with other traffic participants. As Fig. 9 (a)
shows, the vehicle executes a lane-changing maneuver when
the current lane is occupied by a slowly moving vehicle in
1165
front. It can be seen In Fig. 9(b) that although the current
lane is taken up by a vehicle in front, which has a relative
higher speed than the AGV. In this case, the AGV executes a
vehicle following maneuvers. Besides, the trajectory planner
is also capable of planning a trajectory which keeps a certain
safe distance from the oncoming vehicle in the adjacent lane.
(a) (b)
Fig. 9: Interact with the other traffic participants. (a) lane
changing, (b) vehicle following
VI. CONCLUSIONS
This paper has proposed a practical and efficient trajec-
tory planning framework for autonomous driving in urban
environments. The presented trajectory planning strategy
employs a hierarchical strategy. A reference path is extracted
from the digital map relying on the accurate and robust
localization information using LIDAR-based localization
technology. The reference path is refined and interpolated
via the nonlinear optimization algorithm and parametric
algorithm respectively. Dividing the trajectory planning into
spatial path generation and velocity profile generation has
significantly reduced the solution space and enabled the
planner to generate a rich set of drivable trajectory candi-
dates, which are aligned with road geometry and capable
of handling a variety of dynamic traffic situations, such as
lane keeping, lane changing, vehicle following, static and
moving objects avoidance. Although the presented planning
framework focuses on solving the motion planning in on-
road environments, it can easily be extended to integrate
with the graph-search algorithm in off-road environments.
Further research will consider uncertainty issues resulting
from localization, perception and control systems to interact
with the other traffic participants more naturally in urban
environments.
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