Control Methods of Mobile Robot Rough-Terrain Trajectory Tracking by ashi7790

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									2010 8th IEEE International Conference on                                                                                       ThB3.4
Control and Automation
Xiamen, China, June 9-11, 2010



             Control Methods of Mobile Robot Rough-Terrain Trajectory
                                    Tracking
                Yang. Yi, Graduate Student Member, IEEE, Fu. Mengyin, Zhu. Hao, Xiong. Guangming
                                              and Sun. Changsheng


   Abstract—This paper presents control methods and                        dynamic feedback linearization paradigm. In [3], the authors
simulation experiments of wheeled skid-steering mobile robot               applied experimental results to enable Fuzzy Logic modelling
trajectory tracking on the rough terrain. According to dynamics            of the vehicle-ground interactions in an integrated manner.
analysis of the robot, a motion constraint of the robot is put             These results illustrate the complexity of modelling
forward. To address the issue of uncertain disturbance factors
                                                                           systematically the ground conditions and the necessity of
during the robot running on the rough terrain, a practical fuzzy
lateral control law is presented, and the globally asymptotically          using two variables in identifying the surface properties. In
stable of the control law is proven. At the same time, according           [4], the authors described relevant rover safety and health
to the requirement of the robot motion control, the longitudinal           issues and presents an approach to maintaining vehicle safety
control law and the sensor pan-tilt control law are also proposed.         in a navigational context. Fuzzy logic approaches to
Using virtual prototype technology, the mobile robot and the               reasoning about safe attitude and traction management are
experimental field are established on the ADAMS and
                                                                           presented. In [5], the authors introduced a model-based
MATLAB co-simulation platform, and the robot trajectory
tracking in the simulation environment is performed. The                   control for fast autonomous mobile robots on soft soils. This
simulation experimental results indicate that the control                  control strategy takes into account slip and skid effects to
methods are robust and effective for the mobile robot running              extend the mobility over planar granular soils. Different from
on the rough terrain.                                                      above researches, which control the robots on the tarmac,
                                                                           grass, sand, gravel or soil, this paper focuses on the motion
                         I. INTRODUCTION                                   control for skid-steering vehicles on the bumpy and rocklike

A    UTONOMOUS automobile technology is a rapidly
     developing field, with interest in both academia and
industry[1]. Outdoor navigation of autonomous vehicles,
                                                                           terrain, and presents novel and effective trajectory tracking
                                                                           control methods, including the longitudinal, lateral, and
                                                                           sensors pan-tilt control law. Furthermore, based on
especially for rough-terrain driving, has already been a new               ADAMS&MATLAB co-simulation platform, iRobot
research focus. DARPA Grand Challenge and LAGR                             ATRV2 is modelled and the bumpy off-road terrain is
program stand for the top development level in this research               constructed, at the same time, trajectory tracking control
region. Rough-terrain driving research offers a challenge that             methods are validated effectively on this platform.
the in-vehicle control system must be able to handle rough
and curvy roads, and quickly varying terrain types, such as                          II. MOBILE ROBOT DYNAMIC ANALYSIS
gravel, loose sand, and mud puddles – while stably tracking
trajectories between closely spaced hazards. The vehicle must                 To research on the motion of skid-steering robots, the
be able to recover from large disturbances, without                        4-wheeled differentially driven robot, which is moving on the
intervention[1].                                                           horizontal road normally without longitudinal wheel slippage,
   Since robotics autonomous navigation tasks in outdoor                   is analyzed for kinematics and dynamics. As shown in Fig. 1
environment can be effectively performed by skid-steering                  (a), global Descartes frame and in-vehicle Descartes frame
vehicles, these vehicles are being widely used in military                 are established. In Global frame OXYZ , its origin O is
affairs, academia research, space exploration and so on. In [2],           sited on the horizontal plane where the robot is running, and
a model-based nonlinear controller is designed, following the               Z axis is orthogonal to the plane; in in-vehicle frame oxyz ,
                                                                           its origin o is located at the robot center of mass, z axis is
   Manuscript received October 29, 2009. This work was supported in part   orthogonal to the chassis of robot, x axis is parallel to the
by National Natural Science Foundation of China (NSFC 60773044) and        rectilinear translation orientation of the robot and y axis is
Certain National Defence Key Research Foundation, The PLA General
Armament Department (****0178) .                                           orthogonal to the translation orientation in the plane of the
   Yang. Yi is with Beijing Institute of Technology, Beijing, 100081,      chassis. The robot wheelbase is A and the distance between
CHINA. (corresponding author to provide phone: 86-10-6891-4570; fax:
86-10-6891-4570; e-mail: yang_yi@bit.edu.cn).                              the left and right wheels is B . According to the relation
   Fu. Mengyin is with Beijing Institute of Technology, Beijing, 100081,   between OXYZ and oxyz , the kinematics equation is as
CHINA. (e-mail: youngeecn@126.com).
   Zhu. Hao is with Beijing Institute of Technology, Beijing, 100081,      follows.
CHINA.
   Xiong. Guangming is with Beijing Institute of Technology, Beijing,
100081, CHINA.

978-1-4244-5196-8/10/$26.00 ©2010 IEEE                                 731
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                                                                         centripetal force f cen , the equation of which is,

                                                                                    f cen cos E
                                                                                              f y 3  f y 4  f y1  f y 2 (4)
                                                                                                                   JJJK
                                                                            In (4), E is the angle between Coo and y axis.
                                                                         Accordingly, when the centripetal acceleration is considered,
                                                                         assume E | 0 , then the equation of the tractive force of the
                                                                         robot is,
                                                                           ­            mg hma y         ma y xco Ps mgA ª § a y · º
                                                                                                                                   2
                    (a)                              (b)
                                                                           ° Foutside (         ) Pr                  «1  ¨  ¸ »
     Fig. 1.   Dynamics analysis of the robot and the motion               °             2   B             2R       4 B « © g Ps ¹ »
                                                                           °                                             ¬           ¼
     constraint about     Co                                               ®
                                                                                                        ma y xco Ps mgA ª § a y · º
                                                                                                                                  2
                                                                           °           mg hma y
ªX º     ª x cos T  y sin T º           ª cos T    sin T º ª x º         ° Finside (          ) Pr                 «1  ¨   ¸ »
                                                                                        2    B            2R       4 B « © g Ps ¹ »
« »      « x sin T  y cos T »           « sin T                           °                                            ¬           ¼
                                                   cos T » « y »
                                                                   (1)     ¯
¬Y ¼     ¬                   ¼           ¬                 ¼¬ ¼                                         (5)
  The derivative of equation (1) with respect to time is
                                                                         where h is the height of the robot center of mass, that is the
         ªX º           sin T º ª x  yT º
                    ªcos T                                               distance between the robot center of mass and the ground, and
         « »        « sin T      «        »
         ¬Y ¼       ¬  cos T » « y  xT »
                               ¼¬         ¼ (2)                          R is the radius of the robot turning [6].
                                                                            In the paper, as the motion of the robot is instantaneous
              ªcos T  sin T º ª a x º                                   fixed-axis rotation, obviously, the straight line motion of the
              « sin T cos T » « a »
              ¬                ¼¬ y¼                                     robot can be expressed as R f . Co is the instantaneous
   In the above equations, X , Y , X , Y represent the                   center of the rotation, and the coordinates of Co can be
absolute longitudinal and lateral velocity, and the absolute
                                                                                                       T ªy   x ºT
longitudinal and lateral acceleration respectively; T is the             expressed as ª xco       yco º «           . In Fig. 1 (b), the real
                                                                                      ¬               ¼ ¬T     T»¼
angle between x axis and X axis. x, y , T denote the                     line arrowheads represent the transfer orientations of the four
longitudinal, lateral and angular velocity in in-vehicle frame           wheels of the robot, when Co moves within the wheelbase
respectively, a x , a y are the longitudinal and lateral                 range of the robot; the dashed arrowheads stand for the
acceleration respectively in in-vehicle frame.                           transfer orientations of the four wheels of the robot, when Co ,
 ­        4          4
                                                                                  c
                                                                         that is Co , moves beyond the wheelbase range of the robot.
 ° ma x ¦ Fxi  ¦ f xi
 °       i 1        i 1                                                  Clearly, if Co moves out of the wheelbase range, the lateral
 °           4

 ® ma y  ¦ f yi
                                                                         transfer orientations of four wheels are the same, as a result,
                                               (3)
                                                                         the motion of the robot will be out of control. The motion
 °          i 1
                                                                         constraint is as follows,
 ° J T ( B / 2)((  F  F )  ( F  F ))  M
 °                     x1 x3     x2  x4      r
                                                                                                        ªX º
 ¯                                                                                                      « »
  Let   Pr   and   Ps be       the coefficient of longitudinal rolling
                                                                             >  sin T    cos T      l@ «Y »   0 (l  A 2 )
                                                                                                                                     (6)
                                                                                                        «T »
resistance and the coefficient of lateral friction respectively.                                        ¬ ¼
The equations of the robot motion can be shown as (3), where
 J is the moment of inertia of the robot; Fxi denotes the
                                                                         where l is the distance from Co to         y axis. According to
tractive force produced by the i -th wheel, and composes the
outside tractive force Foutside and the inside Finside ; f xi is         Fig. 1 (a), it is l   Aa y cos E 2 Ps g that can be obtained.
                                                                         Therefore, the constraint of the motion, shown as follow, is
the longitudinal resistance of the           i -th wheel; f yi is the    imperative.
lateral resistance of the i -th wheel; M r is the resistive
                                                                                     ( x ) 2 R  Ps g or (T ) 2 R  P s g (7)
moment around the center of o .
 During the turning of the robot, the robot is subject to the              In this paper, a description of trajectory space[7] is
                                                                         presented according to the robot’s dynamic analysis, which is

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defined as the two-dimensional space of the robot’s turning                    objects include the longitudinal velocity, the lateral velocity,
angular speed    T   and longitude velocity Vlong , (Vlong              x) .   and the angles of sensor pan-tilts.
                                                                                  As shown in Fig. 3, in an off-road environment, the robot
This kind of description is very useful during motion control.                 uses laser range finder (LRF) with one degree of freedom
Consider       equation       (7):         (Vlong (t )) 2 / R  P s g    or    (DOF) pan-tilt (only tilt) to scan bumpy situation of the close
                                                                               front ground, on which the robot is moving, and employs
(T (t )) 2 R  Ps g , it is easy to get | Vlong (t ) | Ps gR or               stereo vision with two DOF pan-tilt to perceive drivable
                                                                               situation of far front ground. With the data accessed from
| T (t ) | Ps g / R , then take another constraint into                       laser and vision sensors, the passable path can be planned,
consideration, Vlong        TR ,     now a figure of the robot’s               and the velocities of left side and right side of the robot can be
                                                                               controlled to track the path, consequently, the robot off-road
V  T space (see Fig. 2.) can be obtained. The boundary                        running is completed.
curve in the figure satisfies Vlong (t ) ˜ T (t ) Ps g . When the                               Trajectory Curvature
                                                                                                       Radius
robot’s V  T state is in the shadow region, that’s to say
Vlong (t ) ˜ T (t )  Ps g , the robot is safe, which means the                                   Road Roughness                     Fuzzy
hazardous situation like side slippage won’t occur. As a result,                                                                  Longitudinal
                                                                                                                                    Control
equation (7) is crucial for control decision making.                                                                                  Law
                                                                                                   Sensor System
                                                                                                   Process Time



                                                                                                Velocity Requirement



                                                                                     Fig. 4. The longitudinal control law of the robot

                                                                                 A. Longitudinal Control Law
                                                                                  In this section, a kind of humanoid driving longitudinal
                                                                               control law based on fuzzy logic is proposed. First, the effect
                                                                               factors to the longitudinal velocity are classified. As shown in
                                                                               Fig. 4, these factors include curvature radius of trajectory,
                                                                               road roughness, process time of sensors and speed
    Fig. 2. The V  T space of motion control of the robot. (In this           requirement. Based on the four factors and the analysis of
    figure, Ps 0.49 and g 9.8m / s 2 )                                         kinematics and dynamics, the longitudinal velocity equation
                                                                               can be given,
   III. TRAJECTORY TRACKING CONTROL LAWS DESIGN                                      Vlong      P   cv   ( rc )  Prr ( Rrough )  Pt (Tsen ) Pv (Vre )Vre
   Autonomous mobile robot achieves outdoor navigation by                                                                (8)
three processes, including the environment information                         where Vlong is longitude velocity command,                    Pcv , Prr , Pt
acquired by the perception module, the control decision made
by the planner module, and the motion plan performed by the                    and   Pv    are the weight factors of the curvature radius of
motion control module[8]. Consequently, for safe and accurate                  trajectory rc , road roughness Rrough , processing time of
outdoor navigation it is vital to harmonize the three modules
performance. In this paper, the emphasis is focused on the                     sensors Tsen and speed requirement Vre respectively. The
decision of control laws of the robot, and these controlled                    weight factors can vary within [0,1] .

                                                                                 B. Lateral Control Law
                                                                                  Autonomous vehicle off-road driving is a special control
                                                                               problem because mathematical models are highly complex
                                                                               and can’t be accurately linearized. Fuzzy logic control,
                                                                               however, is robust and efficient for non-linear system
                                                                               control[9], and a well-tested method for dealing with this kind
                                                                               of system, provides good results, and can incorporate human
   Fig. 3. Off-road driving of the robot                                       procedural knowledge into control algorithms. Also, fuzzy

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logic lets us mimic human driving behavior to some extent[10].                   indicated in terms of triangle and rectangle membership
Therefore, the paper has presented a kind of novel fuzzy                         functions:
lateral control law for the robot off-road running.                                Part One: the space of ed is divided into LB , LS , MC ,
   In the paper, the lateral control law is designed for the
purpose of position tracking by adjusting navigation                                 RS , RB . According to the result of the ed division, the
orientation to reduce position error.                                            phenotype rules of the lateral fuzzy control law hold.
                                                                                   Part Two: the space of T e is also divided into LB , LS ,
                                                                                     MC , RS , RB . According to the result of the T e division,
                                                                                 the recessive rules of the control law are obtained.
                                                                                    It is necessary to explain that the phenotype rules are the
                                                                                 basis of the recessive rules, namely each phenotype rule
                                                                                 possesses a group of relevant recessive rules. Each phenotype
                                                                                 rule has already established their own expectation orientation
                                                                                 angle      T e , that is to say the robot is expected to run on this
                                                                                 orientation angle,        T e , and this angle is the       very center angle

                                                                                 of this group recessive rules. When the center angle, T e , of
                                                                                 each group recessive rules is varying, the division of T e of
                                                                                 each group recessive rules changes accordingly.
    Fig. 5. Plots of membership functions of ed and Te . The upper plot            All of the control rules can be expressed as continuous
    stands for P ( ed ) . > 0.1,0.1@ is the range of the center region,         functions, f LB , f LS , f MC , f RS , f RB , consequently, the
    P ( ed ) 1.0 in this region. The lower plot expresses P (Te ) , which        global continuity of the control rules is established.
    is indicated with triangle membership function. In this figure, the            The functions, f LB , f LS , f RS , f RB , which express the
    colorful bands represent the continuous changing course of e .
                                                                 d               rule functions of the non  center region of ed , are as
   Definition: When the robot moves toward the trajectory,                       follows:
the orientation angle of the robot is positive, whichever of the
two regions, namely left error region and right error region of                                             kTe kt (T e  T e )
                                                                                                       T                           ktT tr       (9)
the tracking position, the robot is in. When the robot moves                                                         Ts
against the trajectory, the angle is negative. When the robot
motion is parallel to the trajectory, the angle is zero.                               In (9),   Te   is the expectation tracking-angle in the current
   In the course of trajectory tracking of the robot, position                   position error region, and it monotonically increase about ed .
error ed and orientation error T e , which are the error values
                                                                                                                                                          ked ed
between the robot and the trajectory, are the inputs of the                      Te        can be given by this equation:             Te         arctan             ,
lateral controller. First, the error inputs, including the position                                                                                        Vlong
error and the orientation error, are pre-processed to improve
                                                                                     ked     P DL ( ed )k DL  PDS ( ed )k DS ,     where        PDL    stands for
steady precision of the trajectory tracking, and restrain
oscillation of that. The error E can be written as                               the large error region, including LB and RB , membership
E      E  'E , where E is the result of smoothing filter                        degree of ed , and P DS represents the small error region,

about E , i.e. E
                              i
                             ¦ ei n ;       'E forecasts the error               including LS and RS , membership degree of ed .                            Ttr    is
                          i  n 1
                                                                                 the estimation of the trajectory-angle rate. kT can be worked
produced        in     the      next      system        sample        time,                                                                  e

         i                                                                       out by this equation: kT                  PT L (T e )kT L  PT S (T e )kT S        ,
'E       ¦ kei ei n ( i ! n )      .           As          a         result,                                           e

     i  n 1
                                                                                 where       PT L   stands for the large error region, including LB
       i
E     ¦ (1 kei ) ei n ( i ! n ) , n       4 , kei       f ei ( x, Ts ) , Ts     and RB , membership degree of                Te ,    and    PT S      denotes the
   i  n 1
represents system sample time. Second, the error inputs, after                   small error region, including LS and RS , membership
being pre-processed, are fuzzyfication-processed. As shown                       degree of       T e . k DL , kT L   and k DS , kT S express the standard
in Fig. 5, degree of membership P ( ed ) and P (T e ) are                        coefficients of the large error region of ed or                 Te    and that of


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                                                                                                                                                                ThB3.4

the small error region of ed or           Te    respectively. kt is the        the robot and the trajectory when the robot just enters the

proportional coefficients of the system sample time TS .                           center region. R | 2O                                can be worked out by
                                                                                                                                  D2
 f MC is deduced as follows:                                                   geometry, and in addition, the value of D is very small, so the
                                                                               process of approaching trajectory can be represented as
   When the robot moves into the center region at the                                                  'O
orientation of D , the motion state of the robot can be divided                    'D             D         .
                                                                                                       O
into two kinds of situations.
                                                                                     Situation Two: When                       D 0     or   D ! T cent . If the motion
                                                                               decision from the planner module were the same as Situation
                                                                               One, the motion will not meet (7). According to the above
                                                                               analysis, the error of tracking can not converge until the
                                                                               adjusted            Te      makes      D        be true of Situation One. Therefore,
                                                                               the purpose of control in Situation Two is to decrease                             Te .
                                                                                     Based on the above deduction, f MC is as follow:

                                                                                                                       kt (T e  T e )
                                                                                                                T                       ktT tr (10)
                                                                                                                             Ts
                                                                                                           edT cent
                                                                               where              Te                   ,   O    is the variety range of ed in the
                                                                                                                O
                                                                                   center region, > 0.1m,0@ or >0,0.1m@ . T is the output of (9)
   Fig. 6. Tracking trajectory of the robot. In this Figure, the red
   dashdotted line stands for the trajectory tracked by the robot. The         and (10), at the same time,                       T   is subject to (7), consequently,
   different color dotted lines represent the bounderies of the different
   error regions of   ed .                                                         T    2
                                                                                              R  P g is required by the control rules.
                                                                                                   s
  Situation One: Assume that D has decreased into the rule                        The execution sequence of the control rules is as follows:
admission angular range of center region, i.e.                                    First, the phenotype control rules are enabled, namely to
0 d D d T cent , where T cent , which is subject to (7), is the                estimate which error region ( LB , LS , MC , RS , RB )
critical angle of center region. To make the robot approach                    the current ed of the robot belongs to, and to enable the
the trajectory smoothly, the planner module requires the robot                 relevant recessive rules; Second, the relevant recessive rules
to move along a certain circle path. As the robot moves along
                                                                               are executed, at the same time,                         Te    is established in time.
the circle path in Fig. 6, the values of ed and T e decrease
                                                                                  The lateral control law can be shown as Fig. 7. In this
synchronously. In Fig. 6,       O   is the variety range of ed in the          figure, the different color concentric circle bands represent
center region. D is the angle between the orientation of                       the different position error ed . From the outermost circle
                                                                               band to the center round, the values of ed is decreasing. The
                                                                               red center round stands for MC of ed , that is the center
                                                                               region of ed . At the center point of the red round, ed                                   0.
                                                                               According to the above definition, the orientation range of the
                                                                               robot is  S , S @ , and the two 0 degree axes of                               Te   stand
                                                                               for the 0 degree orientation of the left and right region of the
                                                                               trajectory respectively, at the same time,                               S       axis and
                                                                                                                                                            2
                                                                                   S             axis of       Te   are two common axes of the orientation of
                                                                                              2
                                                                               the robot in the left and right region of the trajectory. In the
                                                                               upper sub-region of 0 degree axes, the orientation of the
 Fig. 7. Plot of the lateral control law of the robot. These dasheds stand     robot is toward the trajectory, and in the lower sub-region, the
 for the parts of the performance result of the control law.                   orientation of the robot is against the trajectory. The result of

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the control rules converges to the center of the concentric                                                                          ed (t )T cent
circle bands according to the direction of the arrowheads in                                                         T e (t )                              (14)
Fig. 7. Based on the analysis of the figure, the global
                                                                                                                                             O
                                                                                               Combine            equation               (11)             and       (14),     then
asymptotic stability of the lateral control law can be
                                                                                                                   e T
established, and iff ed 0 & T e 0 , the robot reaches the                                    e
                                                                                              d
                                                                                                      V
                                                                                                        long O
                                                                                                               sin( d cent ) . In this region,
                                                                                                                                     d                          e is very small,
only equilibrium zero. The proving process is shown as                                                    ed Tcent
                                                                                         consequently,                will also be very small,
follow:                                                                                                       O
                                                                                                   e T         e T
                                                                                         then sin( d cent ) | d cent        is derived. Therefore,
                                                                                                       O           O
                                                                                                     ed Tcent      Vlong Tcent
                                                                                             e        Vlong                                        e          ,    and      then
                                                                                              d                  O                       O            d
                                                                                                                        VlongT cent
                                                                                             e (t )     e ( t ) exp{                        } , where      t1 is the time when
                                                                                              d          d 1                    O
                                                                                         the robot enters the              center region. In other word, ed
    Fig. 8. Trajectory Tracking of the mobile robot
                                                                                         converges to 0 exponentially. Then, according to
                                                                                                  e T
  Proof: From the kinematic model (see Fig. 8.), it can be                               Te ( t ) d cent , T e (t ) converges to 0 . So the origin is the
seen that the position error of the robot ed satisfies the                                           O

following equation,                                                                      only equilibrium in the ed  T e phase space.
                 Vlong (t ) sin(T e (t )) (11)
               ed (t )                                                                        C. LRF Pan-Tilt and Stereo Vision Pan-Tilt Control
  a. When the robot is in the non  center region, a
controller is designed to control the robot’s lateral movement:
                                            ked ed (t )
                 T e (t ) arctan                              (12)
                                            Vlong (t )
Combines equation (11) and (12), then                                                             Fig. 9. LRF Pan-Tilt and Stereo Vision Pan-Tilt motion
                                                                  ked ed (t )              Perception is the key to high-speed off-road driving. A
ed (t )   Vlong (t )sin(arctan(T e (t )))
                                                                                   2     vehicle needs to have maximum data coverage on regions in
                                                                  § k e (t ) ·           its trajectory, but must also sense these regions in time to
                                                              1  ¨ ed d ¸
                                                                  ¨ V (t ) ¸             react to obstacles in its path. In off-road conditions, the
                                                                  © long ¹
                                                                                         vehicle is not guaranteed a traversable path through the
                                            (13)
                                                                                         environment, thus better sensor coverage provides improved
  As the sign of          ed is always opposite that of ed , ed will                     safety when traveling. Therefore, it is important for off-road
converge to 0 . In equation (11), ed (t ) | Vlong (t ) , and                             driving to apply active sensing technology. In the paper, the
                                                                                         angular control of the sensor pan-tilts assisted in achieving
ed (t ) | ked ed (t ) can formed by equation (13). Therefore                             the active sensing of the robot. Equation (15) represents the
the convergence rate of          ed is between linear and exponential.                   relation between the measurement angles, i.e. M c , J c and

When the robot is far away from the trajectory, it’s heading                             J l , of the sensors mounted on the robot and the motion state,
                                                   S                                     i.e. T e and x , of the robot.
for trajectory vertically, then             Te           ,   ed (t )   Vlong (t ) ,
                                                   2
ed (t )   Vlong (t )  ed (t0 ) ; when the robot is near the                                               ªM c º     ª kM c        0           0  º ªT e º
                                                                                                            «J »       «                            »« »
                                                                                                                       «0           kJ c         0  » « x » (15)
trajectory,      ed | 0           ,        then     in         equation          (12),                      « c»
                                                                                                            «J l »
                                                                                                            ¬ ¼        «0
                                                                                                                       ¬             0         kJ c » « x »
                                                                                                                                                    ¼¬ ¼
                      2
    § ke ed ( t ) ·
 1 ¨ d           ¸
    ¨ Vlong ( t ) ¸
                          |1 ,   ed (t )     ked ed (t ) . Now consider                       In (15),     Mc , J c   are the pan angle and tilt angle of the
    ©             ¹
equation (12), since         ed converges to 0 , according to the                        stereo vision respectively.                Jl   is the tilt angle of the LRF. kM c ,

         arctan function, T e converges to 0 .
property of                                                                                  kJ c and kJ l are the experimental coefficients between the
  b. When the robot enters the center region, another                                    measurement angles and the motion state, and they are given
controller is designed,                                                                  by practical experiments of the sensors and connected with

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                                                                                                                            ThB3.4

the measurement range requirement of off-road driving. At          track two different kinds of trajectories, including the straight
the same time, the coordinates of the scanning center are          line path, sinusoidal path and circle path. In Test One, the
 xec xc  hc cot J c cos M c , yec yc  hc cot J c sin M c ;       tracking trajectory consists of the straight line path and
                                                                   sinusoidal path, in which the wavelength of the sinusoidal
and xel    xl  hl cot J l , yel   0 . In the above equations,     path is 5S m , the amplitude is 3m . The simulation result of
xc , yc , xl , yl , respectively, are the coordinates of the       Test One is shown in Fig. 12. In Test Two, the tracking
sense center points of the stereo vision and LRF in in-vehicle     trajectory contains the straight line path and circle path, in
                                                                   which the radius of the circle path is 5m . The simulation
frame. As shown in Fig. 9, hc and hl are their height value,
                                                                   result of Test Two is shown in Fig. 13.
to the ground, accordingly.                                          In Fig. 12, which is the same as Fig. 13, sub-figure a is the
   The angular control and the longitudinal control are            simulation data recorded by ADAMS. In sub-figure a, the
achieved by PI controllers, and they are the same as the           upper-left part is the 3D animation figure of the robot
reference [1].

                   IV. SIMULATION TESTS




                                                                      Fig. 11. The simulation test ground in ADAMS
     Fig. 10. ATRV2 and its model in ADAMS
                                                                   off-road driving on the simulation platform, in which the
                                                                   white path shows the motion trajectory of the robot. The
  A. Simulation Platform Build
                                                                   upper-right part is the velocity magnitude figure of the robot.
  In this section, ADAMS and MATLAB co-simulation                  It is indicated that the velocity of the robot is adjusted
platform is built up. Based on the analysis of the simulation      according to the longitudinal control law. In addition, it is
result, the design of experiments in real world can become         clear that the longitudinal control law, whose change mainly
more reasonable and safer.                                         is due to the curvature radius of the path and the road
  First, based on the characteristics of the robot, ATRV2, the     roughness, can assist the lateral control law to track the
simulation model is accomplished, as shown in Fig. 10.             trajectory more accurately. In Test One, the average velocity
Second, according to the test data of the tires of ATRV2, the
                                                                   approximately is 1.2m / s , and in Test Two, the average
attribute of the tires and the connection character between the
tires and the ground are set. The ADAMS sensor interface           velocity approximately is 1.0m / s . The lower-left part is the
module can be used to define the motion state sensors              figure of the height of the robot mass center during the
parameters, which can provide the information of position          tracking of the robot. In the figure, the road roughness can be
and orientation of the ATRV2 model during its moving.              implied. The lower-right part shows that the kinetic energy
   It is road roughness that affects the dynamic performance       magnitude is required by the robot motion in the course of
of vehicles, the state of driving and the dynamic load of road.    tracking. In Sub-figure b, the angle data of the stereo vision
Therefore, the abilities of overcoming the stochastic road         pan rotation is indicated. The pan rotation angle varies
roughness of vehicles are the key to test the performance of       according to the trajectory. Sub-figure c is the error statistic
the control law during off-road driving. In the paper, the         figure of trajectory tracking. As is shown, the error values
simulation terrain model is built up by Gaussian-distributed       almost converge to 0 . The factors, which produce these
pseudo random number sequence and power spectral density           errors, include the roughness and the curvature variation of
function.                                                          the trajectory. In Fig. 13 (d), the biggest error is yielded at the
   Assign a certain value to the road roughness and adjust the     start point due to the start error between the start point and the
parameters of the special points on the road according to the      trajectory. Sub-figure d is the trajectory tracking figure,
test design, and the simulation test ground is shown in Fig. 11.   which contains the objective trajectory and real tracking
                                                                   trajectory. It is obvious that the robot is able to recover from
  B. Simulation Tests
                                                                   large disturbances, without intervention, and accomplish the
  In this section, the control law is validated with the           tracking accurately.
ADAMS&MATLAB co-simulation platform.
  Based on the position-orientation information provided by                                V. CONCLUSIONS
the simulation sensors and the control law, the lateral,
                                                                     The      ADAMS&MATLAB             co-simulation  platform
longitudinal motion of the robot and the sensors pan-tilts
                                                                   facilitates control method design, and dynamics modeling and
motion are achieved. The test is designed to make the robot

                                                               737
                                                                                                                                               ThB3.4




                                          a                                                                           a




                      b                                 c                                             b                                c




                                      d                                                                               d
      Fig. 12. Plots of the result of Test One (Ts   0.05 s )                        Fig. 13. Plots of the result of Test Two (Ts   0.05 s )

analysis of the robot on the rough terrain. According to the                   [5]  D. Lhomme-Desages, Ch. Grand, J-C. Guinot, “Model-based Control
                                                                                    of a fast Rover over natural Terrain,” PUBLISHED IN THE
practical requirement, the various terrain roughness and                            PROCEEDINGS OF CLAWAR’06: INT. CONF. ON CLIMBING
obstacles can be configured with modifying the relevant                             AND WALKING ROBOTS, SEPT 2006.
parameters of the simulation platform. In the simulation                       [6] J. Y. Wong, “Theory of Ground Vehicles,” John Wiley and Sons, New
                                                                                    York, USA, 1978.
environment, the extensive experiments of control methods
                                                                               [7] Matthew Spenko, Yoji Kuroda,Steven Dubowsky, and Karl Iagnemma,
of rough terrain trajectory tracking of mobile robot can be                         “Hazard avoidance for High-Speed Mobile Robots in Rough Terrain”,
achieved. The experiment results indicate that the control                          Journal of Field Robotics 23(5), pp. 311–331, 2006.
methods are robust and effective for the mobile robot running                  [8] Gianluca Antonell, Stefano Chiaverini, and Giuseppe Fusco. “A
                                                                                    Fuzzy-Logic-Based Approach for Mobile Robot Path Tracking,” IEEE
on the rough terrain. In addition, the simulation platform                          TRANSACTIONS ON FUZZY SYSTEMS, VOL. 15, NO. 2, pp.
makes the experiment results more vivid and credible.                               211-221, 2007.
                                                                               [9] Gao Feng, “A Survey on Analysis and Design of Model-Based Fuzzy
                                                                                    Control Systems,” IEEE TRANSACTIONS ON FUZZY SYSTEMS,
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