relative velocity (vr)。 Distance and follower robot’s velocity are measured parameters, because they are available to the system by an ultrasonic sensor and the encoders attached to the motor, respectively。 The acceleration and relative velocity are unmeasured parameters and need to be estimated in the control algorithm。 A discrete-time Kalman filter, which is based on the linear minimum variance (LMV) estimation of discrete-time system, is utilised to estimate the unmeasured parameters (states) of the system (Ogata, 2001; Powell, 2004)。

For estimating the unmeasured parameters, it is necessary to model the behaviour of the robot in front and then build a model of the overall system, including the two robots。 In this paper, we have assumed that the robot in front travels at a constant speed, however, the variation of the leader robot velocity (vl) acts as a disturbance on the system (Steinbuch, 2010)。 The state-space model of the robot can be obtained by converting from its transfer function equation (1)。 In order to develop the state-space equation for the overall system, the states including the velocity of the leading robot and the distance between the robots, i。e。 inter vehicle dynamic,  given

5。

SIMULATION RESULTS

The ACC system was developed, tested and implemented in the hardware, i。e。 NI starter kit robot, using LabVIEW utilising the fuzzy PID controller。 The robot model which is based on a given second order transfer function, was identified and controlled。 The fuzzy controller was designed through the Fuzzy System Designer。 The ACC system was first designed and tested with simulations and then deployed to the robot’s LabVIEW FPGA module, for comparison purposes。 In the initial experiment the leader robot is virtualised, the sinusoidal signal represents the leader robot’s velocity。 The final stage of the test uses two test robots, i。e。 one for the leader robot and another one for the follower robot。 Tuning of the PID controller was carried out experimentally by the trial and error method; Kp= 1。7, Ki= 1。3 and Kd=0。6。

Fig。 6 illustrates the results for distance tracking control (ACC)。 The initial distance between the robots was set at 0。1 m which is the minimum safe distance do according to our experiments。 Both robots started from zero velocity and time- constant headway Th  was chosen experimentally to be 1。3   s。

by int veh

v  T  are  added  to  the  states  of  the  robot

The ACC system calculates the robot velocity (Fig。 6。c) such

model,  which  are  the  follower  robot’s  acceleration     and

that the distance between the follower and leader robots is

velocity  as x   a

v  T  ,   to   give   the   state   of   the

retained  within  the  desired  distance  (Fig。6。a-b)。  Since, the

desired distance given by (2) is a function of the velocity of

augmented system (Shakouri et al。, 2012):

the follower robot, its variation depends on the velocity。 The values of the root mean square error (RMSE) for the  distance

tracking resulted both from the simulation experiment and

Thereby, the state-space models and their coefficients integrating the dynamic of the robot and that of the tracking (augmented dynamic) can be given as follows in the discrete- time form:

using   the   test   robot   are   0。0211   (m)   and   0。0366  (m),

respectively。

The final test is implemented by utilizing two robots corresponding to the leader and follower robots。 The distance between the robots is measured through an ultrasonic    range