xk 1  Gaug xk  Hauguk

yk   Caug xk  Dauguk

finder。 The ultrasonic sensors are not so accurate in the distance reading, because the measurement can be affected by reflectivity  of the  different  surfaces  and  the environmental

Aaug and Baug are the state and input transition matrices, Caug and Daug are the output and direct (feedthrough) transition matrices, respectively。 The subscript “aug” stands for augmented equation。 the system input (uk) is the velocity setpoint (vsp)。The distance obtained by the ultrasonic   sensor

(d) is used as an output measurement of the system to estimate the unmeasured states of the system (af and vl) utilising the Kalman filter。 The Kalman filter gain matrix is calculated through a recursive algorithm and using the state- space model of the overall system given by (6)-(8)。 The calculated gain matrix by a recursive algorithm is Kk+1=[0。0630 -0。068 0。3452 0。2559]T。 Consequently, the acceleration (af) and relative velocity (vr) can be obtained having the estimated state ( xˆk 1|k 1 ) as:

factors and the gain depends on the location of the obstacle with respect to the sensor。 In order to mitigate the sudden variation of the distance which in turn degrades the controlling process, a Median Filter was used within the program algorithm。 Fig。 7 shows the results obtained  by using two robots。 The longitudinal motion of the  leading robot was defined arbitrary in the tests。 The results of the real-implementation indicate fairly good performance of the ACC system。 Despite the disturbances imposed by the distance measurement as well as the estimation error of the unmeasured parameters, the distance tracking was accomplished at an acceptable level (RMSE from  the distance tracking was 0。0325 (m))。 The parameters estimated by a Kalman filter including the inter-distance, the velocity of the  leading  and  following  robots  and  the  acceleration  are

a   1 0 0

0xˆ

k 1|k 1

(9)

depicted in Fig。 7。 Here, the acceleration indicates a smooth performance of the robot during tracking。 The comparison

v  0    1 0

1xˆ

k 1|k 1

(10)

between the parameters measured by sensors, i。e。 the distance and velocity of the following robot, with the same parameters

where

xˆk 1|k  is  the  estimated  state  by  the  Kalman  filter  at

estimated by  a Kalman filter (Fig。7 a-b) demonstrates     that

time k+1 based on the information given at time k。

they   have   been   estimated   by   small   errors,   which   are

acceptable。 The RMSEs of the estimation for the distance and

velocity of the following robot are 0。0085 (m) and 0。0163 (m), respectively。

Fig。 6。  Distance tracking (ACC) using Fuzzy PID  controller:

(a)inter-distance between the robots using test robot, (b) inter-distance between the robots obtained from simulation, and (c) velocities obtained during distance tracking。

6。IMPLEMENTATION INTO CIRRICULUM AND RESUTLS

The material described in this paper was introduced to the MSc level students in embedded system course。 The costs of the implementation into our courses include the purchase of ten DANI robotic vehicles。

Students were given a set of formal lectures and tutorials, covering real-time embedded system environment and programming Compact RIO using LabVIEW。 Most of the students have participated in the control systems module or have a control background。 The course  was  assessed 100% by coursework。 The design and implementation of automated speed-dependant ECU function for safe distance-keeping of an electric vehicle accounted for 50% of the total marks。 Here we assessed the following learning objectives: