Fig。2 Response of the system (robot) compared with the simulated response by choosing a square signal as a stimulus。

Fig。 3。 Schematic diagram of the ACC using fuzzy PID Controller。

3。CONTROL DESIGN

The fuzzy PID controller proposed for the design of ACC system in this paper is depicted in Fig。 3。 The fuzzy rules calculate the consequent error value by evaluating overall dynamics of the system including the difference between the measured and reference values, i。e。 the desired distance and desired cruising velocity, the velocity difference between leader and follower vehicles, and the acceleration which are estimated from pre-processing step as inputs。 The PID controller calculates the command variable value to the system based on the consequent error value resulted from the fuzzy logic controller。 The advantage of fuzzy PID controller is that it does not have a special operating point。        Another

advantage of the fuzzy logic PID controller over the conventional PID controller is that it can  implement nonlinear control strategies by using linguistic rules。 The fuzzy logic PID controller can consider the error tendency by itself as the error changes (Naranjo et al。, 2003)。

3。1ACC System

ACC systems operate in two different modes depending on the situation in the front - distance tracking or velocity tracking。 If the ultrasonic sensor of the follower (ACC equipped) detects any obstacle, or a slower moving robot in front, the controller adjusts the velocity to maintain the clearance inter-distance (desired distance)。 If the inter- distance measured by the ultrasonic sensor is greater than the desired distance, it will switch to velocity tracking mode, known as cruise control (CC) mode, to track the desired cruising velocity。 The desired headway distance ddes can be computed using the Constant-Time Headway policy (van den Bleek, 2007; Zhou and Peng, 2004):

ddes l ds Thvf d0

where l is the robot length, ds the additional distance between two robots, vf the follower robot velocity, vl the leader robot velocity and Th the constant-time headway (approximated system reaction time) (s)。

The relative velocity-vr, distance error-ed and velocity error-ev are obtained as follows:

where, vdes is the  desired cruising speed。

3。2Fuzzy PID controller

The input variables of the fuzzy logic controller for the ACC system are the distance error, relative velocity, velocity error and acceleration。 The output variable is the consequent error calculated based on the associated fuzzy rules。 Due to the limited space in this conference paper, the rules are not presented here but can be found (Masouminia, 2011)。 Membership functions for input variables and output variable for ACC system are demonstrated in Fig。 4-5。 The center of area (CoA) method was selected to perform defuzzification, as this method calculates the best compromise between the multiple output linguistic terms。 Furthermore, the minimum implication method was selected for the consequent implication and the degree of support for all the rules are 1。 A discrete PID controller (Ogata, 1995) is used to calculate the command variable input value to the system, i。e。 robot’s velocity setpoint (vsp), based on the consequent error value resulted from the fuzzy logic controller (eFL)。

Fig。 4。 Member function for input variables of the fuzzy logic controller for the ACC-(a) distance error (ed), (b) velocity error (ev), (c) relative velocity (vr), and (d) acceleration (af)。

Fig。 5。 Member functions for the output variable of the fuzzy logic controller for the ACC- consequent error (eFL)。

4。UNMEASURED PARAMETER ESTIMATION

The required parameters for operation of the ACC system are distance (d), follower robot velocity (vf), acceleration (af) and