fig4 illustrates the movement of a front and rear wheel steering vehicle according to the present invention . as the vehicle position changes from the position i to the positions ii and iii , the trajectories 4 and 5 of the front wheel 2 and the rear wheel 3 completely coincide each other , and the handling of the vehicle is optimized . fig5 illustrates the theory for achieving such a control method for the rear wheel , and a coordinate system is set along the trajectory 4 of the front wheel 2 using the distance i along the trajectory 4 as the variable . suppose the yaw angle of the vehicle is ψ ( i ), the steer angle of the front wheel 2 relative to the vehicle body is δf ( i ), and the steer angle of the rear wheel 3 is δr ( i ) relative to the vehicle body when the front wheel 2 is at a point p 1 . at this time point , the rear wheel 3 is at a point p o , and the coordinate of this point is set as i - δi . here , it is assumed that the yaw angle of the vehicle was ψ ( i - δi ) and the steer angle of the front wheel was δf ( i - δi ) when the front wheel 2 was at the point p 0 . at this time point , it suffices if the steered direction of the front wheel 2 and the steered direction of the rear wheel 3 coincide each other in the absolute space . in other words , ## equ1 ## the steer angle of the rear wheel 3 with respect to the vehicle body 1 δr ( i ) is given from the above equation as follows : ## equ2 ## in other words , the steer angle of the rear wheel 3 at each point should be set to the value obtained by subtracting the change in the yaw angle from the steer angle of the front wheel at the current position of the rear wheel . fig6 is a simplified plan view of a front and rear wheel steering vehicle which can control the steer angle of its rear wheel according to such an algorithm . the front wheels 2 are steered by a front wheel steering gear box 7 which is actuated by a steering wheel 6 , and the rear wheels 3 are steered by a rear wheel steering gear box 8 which is actuated by an electric motor . the steer angle of the front wheels 2 is detected by steer angle sensor 11 , and the output from the steer angle sensor 11 is supplied to a control computer 10 for determining the steer angle of the rear wheels 3 as described hereinafter . the rear wheel steering gear box 8 is provided with a similar steer angle sensor 11 . the output from the steer angle sensor 12 is used for the servo action for actually achieving the steer angle of the rear wheels as determined by the control computer 10 . further , the output from a travel distance sensor , or vehicle speed sensors 13a , 13b , 14a and 14b , which detect the rotational speeds of the front and rear wheels , is also supplied to the control computer 10 . further , the outputs from a rate gyro 15 for detecting the yaw rate of the vehicle body and a compass 16 for detecting the absolute bearing of the vehicle body are likewise supplied to the control computer 10 . fig7 is a block diagram which illustrates a functional structure for executing the algorithm given by equation ( 2 ). for instance , the travel distance is computed from the outputs of the travel distance sensors 13a through 14b in a travel distance computing circuit 20 , and its output i is supplied to a delay circuit 21 . this delay circuit 21 also receives the value of the front wheel steer angle δf ( i ) obtained from the steer angle sensor 11 . the front wheel steer angle at each point is temporarily stored in memory 22 , and the front wheel steer angle δ ( i - δi ) is produced from the delay circuit 21 after a time delay which corresponds to δi . the yaw rate r , which is given as the output from the rate gyro 15 , is integrated over the time the wheel travels from the point p 0 to the point p 1 or over the time i - δi with an integrator 23 , and the steer angle δr ( i ) is obtained by subtracting the result of integration from the output of the delay circuit 21 . to find the change in the yaw angle δψ , it is also possible to use the compass 16 . alternatively , both the rate gyro 15 and the compass 16 may be used at the same time so that they may complement each other and compensate the influences of the drift arising from the integration process when using the rate gyro 15 and the lack of precision when using the compass 16 . also , it is possible to obtain a reasonable result by approximating the difference δi in the travel distances of the trajectories of the front and rear wheels with the wheel base of the vehicle , and performing approximated computations . now , a method for estimating the change in the yaw angle without using a rate gyro or compass is described in the following . suppose the tread of the vehicle is d , and the travel distances derived from the rotational speeds of the right and left wheels are δir and δil , respectively . then , the change is the yaw angle can be estimated by by using this relationship , the rear wheel steer angle can be computed with the following formula . it is also possible to estimate the change in the yaw according to the following formula . ## equ3 ## where i * is the variable for performing the integration and l is the wheel base which was mentioned earlier . from the above equation , the following equation can be derived . ## equ4 ## thus , the optimum rear wheel steer angle can be computed from the rotational speeds of the wheels and the steer angle of the front wheel alone . in short , the rear wheel steer angle can be computed in terms of the structure illustrated in fig8 in the following manner . first of all , the travel distance is computed in the travel distance computing circuit 30 according to the outputs from the travel distance sensors 13a through 14b , and the output i from this circuit is supplied to the delay circuit 31 . the delay circuit 31 also receives the value of the front wheel steer angle δf ( i ) obtained from the steer angle sensor 11 . the front wheel steer angle at each point is temporarily stored in memory 32 , and the front wheel steer angle δf ( i - δi ) is outputted from the delay circuit 31 after a delay time corresponding to δi . the sum of the output from the integrator 34 and the output from the delay circuit 31 is given as the rear wheel steer angle δr ( i ). the input for the integrator 34 , however , is obtained by subtracting the rear wheel steer angle δr ( i ) from the front wheel steer angle δf ( i ) and multiplying the difference by a multiplier 33 . thus , the handling of the vehicle can be substantially improved , but since there is a difference in the travel distances of the front and rear wheels , a certain problem arises when an attempt is made to carry out the algorithm which was mentioned earlier . specifically , the front wheel steer angle is stored for each time step or each step of the travel distance of the front wheel , but the rear wheels may not coincide with the positions which the front wheels occupied in the past , and some corrections are required . moreover , in the above described embodiments , the algorithm was executed looking only at , for instance , the right wheels of the vehicle , but , as well known , the steer angles of the right and left wheels generally disagree , and it is preferable to steer the four wheels so that they all always have the same center of turning . therefore , if the steering is performed taking only the steer angles of the right wheels into account , the driver may experience a subtle , peculiar feeling . the embodiment described in the following with reference to fig9 to 15 takes these factors into account . fig9 shows the state in which the front and rear wheels are steered by angles δf and - δr , respectively , and have advanced by small distances dsf and dsr , respectively , thereby causing a yaw angle change of dψ . from the illustrated geometrical relationships , one can obtain ## equ5 ## and from equation ( 8b ), ## equ6 ## by substituting equation ( 9a ) into equation ( 8a ), one can obtain ## equ7 ## here , it is assumed that n - 1 travel distance steps are required for the rear wheel to reach the current position of the front wheel . therefore , the steer angles of the front and rear wheels and the yaw angle of the vehicle with respect to the absolute space coordinate system can be expressed as follows ## equ8 ## in order to make the steered direction of the rear wheel coincide with the tangential direction of the trajectory of the past position of the front wheel when it was located at the current position of the rear wheel , the steer angle of the rear wheel at each time point should be given by the following equation . ## equ9 ## fig1 is a plan view showing the steer angles of the wheels as well as the turning center 0 of the vehicle when an imaginary central front wheel and an imaginary central rear wheel are considered . according to the well known geometrical relationship , the following equations ( 11 ) through ( 16 ) are obtained . ## equ10 ## except for the case where δ r = δ f . fig1 is a flow diagram for explaining the algorithm of the present embodiment . the change in the yaw angle dψ is obtained from the steer angle of the imaginary central front wheel δf , the travel distance the front wheel sf and the steer angle of the imaginary central rear wheel δr , using equation ( 9 ). thereafter , the steer angle of the imaginary front wheel δf , the change in the travel distance of the front wheel dsf and the change in the yaw angle dψ are stored in the memory for each travel distance step i = 1 , . . . , n . here , when the position of the rear wheel sr ( n ) has advanced by one step from a position p 1 which was occupied by the front wheel in the past ( q n → q n + 1 ), the new position q n + 1 may either exceed the next position p 2 of the front wheel or may fall short of the position p 2 . in the latter case , as shown in fig1 , the next step length dsf ( 1 ) of the travel distance sf of the front wheel in the next computation cycle should be in this case , the data points are not shifted , and the number of data points increases by one . in the former case , or when the new position q n + 1 of the rear wheel exceeds the next position p 2 of the front wheel , the first step length dsf ( 1 ) of the travel distance of the front wheel in the new cycle of computation should be in this case , the old sf ( 1 ) is cleared and the data points are all shifted up . since the change in the yaw angle in equation ( 9a ) depends on the change in the step length of the front wheel travel distance , in the case given in fig1 , dψ ( 1 ) in the new cycle of computation should be and , in the case given in fig1 , d1 / 8 ( 1 ) in the new cycle of computation should be in this way , the steer angle δr of the imaginary rear wheel at each time point is obtained from equation ( 10 ). here , a limit is imposed upon the reading of data until the vehicle has traveled more than a certain distance to the end of preventing memory overflow when the vehicle speed is too small . further , as initial data , the front wheel steer angle is set to zero , the yaw angle also to zero and the front wheel travel distance as the wheel base , respectively , and the internal data are initialized when the vehicle starts off or moves backward . as mentioned above , the right and left , front and rear wheels must be steered so that they may have the same turning center as the imaginary front and rear wheels . therefore , after the steer angles of the imaginary front and rear wheels δf and δr are obtained , the steer angles of the right and left , front wheels δfr and δfl and the steer angles of the right and left , rear wheels δrr and δrl are computed according to equations ( 11 ) through ( 16 ) and the wheels are steered to the corresponding steer angles . fig1 shows a model of the front and rear wheel steering vehicle whose front and rear wheels can be steered according to such an algorithm . in this vehicle , the front wheels 102 and 103 and the rear wheels 104 and 105 are steered by individual steering motors 106 through 109 which are in turn controlled by a control computer 110 by way of a motor driver 111 . the steer angles of the wheels 102 through 105 , the steering angle of the steering wheel 116 , the yaw rate of the vehicle body 101 , the absolute bearing of the vehicle body 101 and the vehicle speed are detected by steer angle sensors 112 through 115 , a steer angle sensor 117 , a rate gyro 118 , a compass 119 and a vehicle speed sensor 120 , respectively , and their output signals are supplied to the control computer 110 . generally speaking , the rear wheels are required to be steered so as to follow the trajectories of the front wheels only when the vehicle travels on tortuous roads , such as s - shaped roads , crank - shaped roads , and so on , at low speed . therefore , it is conceivable to control the rear wheels so as to follow the trajectories of the front wheels only in low speed range and deactivate this control in high speed range . fig1 shows such an example of the steer angle gain in relation with the vehicle speed . in extremely low speed range , the steer angle command for the rear wheels are produced so as to make the trajectories of the front and rear wheels coincide each other , but as the vehicle speed increases , the steer angles of the rear wheels are reduced as the vehicle speed is increased as indicated by the region i so as to prevent abrupt turning motion of the vehicle . in other regions ii and iii , by determining the steer angle ratio of the rear wheels with respect to the front wheels according to the vehicle speed , the action of the existing , speed - dependent four wheel steering vehicle can be obtained . if the rear wheel steer angles are determined according to the steer angles of the front wheels instead of the vehicle speed , the action of the steer - angle - dependent four wheel steering vehicle can be obtained . further , by fixing the rear wheel steer angles to zero , the action of the conventional two wheel steering vehicle can be obtained . thus , according to the present invention , since the handling of a vehicle can be much improved by steering the rear wheels according to a relatively simple algorithm , a substantial advantage can be obtained . further , the present invention is not limited to the four wheel passenger vehicles but may be applicable to other front and rear wheel steering vehicles such as industrial vehicles and earth moving machinery having four or more wheels .