We have bought 2WD turtle bot with Arduino. http://www.dfrobot.com/index.php?route=product/product&product_id=65#.UZxObIoW3RQ Now we need to turn it to 90 angle. We need to understand how we can do it. We don't have encoders.
Drive the left and right motors in opposite directions.
If your design requirements constrain you to having no feedback, your best bet is to experiment with the time you turn on your motors. Note that this value can change based on things like the battery voltage and floor texture.
Since it has an Arduino, I'd suggest adding a nice gyroscope and integrating the output to find your angular displacement. Or some other way to find out how far you've turned.
The turtle bot has two geared motors. These can be turned ON and OFF and FORWARD and REVERSE. Without an encoder to measure the actual rotation you will need to basically guess (experiment with) the LENGTH OF TIME (DELAY) you activate the motors.
There are two ways you can turn a 90 degree angle.
(i) Turn ONE motor ON for a 'lazy' turn that will pivot around the other wheel. Depending on the speed of the geared down motor start with a 1 second DELAY and measure the angle turned. From this value (degrees per second) you can calculate the delay needed to turn 90 degrees.
(ii) Turn one motor ON + FORWARD, turn the other motor ON + REVERSE. This will produce a 'sharp' turn pivoting about a central point on the axis. This turn is much faster and effectively turns the bot on the spot. Again experiment with a given time (DELAY) and measure the angle turned the calculate the delay time needed.
You can know, approximately, how fast the motor is turning by sensing the back-EMF of the motors without encoders. See How can I measure back-EMF to infer the speed of a DC motor?
Unfortunately this doesn't really tell you how much the robot has turned. Any error in your measurement will accumulate, and these errors will be significant. You will have errors from your back-EMF measurement. Most likely you will have more serious errors from wheel slip, which will vary based on the surface the robot is on and the dust accumulating on the wheels. Thus, back-EMF measurement, or even direct motor speed measurement with encoders, may not be productive.
A gyroscope would allow your robot to measure how much its turned. Integrate this into a feedback loop. A gyroscope is still subject to drift, but much less than other methods. An alternate method would be using a magnetometer to sense Earth's magnetic field like a compass.