Friday, May 19, 2017

The PID controller

Key element of our robot's power control is the closed loop comprised of the gyroscope that measures the direction of the chassis ("yaw") and and the motors moving the chassis and eventually causing deviation from the desired direction. The control problem seems simple enough; we would like to keep the direction error 0 (in case of straight drive) or make the error 0 (in case of turning). The reality is that there will be error, however. In case of turning the large error is already present at the beginning of the movement (because the chassis is oriented in a different direction than the desired one), in case of straight drive the error will appear inevitably as the imperfect power estimation, small obstacles, etc. will cause the robot to deviate from the "straight" direction. This post explains, how the robot software handles this error.

This problem is more complicated than it seems. For starter, the inertia of the robot chassis is always present. Just because we switch off the motors, the chassis will keep moving. In case of turning, one can typically calculate with 20 degrees of rotation after the motors have been switched off. The exact correction tag depends on a lot of factors that are impossible to calculate in closed form as our robot kits exhibit quite a variety in terms of mechanical parameters. So the approach is to adapt the motor power according to the errors that we measure and report success if the error is small enough.

One time-tested algorithm able to perform such a control is the PID controller. The algorithm is more than 100 years old and was originally developed for torpedo depth control. The assumption is that we have an error that is calculated from desired and measured values of a parameter and we would like to calculate an actuator signal that influences the controlled system. In our robot, the error value is calculated from the desired and real direction angle and the actuator signal is the relative power of the motors. These relative values will be turned into PWM values by two calibration tables as described in the previous post.

The PID controller's output is used differently in the straight drive and turning movements. In case of the straight drive the user specifies the power applied to the robot's wheels. The wheel on the same side as the deviation gets this power, the wheel opposite to the deviation gets user-defined power minus PID controller output. In case of the turning movement, the wheels receive the power determined by the PID controller's output but in opposite direction.

Check out TwoWDRobot::motor_pid_controller for the implementation of our PID controller. The proportional-integral-derivative parameters have been found out by some experimentation and I do not claim that the tuning cannot be more perfect. Consider, however, the diagrams below that show the operation of the controller in case of 4x90 degree turns, performed by the same robot, at the same location, in immediate succession. The experiment was done on a parquet which is somewhat slippery and you can observe the same oscillation movement that can be seen in this video when the robot turns.

So here are the four diagrams.

There are obviously large differences that can be explained by the control system's timing relative to the state of the mechanical system.  The controller's timing is determined by the gyro's 100 Hz sampling rate. This sounds fast enough but if you consider that the entire turn is over in about 1.5 sec (that means 150 gyro samples), you can realize too that no two movements are the same from the digital system's point of view. The PID controller's tuning must also consider different soil types and the quite large variety of the DC motors that come with the robot kits. I found this "aggressively tuned" controller appropriate for my purposes.

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