A large part of developing robotic systems involves measuring the state of the robot and then executing some action, to change the state of the robot. Because there is usually not an exact correspondence between the action and the desired state and because it’s also usually necessary to measure the new state, some method of control is required. It’s helpful if the control method can take into account all of the current state of the robot, the previous changes to the state and their corresponding effect and the new state. One typical method is called PID control.

PID control is useful when the state of some part of the robot can be measured and represented as a numerical value. The actual value is the difference between the actual measurement, called the process variable, and the desired measurement, called the setpoint. The PID control works to bring the difference between the process variable and the setpoint to zero and keep it there. As an example, assume we have a robot which we wish to move at a constant speed. The speed of the robot is based upon the voltage applied to its drive motors. Apply more voltage and it goes faster, apply less voltage and it goes slower. The challenge arises because the change in voltage is not instantaneous and also because the robot is not always travelling over exactly the same surface and with the same load. Sometimes the same voltage will make it go a bit faster and other times a bit slower.

The PID control attempts to reduce the difference between the process variable and the setpoint by calculating a control value and then applying that control value to the process. In our example, the setpoint is the robot speed wanted, the process variable is the actual, current robot speed and the control value is the voltage to apply.

Proportional Gain

The first part of the PID control is the proportional or P adjustment. This is, perhaps, the simplest part of the PID control and responds in proportion to the difference between process value and setpoint. When that difference is large, the P control produces a large control value. When the difference is small the P control produces a small control value. So, let’s say that the voltage range in this example is from 0 to 12. 0 Volts causes the robot to stop (eventually) and 12 Volts causes it to travel at its top speed (again, eventually). We can then write an equation to calculate the control value, based on the setpoint and the process variable:

ControlValue = [P x (SetPoint – ProcessVariable) x (MaxVoltage – CurrentVoltage)] + CurrentVoltage

The ProcessVariable is the current speed of the robot. The SetPoint is the desired speed. The CurrentVoltage is assumed to be what’s causing the robot to move at its current speed. P is the proportional gain, from the P in PID Control, and is used to determine just how much voltage change is applied to the current state of the robot, in order to move the ProcessVariable closer to the SetPoint.

At this point, what we have is a way to adjust the speed of our robot, which responds proportionally to the difference between the actual speed and the desired speed. In other words, if the actual speed is close to the desired speed, this control method will only make a small adjustment. When the difference is great, a large adjustment will be made. This would seem to be a good thing, until we consider latency, in terms of the delay between measuring the speed and responding to the speed and in terms of the delay between applying a new voltage and reaching the full effect of that new voltage. Because of these possible latencies, the system being controlled can have a tendency to oscillate, above and below the desired speed, and never actually reach the desired speed.

Fortunately, the PID control method can deal with that and it’s specifically the D part of the method which I’ll describe next.

Derivative gain

to be continued …

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