Robotics Feedback Control - Basics

Feedback control is the means of how a system gets to achieve a desired state by comparing the current state with the desired one continuously. Usually implemented and used at a low level, for controlling actuators like wheels.

Given the actual state and the desired state as points in a set, the error would be the difference between those two states. Knowing the magnitud and the direction of the error we can then calculate the actions that have to be performed in order to reduce the error and get closer to the desired state.

The feedback is the information that is sent back to the controller.

When the desired state is achieved, you can be done and not perform any additional action or you can try to maintain it continuously.

The sampling rate is the rate of computing and sensing in a given unit of time.

The gains are the parameters that determine the magnitude of the system response. These are calibrated and tested by trial and error.

Damping is the process of systematically reducing oscillations. The robot actions have an error, which can make the state to oscillate, and to reduce them, you have to properly calibrate the gains.

Types of feedback control

P - PD - PID

Note: K corresponds to a constant, dependent on each system.

  • P: Proportional control. The systems responds in proportion to the error using direction and magnitude.

    o = Kpi

  • D: Derivative control. The system responds to the derivative error, the momentum changes when close to the desired state.

    $o=K_d\frac{di}{dt}$

  • I: Integral control. The systems keeps track of its own errors and over time responds to correct them.

    o = Ki∫i(t)d**t

  • PD: Proportional + Derivative

    $o=K_pi+K_d\frac{di}{dt}$

  • PID: Proportional + Derivative + Integral

    $o=K_pi+K_d\frac{di}{dt}+K_i\int i(t)dt$

Notes References

20210514183815 INDEX - Robotics

References