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This is a guide intended to introduce you to the practical side of creating multi-dimensional control systems. Multidimensional non-linear control systems is not a new topic, however, it has come to my attention that despite plentiful academic literature, there is no accessible guide for those who seek to enter the world of robotics software, but lack experience in the field.
This is NOT an academic paper, I will not go in depth into control theory, mathematic tools associated with it or formal performance metrics. This resource is intended to develop intuition for controls, rather than being comprehensive. In order to learn formal control theory I advice you to acquaint yourself with Brian Douglas' channel or take one of many courses on Linear Control systems or Robotics.
In this guide I will cover:
- What a control system is and why we need it?
- Robot state and control vectors
- Performance and Stability
- PID (Proportional Integral Derivative) controller
- Linear 1-dimensional control
- Linearization of non-linear systems
- Multiple control vectors, degrees of freedom
- Using symbolic math to create physical simulations and calculating control output