I originally wrote this as a final project for an undergraduate technical writing class I took at University of California, Santa Cruz in Spring 2017 (CMPE 185). It is intended as a digest of graduate-level control theory aimed at veteran FIRST Robotics Competition (FRC) students who know algebra and a bit of physics. As I learned the subject of control theory, I found that it wasn't particularly difficult, but very few resources exist outside of academia for learning it. This book is intended to rectify that situation and provide a lower the barrier to entry to the field.
This book reads a lot like a reference manual on control theory and related tools. It teaches the reader how to start designing and implementing control systems for practical systems with an emphasis on pragmatism rather than theory. While the theory is mathematically elegant at times and helps inform what is going on, one shouldn't lose sight of how it behaves when applied to real systems.
A PDF version is available at https://controls-in-frc.link (full link: https://file.tavsys.net/control/controls-engineering-in-frc.pdf).
Example Python scripts can be obtained from frccontrol's Git repository at https://github.com/calcmogul/frccontrol/tree/master/examples. Furthermore, all scripts in the code directory are runnable by the user. They require Python 3.5+ and frccontrol. frccontrol can be installed with the following command.
pip3 install --user frccontrol
Some also use bookutil, a Python package containing common utilities for this
book. That can be installed by running pip3 install --user -e bookutil from
the root of this Git repository.
The scripts can be run as follows:
./elevator.py
Some Linux platforms use tk as a backend for matplotlib, so that may need to be installed to see the plots.
After installing the dependencies, just run make. It will produce a PDF named
controls-engineering-in-frc.pdf.
To compile the book, the following packages are required.
These can be installed via make setup_arch.
- base-devel (for
maketo run the makefile) - biber (for generating bibliography)
- ghostscript (to reduce size of final PDF for publishing)
- inkscape (to convert SVGs to PDFs)
- texlive-bibtexextra (for additional BibTeX styles and bibliography databases)
- texlive-core (for latexmk and xelatex)
- texlive-latexextra (for bibtex and makeglossaries)
- python >= 3.6 (for generating plots)
- python-pip (for installing required Python packages)
These can be installed via make setup_ubuntu.
- biber (for generating bibliography)
- build-essential (for
maketo run the makefile) - cm-super (for type1ec.sty)
- ghostscript (to reduce size of final PDF for publishing)
- inkscape (to convert SVGs to PDFs)
- latexmk
- texlive-bibtex-extra (for additional BibTeX styles and bibliography databases)
- texlive-generic-extra (for miscellaneous LaTeX .sty files)
- texlive-latex-extra (for bibtex and makeglossaries)
- texlive-xetex (for xelatex)
- python3 >= 3.6 (for generating plots)
- python3-pip (for installing required Python packages)
These packages are installed via pip3 (e.g., pip3 install --user frccontrol).
- frccontrol (to provide FRC wrappers for Python Control and generate plots and state-space results)
The book's build process automatically sets these up in a venv so they don't
have to be installed manually. Modifications to the Python package folders in
build will be reflected in any scripts which use the venv.
The following packages are optional because the book can compile without them.
- black (to format Python source code)
- requests (for .tex HTTP link checker)
All LaTeX labels, including bibliography entries, should use underscores to
represent spaces between words instead of hyphens. Hyphens should only be used
where the character being written is already a hyphen. .tex file names should
use hyphens and .py file names should use underscores.
Glossary entries in glossary-entries.tex should be lexographically sorted by entry key. The entry key should be the same as the name. The words in the name should be lowercase, and the description should start with a capital letter and end with a period. The first sentence should be a fragment, but sentences after that, if applicable, should be complete.
Bibliography entries in
controls-engineering-in-frc.bib should be
sorted lexographically by label. Links to online videos should use the @misc
tag. Links to online static resources like PDFs should use the @online tag.
Book content should answer the question why something works the way it does and how and when to use it to solve problems.
The book is still somewhat dense and fast-paced (it covers three classes of feedback control, two of which are for graduate students, in one short book). More examples of concepts should help slow the pace down. I should read through this book as if I was explaining it to my veteran software students and anticipate gaps in their understanding.
Add stubs for missing chapters, missing sections, and todo items.
- Fix book glossary (less self-referential?) and define terms on first use
- Box at beginning of each chapter with terms?
- Redefine variables used at start of each chapter, or when saying "using this thing from a previous section".
- Add summary page to each chapter with relevant equations.
- Add executive summaries of each chapter to facilitate tl;drs similar to what has been said in 1-on-1 discussions online when students don't understand.
- Decompress walls of math. The Kalman filter derivation is a particularly big offender.
- Reintroduce variables in later chapters that came from earlier chapters to avoid confusion and needing to trace a tree of references.
- Add exercises at the end of each chapter (with solutions) for reader practice.
This book is supposed to be "practical" after all.
- This should help me see the points I want to teach in each chapter (since the students should be able to complete the problems) so I can make sure the chapter teaches it sufficiently.
- Basically like implicit learning outcomes?
- Add test of P vs PD controller for flywheel
- Simulate flywheel with stochastic force applied to slow it down (simulates shots)
- Try P controller, PD controller, P + FF, PD + FF, and P + FF + u_error
- Add information on controllability and observability Grammians
- Link to controllability Grammian video by Steve Brunton
- Add links to implementations
- Add examples of input error state-space models to frccontrol and reference them in the book. Also do C++ examples.
- Ramsete improvements
- Add diagram to Ramsete that shows global and vehicle coordinate frames to help explain what the pose represents.
- Manipulator equations and Jacobians
- Try deriving all models using Lagrangian mechanics instead and introduce
manipulator equations
- See this post and previous post on Jacobians
- Try deriving all models using Lagrangian mechanics instead and introduce
manipulator equations
- Add troubleshooting advice for models/impls.
- Add "Partial derivative" to calculus methods appendix.
- Finish chapters on calculus and dynamics.
- Add section on controllability/observability Grammian for determining which states are uncontrollable/unobservable or which states are more/less controllable/observable.
- Finish implicit model following
- Add implicit model following simulation
- Add a section on polytopes for convex optimization? So far, I've seen it used
for handling saturated control inputs to prioritize tracking some states over
others using the limited control input.
- See 971/y2017/control_loops/python/polydrivetrain.py
- Start with how to turn a set of constraints into a matrix equation of the proper form for a polytope, then how to leverage the polytope libs for enforcing those constraints.
- Add an appendix on Ito calculus to explain where the Wiener process comes from?
- Add KF examples for nonlinear drivetrain pose estimation
- EKF, UKF, and comparison of the two
- Derive the two-sensor problem from first principles. The two-sensor problem uses p(x) and p(z_1|x).
- Add derivations for trapezoid and S-curve profiles to derivations appendix
Any other results that are good for background but are unnecessary should be included in an appendix.
- Modify pareto_boundary.py to find and plot real Pareto boundary for LQR instead of using a hand-wavey approximation
- Make ramsete_traj.py use frccontrol's update_plant() and update_controller()
- Double check drivetrain J calculation. It doesn't include robot radius, which seems suspicious.
This project, except for the software, is released under the Creative Commons Attribution-ShareAlike 4.0 International license. The software is released under the 3-clause BSD license.