The wpimath APIs use std::array, which doesn't do size checking. Passing
an array with the wrong size can result in uninitialized elements
instead of a compilation error.
This is a breaking change but is worthwhile to avoid hard-to-debug errors.
There were three options for where to put this function:
1. A free function in LinearQuadraticRegulator.h. Returning a K matrix
means the user can't use the LinearQuadraticRegulator in a loop
anymore.
2. A default argument added to ctors in LinearQuadraticRegulator for a
time delay (default of 0). This has the smallest API footprint from
the user perspective, but it bloats the already substantial
constructor overload set of LinearQuadraticRegulator.
3. A member function in LinearQuadraticRegulator that modifies the
internal K. This would still have to take in a LinearSystem or (A, B)
pair because the ctor doesn't store it. Storing it internally feels
like paying for what we don't use most of the time.
I went with option 3.
I verified the tests's expected values in Python with
scipy.linalg.fractional_matrix_power().
Closes#2877.
This helps reduce compilation overhead. I tried slimming down includes
of <Eigen/QR>, but the householderQr() function we use from there
requires including dependency headers from Eigen that don't fit with
lexographic ordering. It didn't seem worth the effort to work around.
This won't affect user code at all since all the Eigen feature usage
here is internal only; users generally only need <Eigen/Core>.
It was added as part of Bryson's rule described in
https://file.tavsys.net/control/controls-engineering-in-frc.pdf. It
doesn't really simplify usage though, and the same thing can be
replicated by multiplying the elements of Q by rho manually. It's easier
to do it that way, it's how 3512 has been doing controller debugging for
a while, and it's probably what other teams will do as well instead of
using the "more structured" way.
Removing these unhelpful overloads also simplifies the LQR interface.
