docs(mpc_lateral_controller): modify mathjax visualization error

[sak-0822]

Description

Fix 2 mathjax visualization error

Missing or unrecognized delimiter for \left

github-mathjax doesn't recognize
\left{ }\right

orsharir/github-mathjax#16

So I fix it as \lbrace, \rbrace.

Some equation aren't output because of "\dot{u}.

So I fix it as \dot u

Tests performed

Not applicable.

Effects on system behavior

Not applicable.

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[takayuki5168]

@sak-0822
Thank you so much!

Some of the matrix was converted to the vector by this PR as follows for example. Can you fix them? \ means the new row for the matrix.

[sak-0822]

@takayuki5168
Thank you for your reviewing.

Some of the matrix was converted to the vector by this PR as follows for example. Can you fix them? \ means the new row for the matrix.

I changed "\" to "\". By doing so, I was able to confirm that the matrix is displayed correctly.
For example:

\begin{align} \begin{bmatrix} -1 & 1 & 0 \\\ 1 & -1 & 0 \\\ 0 & -1 & 1 \\\ 0 & 1 & -1 \end{bmatrix}\begin{bmatrix} u_{0} \\\ u_{1} \\\ u_{2} \end{bmatrix} \leq \begin{bmatrix} \dot u_{max}\text{d}t \\\ -\dot u_{min}\text{d}t \\\ \dot u_{max}\text{d}t \\\ -\dot u_{min}\text{d}t \end{bmatrix} \end{align}

The output:

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 14.79%. Comparing base (44e4be7) to head (0856bfa).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #6486   +/-   ##
=======================================
  Coverage   14.79%   14.79%           
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  Files        1917     1917           
  Lines      132001   132001           
  Branches    39228    39228           
=======================================
  Hits        19524    19524           
  Misses      90688    90688           
  Partials    21789    21789           

Flag	Coverage Δ		*Carryforward flag
differential	45.00% <ø> (?)
total	14.79% <ø> (ø)		Carriedforward from 44e4be7

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[github-actions]

Documentation URL: https://autowarefoundation.github.io/autoware.universe/pr-6486/
Modified URLs:

• https://autowarefoundation.github.io/autoware.universe/pr-6486/control/mpc_lateral_controller/model_predictive_control_algorithm/

[takayuki5168]

@sak-0822
All the CI has passed. Now you can merge the PR anytime.
Thank you for your contribution!

Just FYI, we have a similar document in the following, and the same issue is happening. We are very happy if you have time to fix it.
https://autowarefoundation.github.io/autoware.universe/pr-6486/planning/obstacle_avoidance_planner/docs/mpt/