[ShisatoYano]

Closes #170. Closes #75.

Change

Chapter 4

• doc/4_path_tracking/4_1_stanley_controller.md moves to doc/path_tracking/stanley.md as section 4.3, linked from the chapter page. Its figure script moves with it.

Chapter 10: the MPC and MPPI design documents are rewritten as the theory layer of the writing guide.

• 10.3 MPC (doc/optimal_control/mpc.md):
  • The prediction model (1). It is Euler with the steering angle as input, slightly simpler than the simulator's update.
  • The reference spaced by $v,\Delta t$ along the course.
  • The cost (2) and the constrained problem (3), solved with IPOPT, CasADi and do-mpc.
  • The receding horizon loop, limits, literalincludes of _build_model and _build_mpc, and measured experiments.
• 10.4 MPPI (doc/optimal_control/mppi.md):
  • Sampling (1), the sample cost (2), the weights (3) and the update (4), and what $\lambda$ does.
  • A comparison table of MPC and MPPI, limits, literalincludes, and a table of measured experiments.
  • New figure figures/mppi_samples.py: one MPPI update with the samples shaded by weight. It replaces mppi.png, which was copied from a blog (the writing guide doesn't allow copied figures).
• The texts follow the code where the old documents didn't:
  • MPC's set_rterm() penalizes only the change of the input; the code has no separate penalty on its size.
  • The default v_min is 0, not −1.
  • MPPI's errors are measured to the nearest course point, not a time-indexed reference.
• Symbols: a new "Optimal control" table in NOTATION.md. Weights are $W$, not $Q$ and $R$, which the book uses for noise. Samples are $M$, not $K$, which is the Kalman gain.
• The authors are credited at the end of each section (Mohit Kumar for MPC and the first documents, Erwin Lejeune for the MPPI controller).

The stopgaps listed in #170

• SECTION_PAGES is replaced by a rule in add_section_toctree(): a chapter page (<chapter>/index.md) gets a hidden toctree of the pages in its own folder that it links to, in link order. A new section only needs a link from its chapter page.
• suppress_warnings = ["myst.header"] is removed: every page now starts at H1.
• The front page's tab title no longer repeats the book title.
• DESIGN_DOCUMENT.md and its exclude_patterns entry are removed. CLAUDE.md points to the book instead.

Check

• The book builds with -W, with no warnings and no suppressed warning; test_book_chapters.py passes.

• All 26 display equations of the built book render in MathJax 3.

• The sidebar nests "4.3 Stanley" under chapter 4, and 10.3 and 10.4 under chapter 10.

• Experiments, run headless on the same course:

  Run	Average distance	Largest distance	Steering change
  MPC as set in the simulation	0.13 m	1.0 m	0.108 rad
  MPC with $N = 5$	0.19 m	2.4 m	0.077 rad
  MPPI as set in the simulation	0.16 m	1.3 m	0.064 rad
  MPPI with $M = 50$	0.36 m	2.3 m	0.110 rad
  MPPI with $\lambda = 5$	0.18 m	0.8 m	0.146 rad
  MPPI with $\lambda = 500$	0.42 m	2.0 m	0.034 rad
  MPPI without moving average	0.17 m	1.0 m	0.202 rad

  The steering change is the root mean square of the step-to-step difference. Timing: one MPC solve takes 14 ms (median) and at most 47 ms. One MPPI update takes about 1.3 s, measured alone.

After merge

Issues #199–#206 link to the old Stanley page (4_path_tracking/4_1_stanley_controller.html). Their links need updating to path_tracking/stanley.html.

🤖 Generated with Claude Code