[Dhruv-Sharma29]

Closes #200

Overview

Adds the theory layer of the three remaining sections of chapter 4, one page each, following the writing guide and the Stanley section:

• 4.1 Course generation with cubic splines (doc/path_tracking/cubic_spline.md): the natural cubic spline derived step by step (conditions, coefficients, the tridiagonal system, natural ends), the chord-length parameter of the 2D course, the yaw angle and curvature formulas, and the target speed along the course (switch-backs and the stop at the end).
• 4.2 Pure Pursuit (doc/path_tracking/pure_pursuit.md): the look-ahead point, the arc through it (law of sines), the curvature as a proportional law on the look-ahead point's offset, the steering angle from the bicycle model, the speed-dependent look-ahead distance with a linearized analysis of why it grows with speed, and the adaptive look-ahead distance.
• 4.4 Rear wheel feedback (doc/path_tracking/rear_wheel_feedback.md): the errors at the rear axle, the error dynamics in the course frame, the control law and its Lyapunov argument, the steering angle, and a "Pure Pursuit vs Stanley vs rear wheel feedback" comparison (what each one looks at and how it behaves at speed).

Each page has a figure script in doc/path_tracking/figures/ (cubic_spline_course.py, pure_pursuit_geometry.py, rear_wheel_feedback_errors.py) that computes its geometry with the page's equations. The pages are listed on the chapter page, and the new symbols $s$, $l_d$ and $\alpha$ are added to Notation and Units.

The Limits sections also say where the code differs from the theory, for example that RearWheelFeedbackController sets the whole yaw rate to 0 when the heading error is exactly 0, and that the simulations' course has a turn of about 1 m radius driven at a constant 20 km/h.

How I checked it

• sphinx-build -W --keep-going -b html doc doc/_build/html builds without warnings, and pytest test/test_book_chapters.py passes.
• Read the three pages in the built book: every equation renders, every figure loads, and the links between the pages work.
• The spline equations of 4.1, implemented in the figure script, give the same coefficients as CubicSpline for the simulations' course.
• The linearized Pure Pursuit result (damping ratio $1/\sqrt{2}$, the same settling distance at any speed) was checked with a short simulation at 2 and 10 m/s.
• The references were checked against the papers: Coulter (1992), Snider (2009), Hoffmann et al. (2007), and Paden et al. (2016), whose equation (V.12) is the law of 4.4 (the original by Samson is cited as given there).

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