% Field-adaptive expansion step.
% (a) the six probe poses D(eta_i) reached with psi in {-psi_max, 0, +psi_max}
%     and delta in {+1,-1} at the baseline step mu_0;
% (b) the resulting per-direction steps mu_j^delta after modulation.
%
% All arcs are drawn with the true geometry of the paper's numbers:
%   L_w = 6.5 m, R_min = 12 m, psi_max = arctan(L_w/R_min) = 28.44 deg,
%   so a constant-psi_max arc of length mu turns mu/R_min rad.
%   mu_0 = 4 m  ->  19.10 deg;  modulated steps use
%   mu = mu_0 [w_min + (w_max-w_min)(1-Utilde)],  [w_min,w_max] = [0.6,1.4].
\documentclass[border=1pt]{standalone}
\input{figstyle}
\begin{document}
\begin{tikzpicture}[
    scale=0.30,
    probe/.style={line width=0.7pt},
    pnode/.style={circle, draw, line width=0.4pt, inner sep=0pt,
                  minimum size=1.5mm},
    lo/.style={corrc},          % low potential -> long step
    hi/.style={confc},          % high potential -> short step
    panel/.style={font=\footnotesize},
  ]

  % =====================================================================
  % (a) six probe poses at the baseline step mu_0
  % =====================================================================
  \begin{scope}

    % boundary that the vehicle is heading towards (source of high U)
    \draw[siteline] (-7.4,7.0) -- (9.0,7.0);
    \draw[pattern=north east lines, pattern color=sitec!45, draw=none]
          (-7.4,7.0) rectangle (9.0,8.6);
    \node[annt, sitec] at (6.2,7.9) {$\mathcal{S}_\text{e}$};

    % current node eta_i
    \fill[parkc] (0,0) circle (0.30);
    \node[annt, parkc, below left] at (0.15,-0.25) {$\boldsymbol{\eta}_i$};
    \draw[->, thin@, parkc] (0,0) -- (2.1,0);
    \node[annt, parkc] at (2.55,-0.55) {$\theta$};

    % --- forward arcs (delta = +1), sweep 19.0986 deg over mu_0 = 4 m ---
    % left: centre at (0, +R), arc from angle -90 to -90+19.0986
    \draw[probe, hi]  (0,0) arc[start angle=-90, end angle=-70.9014, radius=12];
    % straight
    \draw[probe, sitec] (0,0) -- (4,0);
    % right: centre at (0, -R)
    \draw[probe, sitec] (0,0) arc[start angle=90, end angle=70.9014, radius=12];

    % --- reverse arcs (delta = -1) --------------------------------------
    \draw[probe, lo] (0,0) arc[start angle=-90, end angle=-109.0986, radius=12];
    \draw[probe, lo] (0,0) -- (-4,0);
    \draw[probe, sitec] (0,0) arc[start angle=90, end angle=109.0986, radius=12];

    % --- probe nodes (computed endpoints) -------------------------------
    \node[pnode, hi,    fill=confc!25] at ( 3.927, 0.659) {};
    \node[pnode, sitec, fill=fillc]    at ( 4.000, 0.000) {};
    \node[pnode, sitec, fill=fillc]    at ( 3.927,-0.659) {};
    \node[pnode, lo,    fill=corrc!25] at (-3.927, 0.659) {};
    \node[pnode, lo,    fill=corrc!25] at (-4.000, 0.000) {};
    \node[pnode, sitec, fill=fillc]    at (-3.927,-0.659) {};

    \node[annt, hi] at (6.3,1.9) {high $U$};
    \node[annt, lo] at (-6.4,2.2) {low $U$};

    % baseline step annotation
    \draw[dimline] (0,-2.5) -- (4,-2.5);
    \node[annt, fill=white, inner sep=0.3pt] at (2,-2.5) {$\mu_0$};

    \node[annt, sitec] at (0,-4.6)
         {$\psi\in\{-\psi_\text{max},0,\psi_\text{max}\},\ \delta=\pm1$};
    \node[panel] at (0,-6.6) {(a) six probes $\mathcal{D}(\boldsymbol{\eta}_i)$};
  \end{scope}

  % =====================================================================
  % (b) modulated steps -- same six directions, lengths from eq (step)
  % =====================================================================
  \begin{scope}[shift={(0,-17.5)}]

    \draw[siteline] (-8.6,7.0) -- (9.0,7.0);
    \draw[pattern=north east lines, pattern color=sitec!45, draw=none]
          (-8.6,7.0) rectangle (9.0,8.6);

    \fill[parkc] (0,0) circle (0.30);
    \node[annt, parkc, below left] at (0.15,-0.25) {$\boldsymbol{\eta}_i$};

    % fwd-left : Utilde = 1.00 -> w = 0.60, mu = 2.400 m, sweep 11.4592 deg
    \draw[probe, hi] (0,0) arc[start angle=-90, end angle=-78.5408, radius=12];
    \node[pnode, hi, fill=confc!25] at (2.383,0.238) {};
    % fwd-straight : Utilde = 0.72 -> w = 0.824, mu = 3.296 m
    \draw[probe, sitec] (0,0) -- (3.296,0);
    \node[pnode, sitec, fill=fillc] at (3.296,0) {};
    % fwd-right : Utilde = 0.48 -> w = 1.016, mu = 4.064 m, sweep 19.4042
    \draw[probe, sitec] (0,0) arc[start angle=90, end angle=70.5958, radius=12];
    \node[pnode, sitec, fill=fillc] at (3.988,-0.680) {};
    % rev-left : Utilde = 0.30 -> w = 1.160, mu = 4.640 m, sweep 22.1544
    \draw[probe, lo] (0,0) arc[start angle=-90, end angle=-112.1544, radius=12];
    \node[pnode, lo, fill=corrc!25] at (-4.525,0.884) {};
    % rev-straight : Utilde = 0.08 -> w = 1.336, mu = 5.344 m
    \draw[probe, lo] (0,0) -- (-5.344,0);
    \node[pnode, lo, fill=corrc!25] at (-5.344,0) {};
    % rev-right : Utilde = 0.00 -> w = 1.400, mu = 5.600 m, sweep 26.7380
    \draw[probe, lo] (0,0) arc[start angle=90, end angle=116.7380, radius=12];
    \node[pnode, lo, fill=corrc!25] at (-5.399,-1.283) {};

    % shortest / longest annotations
    \node[annt, hi] at (4.9,1.75) {$w_\text{min}\mu_0$};
    \draw[->, line width=0.4pt, hi] (3.7,1.35) -- (2.6,0.55);
    \node[annt, lo] at (-6.9,-2.7) {$w_\text{max}\mu_0$};
    \draw[->, line width=0.4pt, lo] (-6.3,-2.15) -- (-5.4,-1.35);

    \node[annt, sitec, align=center] at (0,-4.6)
         {$\mu_j^\delta=\mu_0\bigl[w_\text{min}
           +(w_\text{max}-w_\text{min})(1-\tilde U_j^\delta)\bigr]$};
    \node[panel] at (0,-6.6) {(b) modulated steps};
  \end{scope}

\end{tikzpicture}
\end{document}
