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<h1>Source code for PathPlanning.BSplinePath.bspline_path</h1><div class="highlight"><pre>
<span></span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">Path Planner with B-Spline</span>
<span class="sd">author: Atsushi Sakai (@Atsushi_twi)</span>
<span class="sd">&quot;&quot;&quot;</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="kn">import</span> <span class="nn">pathlib</span>
<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">pathlib</span><span class="o">.</span><span class="n">Path</span><span class="p">(</span><span class="vm">__file__</span><span class="p">)</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="p">))</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">scipy.interpolate</span> <span class="k">as</span> <span class="nn">interpolate</span>
<span class="kn">from</span> <span class="nn">utils.plot</span> <span class="kn">import</span> <span class="n">plot_curvature</span>
<div class="viewcode-block" id="approximate_b_spline_path"><a class="viewcode-back" href="../../../modules/path_planning/bspline_path/bspline_path.html#PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path">[docs]</a><span class="k">def</span> <span class="nf">approximate_b_spline_path</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="nb">list</span><span class="p">,</span>
<span class="n">y</span><span class="p">:</span> <span class="nb">list</span><span class="p">,</span>
<span class="n">n_path_points</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
<span class="n">degree</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Approximate points with a B-Spline path</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> x : array_like</span>
<span class="sd"> x position list of approximated points</span>
<span class="sd"> y : array_like</span>
<span class="sd"> y position list of approximated points</span>
<span class="sd"> n_path_points : int</span>
<span class="sd"> number of path points</span>
<span class="sd"> degree : int, optional</span>
<span class="sd"> B Spline curve degree. Must be 2&lt;= k &lt;= 5. Default: 3.</span>
<span class="sd"> s : int, optional</span>
<span class="sd"> smoothing parameter. If this value is bigger, the path will be</span>
<span class="sd"> smoother, but it will be less accurate. If this value is smaller,</span>
<span class="sd"> the path will be more accurate, but it will be less smooth.</span>
<span class="sd"> When `s` is 0, it is equivalent to the interpolation. Default is None,</span>
<span class="sd"> in this case `s` will be `len(x)`.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> x : array</span>
<span class="sd"> x positions of the result path</span>
<span class="sd"> y : array</span>
<span class="sd"> y positions of the result path</span>
<span class="sd"> heading : array</span>
<span class="sd"> heading of the result path</span>
<span class="sd"> curvature : array</span>
<span class="sd"> curvature of the result path</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">distances</span> <span class="o">=</span> <span class="n">_calc_distance_vector</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">spl_i_x</span> <span class="o">=</span> <span class="n">interpolate</span><span class="o">.</span><span class="n">UnivariateSpline</span><span class="p">(</span><span class="n">distances</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">degree</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">)</span>
<span class="n">spl_i_y</span> <span class="o">=</span> <span class="n">interpolate</span><span class="o">.</span><span class="n">UnivariateSpline</span><span class="p">(</span><span class="n">distances</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">degree</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">)</span>
<span class="n">sampled</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">distances</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">n_path_points</span><span class="p">)</span>
<span class="k">return</span> <span class="n">_evaluate_spline</span><span class="p">(</span><span class="n">sampled</span><span class="p">,</span> <span class="n">spl_i_x</span><span class="p">,</span> <span class="n">spl_i_y</span><span class="p">)</span></div>
<div class="viewcode-block" id="interpolate_b_spline_path"><a class="viewcode-back" href="../../../modules/path_planning/bspline_path/bspline_path.html#PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path">[docs]</a><span class="k">def</span> <span class="nf">interpolate_b_spline_path</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span>
<span class="n">n_path_points</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
<span class="n">degree</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">3</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Interpolate x-y points with a B-Spline path</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> x : array_like</span>
<span class="sd"> x positions of interpolated points</span>
<span class="sd"> y : array_like</span>
<span class="sd"> y positions of interpolated points</span>
<span class="sd"> n_path_points : int</span>
<span class="sd"> number of path points</span>
<span class="sd"> degree : int, optional</span>
<span class="sd"> B-Spline degree. Must be 2&lt;= k &lt;= 5. Default: 3</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> x : array</span>
<span class="sd"> x positions of the result path</span>
<span class="sd"> y : array</span>
<span class="sd"> y positions of the result path</span>
<span class="sd"> heading : array</span>
<span class="sd"> heading of the result path</span>
<span class="sd"> curvature : array</span>
<span class="sd"> curvature of the result path</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">return</span> <span class="n">approximate_b_spline_path</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">n_path_points</span><span class="p">,</span> <span class="n">degree</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span></div>
<span class="k">def</span> <span class="nf">_calc_distance_vector</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="n">dx</span><span class="p">,</span> <span class="n">dy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">hypot</span><span class="p">(</span><span class="n">idx</span><span class="p">,</span> <span class="n">idy</span><span class="p">)</span> <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">idy</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">)])</span>
<span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(([</span><span class="mf">0.0</span><span class="p">],</span> <span class="n">distances</span><span class="p">))</span>
<span class="n">distances</span> <span class="o">/=</span> <span class="n">distances</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <span class="n">distances</span>
<span class="k">def</span> <span class="nf">_evaluate_spline</span><span class="p">(</span><span class="n">sampled</span><span class="p">,</span> <span class="n">spl_i_x</span><span class="p">,</span> <span class="n">spl_i_y</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">spl_i_x</span><span class="p">(</span><span class="n">sampled</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">spl_i_y</span><span class="p">(</span><span class="n">sampled</span><span class="p">)</span>
<span class="n">dx</span> <span class="o">=</span> <span class="n">spl_i_x</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">1</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
<span class="n">dy</span> <span class="o">=</span> <span class="n">spl_i_y</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">1</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
<span class="n">heading</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span>
<span class="n">ddx</span> <span class="o">=</span> <span class="n">spl_i_x</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">2</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
<span class="n">ddy</span> <span class="o">=</span> <span class="n">spl_i_y</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">2</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
<span class="n">curvature</span> <span class="o">=</span> <span class="p">(</span><span class="n">ddy</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">-</span> <span class="n">ddx</span> <span class="o">*</span> <span class="n">dy</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="n">dx</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">+</span> <span class="n">dy</span> <span class="o">*</span> <span class="n">dy</span><span class="p">,</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">y</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span><span class="p">,</span>
<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
<span class="nb">print</span><span class="p">(</span><span class="vm">__file__</span> <span class="o">+</span> <span class="s2">&quot; start!!&quot;</span><span class="p">)</span>
<span class="c1"># way points</span>
<span class="n">way_point_x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
<span class="n">way_point_y</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]</span>
<span class="n">n_course_point</span> <span class="o">=</span> <span class="mi">50</span> <span class="c1"># sampling number</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">rax</span><span class="p">,</span> <span class="n">ray</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span> <span class="o">=</span> <span class="n">approximate_b_spline_path</span><span class="p">(</span>
<span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="n">n_course_point</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rax</span><span class="p">,</span> <span class="n">ray</span><span class="p">,</span> <span class="s1">&#39;-r&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Approximated B-Spline path&quot;</span><span class="p">)</span>
<span class="n">plot_curvature</span><span class="p">(</span><span class="n">rax</span><span class="p">,</span> <span class="n">ray</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;B-Spline approximation&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="s1">&#39;-og&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;way points&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">rix</span><span class="p">,</span> <span class="n">riy</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span> <span class="o">=</span> <span class="n">interpolate_b_spline_path</span><span class="p">(</span>
<span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="n">n_course_point</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rix</span><span class="p">,</span> <span class="n">riy</span><span class="p">,</span> <span class="s1">&#39;-b&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Interpolated B-Spline path&quot;</span><span class="p">)</span>
<span class="n">plot_curvature</span><span class="p">(</span><span class="n">rix</span><span class="p">,</span> <span class="n">riy</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;B-Spline interpolation&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="s1">&#39;-og&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;way points&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="n">main</span><span class="p">()</span>
</pre></div>
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