@@ -716,11 +716,11 @@ <h1>se(2) twist<a class="headerlink" href="#se-2-twist" title="Link to this head
 <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">Twist3</span></a><span class="p">(</span><span class="n">SE3</span><span class="o">.</span><span class="n">Rand</span><span class="p">())</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a>
-<span class="go">Twist3([-1.2116, 0.049677, 0.66232, 0.70184, -0.04326, 1.066])</span>
+<span class="go">Twist3([-0.049077, 0.74883, -0.57515, 1.2958, -1.1632, 0.36528])</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.inv" title="spatialmath.twist.Twist3.inv"><span class="n">S</span><span class="o">.</span><span class="n">inv</span></a><span class="p">()</span>
-<span class="go">Twist3([1.2116, -0.049677, -0.66232, -0.70184, 0.04326, -1.066])</span>
+<span class="go">Twist3([0.049077, -0.74883, 0.57515, -1.2958, 1.1632, -0.36528])</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3" title="spatialmath.twist.Twist3"><span class="n">S</span></a> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="3d_pose_twist.html#spatialmath.twist.Twist3.inv" title="spatialmath.twist.Twist3.inv"><span class="n">S</span><span class="o">.</span><span class="n">inv</span></a><span class="p">()</span>
-<span class="go">Twist3([0, 2.2204e-16, 5.5511e-17, 0, 0, 0])</span>
+<span class="go">Twist3([-5.5511e-17, 0, 4.1633e-17, 0, 0, 0])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -836,8 +836,7 @@ <h1>se(2) twist<a class="headerlink" href="#se-2-twist" title="Link to this head
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">T</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">SE2</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">S</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">Twist2</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">T</span></a><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2.unit" title="spatialmath.twist.Twist2.unit"><span class="n">S</span><span class="o">.</span><span class="n">unit</span></a><span class="p">()</span>
-<span class="go">!! [RUNBLOCK-ERROR] spatialmath/twist.py:docstring of spatialmath.twist.Twist2.unit:574</span>
-<span class="go">    ValueError: bad twist value</span>
+<span class="go">Twist2([4.3083, 6.1166, 1])</span>
 </pre></div>
 </div>
 </dd></dl>
@@ -924,8 +923,7 @@ <h1>se(2) twist<a class="headerlink" href="#se-2-twist" title="Link to this head
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">T</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">SE2</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">S</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">Twist2</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">T</span></a><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2.unit" title="spatialmath.twist.Twist2.unit"><span class="n">S</span><span class="o">.</span><span class="n">unit</span></a><span class="p">()</span>
-<span class="go">!! [RUNBLOCK-ERROR] spatialmath/twist.py:docstring of spatialmath.twist.Twist2.ad:647</span>
-<span class="go">    ValueError: bad twist value</span>
+<span class="go">Twist2([4.3083, 6.1166, 1])</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
@@ -1018,15 +1016,14 @@ <h1>se(2) twist<a class="headerlink" href="#se-2-twist" title="Link to this head
 <dd class="field-even"><p>ndarray(2)</p>
 </dd>
 </dl>
-<p><code class="docutils literal notranslate"><span class="pre">X.pole()</span></code> is a point on the twist axis. For a pure translation
+<p><code class="docutils literal notranslate"><span class="pre">X.pole</span></code> is a point on the twist axis. For a pure translation
 this point is at infinity.</p>
 <p>Example:</p>
 <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">SE2</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">Twist2</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">T</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">SE2</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">S</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2" title="spatialmath.twist.Twist2"><span class="n">Twist2</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="2d_pose_SE2.html#spatialmath.pose2d.SE2" title="spatialmath.pose2d.SE2"><span class="n">T</span></a><span class="p">)</span>
-<span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2.pole" title="spatialmath.twist.Twist2.pole"><span class="n">S</span><span class="o">.</span><span class="n">pole</span></a><span class="p">()</span>
-<span class="go">!! [RUNBLOCK-ERROR] spatialmath/twist.py:docstring of spatialmath.twist.Twist2.pole:735</span>
-<span class="go">    TypeError: 'numpy.ndarray' object is not callable</span>
+<span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="2d_pose_twist.html#spatialmath.twist.Twist2.pole" title="spatialmath.twist.Twist2.pole"><span class="n">S</span><span class="o">.</span><span class="n">pole</span></a>
+<span class="go">array([-1.835 ,  1.2925])</span>
 </pre></div>
 </div>
 </dd></dl>
 
@@ -490,9 +490,9 @@ <h1>SO(3) matrix<a class="headerlink" href="#so-3-matrix" title="Link to this he
 <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3" title="spatialmath.pose3d.SO3"><span class="n">SO3</span></a>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3" title="spatialmath.pose3d.SO3"><span class="n">x</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3.Rand" title="spatialmath.pose3d.SO3.Rand"><span class="n">SO3</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">()</span>
 <span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_orient_SO3.html#spatialmath.pose3d.SO3" title="spatialmath.pose3d.SO3"><span class="n">x</span></a>
-<span class="go">SO3(array([[ 0.2465, -0.9124, -0.3268],</span>
-<span class="go">           [ 0.2923, -0.2515,  0.9227],</span>
-<span class="go">           [-0.924 , -0.323 ,  0.2047]]))</span>
+<span class="go">SO3(array([[-0.9686, -0.2487, -0.005 ],</span>
+<span class="go">           [-0.0431,  0.1479,  0.9881],</span>
+<span class="go">           [-0.245 ,  0.9572, -0.154 ]]))</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
 
@@ -453,11 +453,11 @@ <h1>Unit quaternion<a class="headerlink" href="#unit-quaternion" title="Link to
 <p>Example:</p>
 <div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion" title="spatialmath.quaternion.UnitQuaternion"><span class="n">UnitQuaternion</span></a> <span class="k">as</span> <span class="n">UQ</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion.Rand" title="spatialmath.quaternion.UnitQuaternion.Rand"><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">())</span>
-<span class="go"> 0.5660 &lt;&lt; -0.6913,  0.1026,  0.4372 &gt;&gt;</span>
+<span class="go"> 0.8856 &lt;&lt;  0.2108, -0.0807,  0.4059 &gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion.Rand" title="spatialmath.quaternion.UnitQuaternion.Rand"><span class="n">UQ</span><span class="o">.</span><span class="n">Rand</span></a><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
-<span class="go"> 0.8051 &lt;&lt;  0.2053,  0.0975,  0.5479 &gt;&gt;</span>
-<span class="go"> 0.7722 &lt;&lt; -0.1075, -0.6262, -0.0032 &gt;&gt;</span>
-<span class="go"> 0.4734 &lt;&lt; -0.1563, -0.7304, -0.4669 &gt;&gt;</span>
+<span class="go"> 0.3781 &lt;&lt; -0.2618,  0.3380,  0.8211 &gt;&gt;</span>
+<span class="go"> 0.7840 &lt;&lt; -0.1203,  0.1768, -0.5827 &gt;&gt;</span>
+<span class="go"> 0.4215 &lt;&lt; -0.7788,  0.4268, -0.1837 &gt;&gt;</span>
 </pre></div>
 </div>
 <dl class="field-list simple">
@@ -1509,10 +1509,44 @@ <h1>Unit quaternion<a class="headerlink" href="#unit-quaternion" title="Link to
 </dl>
 <p><code class="docutils literal notranslate"><span class="pre">q.conj()</span></code> is the quaternion <code class="docutils literal notranslate"><span class="pre">q</span></code> with the vector part negated, ie.
 <span class="math notranslate nohighlight">\(q = s \langle -v_x, -v_y, -v_z \rangle\)</span></p>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>For a <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> this deliberately does <strong>not</strong>
+canonicalize the result’s scalar part to be non-negative, unlike
+normal <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> construction. <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code>
+construction canonicalizes because <span class="math notranslate nohighlight">\(q\)</span> and <span class="math notranslate nohighlight">\(-q\)</span>
+represent the same rotation, which is the right behaviour when
+building a unit quaternion from arbitrary data. But conjugation
+is an algebraic operation, not a re-representation of a
+rotation: it must satisfy <span class="math notranslate nohighlight">\(q \cdot \bar{q} = 1\)</span> for any
+downstream algebra to be correct (e.g. dual-quaternion
+translation extraction, which relies on exactly this identity).
+Re-canonicalizing the conjugate would silently return
+<span class="math notranslate nohighlight">\(-\bar{q}\)</span> whenever <code class="docutils literal notranslate"><span class="pre">q</span></code> has negative scalar part,
+breaking that identity. See the example below: the scalar part
+of the result matches the input’s sign, it is not forced
+positive.</p>
+</div>
+<div class="versionchanged">
+<p><span class="versionmodified changed">Changed in version 1.1.18: </span>Fixes a bug present in 1.1.17 and earlier: <code class="docutils literal notranslate"><span class="pre">UnitQuaternion.conj()</span></code>
+re-canonicalized its result’s sign, silently returning
+<span class="math notranslate nohighlight">\(-\bar{q}\)</span> instead of the true conjugate whenever <code class="docutils literal notranslate"><span class="pre">q</span></code> had
+negative scalar part. This broke any algebra relying on
+<span class="math notranslate nohighlight">\(q \cdot \bar{q} = 1\)</span>, including <code class="xref py py-class docutils literal notranslate"><span class="pre">DualQuaternion</span></code>
+translation extraction (<code class="docutils literal notranslate"><span class="pre">SE3()</span></code>), <code class="docutils literal notranslate"><span class="pre">norm()</span></code> (which could raise
+<code class="docutils literal notranslate"><span class="pre">ValueError</span></code> from taking the square root of a small negative
+float), and point transformation via <code class="docutils literal notranslate"><span class="pre">dq</span> <span class="pre">*</span> <span class="pre">v</span></code>.</p>
+</div>
 <p>Example:</p>
-<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_quaternion.html#spatialmath.quaternion.Quaternion" title="spatialmath.quaternion.Quaternion"><span class="n">Quaternion</span></a>
+<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath</span><span class="w"> </span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="3d_quaternion.html#spatialmath.quaternion.Quaternion" title="spatialmath.quaternion.Quaternion"><span class="n">Quaternion</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion" title="spatialmath.quaternion.UnitQuaternion"><span class="n">UnitQuaternion</span></a>
+<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span><span class="w"> </span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy"><span class="nn">numpy</span></a><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_quaternion.html#spatialmath.quaternion.Quaternion.Pure" title="spatialmath.quaternion.Quaternion.Pure"><span class="n">Quaternion</span><span class="o">.</span><span class="n">Pure</span></a><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span><span class="o">.</span><a class="sphinx-codeautolink-a" href="3d_quaternion.html#spatialmath.quaternion.Quaternion.conj" title="spatialmath.quaternion.Quaternion.conj"><span class="n">conj</span></a><span class="p">())</span>
 <span class="go"> 0.0000 &lt; -1.0000, -2.0000, -3.0000 &gt;</span>
+<span class="gp">&gt;&gt;&gt; </span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion" title="spatialmath.quaternion.UnitQuaternion"><span class="n">q</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion" title="spatialmath.quaternion.UnitQuaternion"><span class="n">UnitQuaternion</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">]]),</span> <span class="n">norm</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion" title="spatialmath.quaternion.UnitQuaternion"><span class="n">q</span></a><span class="p">)</span>
+<span class="go">-0.5000 &lt;&lt;  0.5000,  0.5000,  0.5000 &gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="3d_orient_unitquaternion.html#spatialmath.quaternion.UnitQuaternion.conj" title="spatialmath.quaternion.UnitQuaternion.conj"><span class="n">q</span><span class="o">.</span><span class="n">conj</span></a><span class="p">())</span>
+<span class="go">-0.5000 &lt;&lt; -0.5000, -0.5000, -0.5000 &gt;&gt;</span>
 </pre></div>
 </div>
 <dl class="field-list simple">