python: rework a bit the skew exposure and add skewSquare

bindings/python/spatial/expose-skew.cpp

 //
-// Copyright (c) 2015-2019 CNRS INRIA
-// Copyright (c) 2015 Wandercraft, 86 rue de Paris 91400 Orsay, France.
+// Copyright (c) 2015-2020 CNRS INRIA
+// Copyright (c) 2020 Wandercraft
 //
 
-#include "pinocchio/bindings/python/fwd.hpp"
 #include <boost/python.hpp>
+
+#include "pinocchio/bindings/python/fwd.hpp"
+#include "pinocchio/spatial/se3.hpp"
 #include "pinocchio/spatial/skew.hpp"
 
 namespace pinocchio
@@ -13,29 +15,40 @@ namespace pinocchio
   {
     namespace bp = boost::python;
   
-    Eigen::Matrix3d skew_proxy(const Eigen::Vector3d & v)
-    {
-      return pinocchio::skew(v);
-    }
-
-    Eigen::Vector3d unSkew_proxy(const Eigen::Matrix3d & M)
+    // We need to resort to another call, because it seems that Boost.Python is not aligning the Eigen::MatrixBase. TODO: fix it!
+    template<typename Matrix3>
+    Eigen::Matrix<typename Matrix3::Scalar,3,1,Matrix3::Options> unSkew(const Matrix3 & mat)
     {
-      return pinocchio::unSkew(M);
+      return pinocchio::unSkew(mat);
     }
   
     void exposeSkew()
     {
-
-      bp::def("skew",&skew_proxy,
-              bp::arg("Angular velocity (vector of size 3)"),
-              "Computes the skew representation of a given 3D vector, "
-              "i.e. the antisymmetric matrix representation of the cross product operator.");
-
-      bp::def("unSkew",&unSkew_proxy,
-              bp::arg("M: a 3x3 matrix."),
-              "Inverse of skew operator. From a given skew-symmetric matrix M "
-              "of dimension 3x3, it extracts the supporting vector, i.e. the entries of M."
-              "Mathematically speacking, it computes v such that M x = cross(x, v).");
+      typedef SE3::Matrix3 Matrix3;
+      typedef SE3::Vector3 Vector3;
+      
+      bp::def("skew",&skew<Vector3>,
+              bp::arg("u"),
+              "Computes the skew representation of a given 3d vector, "
+              "i.e. the antisymmetric matrix representation of the cross product operator, aka U = [u]x.\n"
+              "Parameters:\n"
+              "\tu: the input vector of dimension 3");
+      
+      bp::def("skewSquare",&skewSquare<Vector3,Vector3>,
+              bp::args("u","v"),
+              "Computes the skew square representation of two given 3d vectors, "
+              "i.e. the antisymmetric matrix representation of the chained cross product operator, u x (v x w), where w is another 3d vector.\n"
+              "Parameters:\n"
+              "\tu: the first input vector of dimension 3\n"
+              "\tv: the second input vector of dimension 3");
+
+      bp::def("unSkew",&unSkew<Matrix3>,
+              bp::arg("U"),
+              "Inverse of skew operator. From a given skew symmetric matrix U (i.e U = -U.T)"
+              "of dimension 3x3, it extracts the supporting vector, i.e. the entries of U.\n"
+              "Mathematically speacking, it computes v such that U.dot(x) = cross(u, x).\n"
+              "Parameters:\n"
+              "\tU: the input skew symmetric matrix of dimension 3x3.");
     }
 
   } // namespace python

src/spatial/skew.hpp

@@ -185,7 +185,7 @@ namespace pinocchio
   /// \param[in] u A 3 dimensional vector.
   /// \param[in] v A 3 dimensional vector.
   ///
-  /// \return The square cross product matrix C.
+  /// \return The square cross product matrix skew[u] * skew[v].
   ///
   template <typename V1, typename V2>
   inline Eigen::Matrix<typename V1::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(V1)::Options>