[rpy] Implement rpyToJacDerivative

src/math/rpy.hpp

@@ -93,6 +93,26 @@ namespace pinocchio
     template<typename Vector3Like>
     inline Eigen::Matrix<typename Vector3Like::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like)::Options>
     rpyToJacInv(const Eigen::MatrixBase<Vector3Like> & rpy, const ReferenceFrame rf=LOCAL);
+
+    ///
+    /// \brief Compute the time derivative Jacobian of the Roll-Pitch-Yaw conversion
+    ///
+    /// Given \f$\phi = (r, p, y)\f$ and reference frame F (either LOCAL or WORLD),
+    /// the Jacobian is such that \f$ {}^F\omega = J_F(\phi)\dot{\phi} \f$,
+    /// where \f$ {}^F\omega \f$ is the angular velocity expressed in frame F
+    /// and \f$ J_F \f$ is the Jacobian computed with reference frame F
+    ///
+    /// \param[in] rpy     Roll-Pitch-Yaw vector
+    /// \param[in] rpydot  Time derivative of the Roll-Pitch-Yaw vector
+    /// \param[in] rf      Reference frame in which the angular velocity is expressed
+    ///
+    /// \return The time derivative of the Jacobian of the Roll-Pitch-Yaw conversion in the appropriate frame
+    ///
+    /// \note for the purpose of this function, WORLD and LOCAL_WORLD_ALIGNED are equivalent
+    ///
+    template<typename Vector3Like0, typename Vector3Like1>
+    inline Eigen::Matrix<typename Vector3Like0::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like0)::Options>
+    rpyToJacDerivative(const Eigen::MatrixBase<Vector3Like0> & rpy, const Eigen::MatrixBase<Vector3Like1> & rpydot, const ReferenceFrame rf=LOCAL);
   } // namespace rpy
 }
 

src/math/rpy.hxx

@@ -141,6 +141,47 @@ namespace pinocchio
         }
       }
     }
+
+    template<typename Vector3Like0, typename Vector3Like1>
+    inline Eigen::Matrix<typename Vector3Like0::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like0)::Options>
+    rpyToJacDerivative(const Eigen::MatrixBase<Vector3Like0> & rpy, const Eigen::MatrixBase<Vector3Like1> & rpydot, const ReferenceFrame rf)
+    {
+      typedef typename Vector3Like0::Scalar Scalar;
+      Eigen::Matrix<Scalar,3,3> J;
+      const Scalar p = rpy[1];
+      const Scalar dp = rpydot[1];
+      Scalar sp, cp;
+      SINCOS(p, &sp, &cp);
+      switch (rf)
+      {
+        case LOCAL:
+        {
+          const Scalar r = rpy[0];
+          const Scalar dr = rpydot[0];
+          Scalar sr, cr; SINCOS(r, &sr, &cr);
+          J << Scalar(0.0), Scalar(0.0),               -cp*dp,
+               Scalar(0.0),      -sr*dr,  cr*cp*dr - sr*sp*dp,
+               Scalar(0.0),      -cr*dr, -sr*cp*dr - cr*sp*dp;
+          return J;
+        }
+        case WORLD:
+        case LOCAL_WORLD_ALIGNED:
+        {
+          const Scalar y = rpy[2];
+          const Scalar dy = rpydot[2];
+          Scalar sy, cy; SINCOS(y, &sy, &cy);
+          J << -sp*cy*dp - cp*sy*dy,      -cy*dy, Scalar(0.0),
+                cp*cy*dy - sp*sy*dp,      -sy*dy, Scalar(0.0),
+                             -cp*dp, Scalar(0.0), Scalar(0.0);
+          return J;
+        }
+        default:
+        {
+          throw std::invalid_argument("Bad reference frame.");
+        }
+      }
+    }
+
   } // namespace rpy
 }
 #endif //#ifndef __pinocchio_math_rpy_hxx__

unittest/rpy.cpp

@@ -4,6 +4,7 @@
 
 #include <pinocchio/math/rpy.hpp>
 #include <pinocchio/math/quaternion.hpp>
+#include <pinocchio/spatial/skew.hpp>
 
 #include <boost/variant.hpp> // to avoid C99 warnings
 
@@ -208,4 +209,70 @@ BOOST_AUTO_TEST_CASE(test_rpyToJacInv)
   BOOST_CHECK(jAinv.isApprox(jA.inverse()));
 }
 
+
+BOOST_AUTO_TEST_CASE(test_rpyToJacDerivative)
+{
+  // Check zero at zero velocity
+  double r = static_cast <double> (rand()) / (static_cast <double> (RAND_MAX/(2*M_PI))) - M_PI;
+  double p = static_cast <double> (rand()) / (static_cast <double> (RAND_MAX/M_PI)) - (M_PI/2);
+  double y = static_cast <double> (rand()) / (static_cast <double> (RAND_MAX/(2*M_PI))) - M_PI;
+  Eigen::Vector3d rpy(r, p, y);
+  Eigen::Vector3d rpydot(Eigen::Vector3d::Zero());
+  Eigen::Matrix3d dj0 = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot);
+  BOOST_CHECK(dj0.isZero());
+  Eigen::Matrix3d djL = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL);
+  BOOST_CHECK(djL.isZero());
+  Eigen::Matrix3d djW = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::WORLD);
+  BOOST_CHECK(djW.isZero());
+  Eigen::Matrix3d djA = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL_WORLD_ALIGNED);
+  BOOST_CHECK(djA.isZero());
+
+  // Check correct identities between different versions
+  rpydot = Eigen::Vector3d::Random();
+  dj0 = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot);
+  djL = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL);
+  djW = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::WORLD);
+  djA = pinocchio::rpy::rpyToJacDerivative(rpy, rpydot, pinocchio::LOCAL_WORLD_ALIGNED);
+  BOOST_CHECK(dj0 == djL);
+  BOOST_CHECK(djW == djA);
+
+  Eigen::Matrix3d R = pinocchio::rpy::rpyToMatrix(rpy);
+  Eigen::Matrix3d jL = pinocchio::rpy::rpyToJac(rpy, pinocchio::LOCAL);
+  Eigen::Matrix3d jW = pinocchio::rpy::rpyToJac(rpy, pinocchio::WORLD);
+  Eigen::Vector3d omegaL = jL * rpydot;
+  Eigen::Vector3d omegaW = jW * rpydot;
+  BOOST_CHECK(omegaW.isApprox(R*omegaL));
+  BOOST_CHECK(djW.isApprox(pinocchio::skew(omegaW)*R*jL + R*djL));
+  BOOST_CHECK(djW.isApprox(R*pinocchio::skew(omegaL)*jL + R*djL));
+
+  // Check against finite differences
+  double const eps = 1e-7;
+  double const tol = 1e-5;
+  Eigen::Vector3d rpyEps = rpy;
+
+  rpyEps[0] += eps;
+  Eigen::Matrix3d djLdr = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::LOCAL) - jL) / eps;
+  rpyEps[0] = rpy[0];
+  rpyEps[1] += eps;
+  Eigen::Matrix3d djLdp = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::LOCAL) - jL) / eps;
+  rpyEps[1] = rpy[1];
+  rpyEps[2] += eps;
+  Eigen::Matrix3d djLdy = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::LOCAL) - jL) / eps;
+  rpyEps[2] = rpy[2];
+  Eigen::Matrix3d djLf = djLdr * rpydot[0] + djLdp * rpydot[1] + djLdy * rpydot[2];
+  BOOST_CHECK(djL.isApprox(djLf, tol));
+
+  rpyEps[0] += eps;
+  Eigen::Matrix3d djWdr = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::WORLD) - jW) / eps;
+  rpyEps[0] = rpy[0];
+  rpyEps[1] += eps;
+  Eigen::Matrix3d djWdp = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::WORLD) - jW) / eps;
+  rpyEps[1] = rpy[1];
+  rpyEps[2] += eps;
+  Eigen::Matrix3d djWdy = (pinocchio::rpy::rpyToJac(rpyEps, pinocchio::WORLD) - jW) / eps;
+  rpyEps[2] = rpy[2];
+  Eigen::Matrix3d djWf = djWdr * rpydot[0] + djWdp * rpydot[1] + djWdy * rpydot[2];
+  BOOST_CHECK(djW.isApprox(djWf, tol));
+}
+
 BOOST_AUTO_TEST_SUITE_END()