[rpy] Implement rpyToJacInv

src/math/rpy.hpp

@@ -73,6 +73,25 @@ namespace pinocchio
     template<typename Vector3Like>
     Eigen::Matrix<typename Vector3Like::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like)::Options>
     rpyToJac(const Eigen::MatrixBase<Vector3Like> & rpy, const ReferenceFrame rf=LOCAL);
+  
+    ///
+    /// \brief Compute the inverse 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] rf  Reference frame in which the angular velocity is expressed
+    ///
+    /// \return The inverse 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 Vector3Like>
+    Eigen::Matrix<typename Vector3Like::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like)::Options>
+    rpyToJacInv(const Eigen::MatrixBase<Vector3Like> & rpy, const ReferenceFrame rf=LOCAL);
   } // namespace rpy
 }
 

src/math/rpy.hxx

@@ -101,6 +101,45 @@ namespace pinocchio
         }
       }
     }
+
+
+    template<typename Vector3Like>
+    Eigen::Matrix<typename Vector3Like::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3Like)::Options>
+    rpyToJacInv(const Eigen::MatrixBase<Vector3Like> & rpy, const ReferenceFrame rf)
+    {
+      typedef typename Vector3Like::Scalar Scalar;
+      Eigen::Matrix<Scalar,3,3> J;
+      const Scalar p = rpy[1];
+      Scalar sp, cp;
+      SINCOS(p, &sp, &cp);
+      Scalar tp = sp/cp;
+      switch (rf)
+      {
+        case LOCAL:
+        {
+          const Scalar r = rpy[0];
+          Scalar sr, cr; SINCOS(r, &sr, &cr);
+          J << Scalar(1.0), sr*tp, cr*tp,
+               Scalar(0.0),    cr,   -sr,
+               Scalar(0.0), sr/cp, cr/cp;
+          return J;
+        }
+        case WORLD:
+        case LOCAL_WORLD_ALIGNED:
+        {
+          const Scalar y = rpy[2];
+          Scalar sy, cy; SINCOS(y, &sy, &cy);
+          J << cy/cp,  sy/cp, Scalar(0.0),
+                 -sy,     cy, Scalar(0.0),
+               cy*tp,  sy*tp, Scalar(1.0);
+          return J;
+        }
+        default:
+        {
+          throw std::invalid_argument("Bad reference frame.");
+        }
+      }
+    }
   } // namespace rpy
 }
 #endif //#ifndef __pinocchio_math_rpy_hxx__

unittest/rpy.cpp

@@ -181,4 +181,31 @@ BOOST_AUTO_TEST_CASE(test_rpyToJac)
   BOOST_CHECK(Rdot.isApprox(pinocchio::skew(omegaW) * R, tol));
 }
 
+
+BOOST_AUTO_TEST_CASE(test_rpyToJacInv)
+{
+  // Check correct identities between different versions
+  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);
+  p *= 0.999; // ensure we are not too close to a singularity
+  double y = static_cast <double> (rand()) / (static_cast <double> (RAND_MAX/(2*M_PI))) - M_PI;
+  Eigen::Vector3d rpy(r, p, y);
+
+  Eigen::Matrix3d j0 = pinocchio::rpy::rpyToJac(rpy);
+  Eigen::Matrix3d j0inv = pinocchio::rpy::rpyToJacInv(rpy);
+  BOOST_CHECK(j0inv.isApprox(j0.inverse()));
+
+  Eigen::Matrix3d jL = pinocchio::rpy::rpyToJac(rpy, pinocchio::LOCAL);
+  Eigen::Matrix3d jLinv = pinocchio::rpy::rpyToJacInv(rpy, pinocchio::LOCAL);
+  BOOST_CHECK(jLinv.isApprox(jL.inverse()));
+
+  Eigen::Matrix3d jW = pinocchio::rpy::rpyToJac(rpy, pinocchio::WORLD);
+  Eigen::Matrix3d jWinv = pinocchio::rpy::rpyToJacInv(rpy, pinocchio::WORLD);
+  BOOST_CHECK(jWinv.isApprox(jW.inverse()));
+
+  Eigen::Matrix3d jA = pinocchio::rpy::rpyToJac(rpy, pinocchio::LOCAL_WORLD_ALIGNED);
+  Eigen::Matrix3d jAinv = pinocchio::rpy::rpyToJacInv(rpy, pinocchio::LOCAL_WORLD_ALIGNED);
+  BOOST_CHECK(jAinv.isApprox(jA.inverse()));
+}
+
 BOOST_AUTO_TEST_SUITE_END()