text: #ifndef MULTIBODYTREE_HPP_
  #define MULTIBODYTREE_HPP_
  
  #include "IDConfig.hpp"
  #include "IDMath.hpp"
  
  namespace btInverseDynamics {
  
  /// Enumeration of supported joint types
  enum JointType {
  	/// no degree of freedom, moves with parent
  	FIXED = 0,
  	/// one rotational degree of freedom relative to parent
  	REVOLUTE,
  	/// one translational degree of freedom relative to parent
  	PRISMATIC,
  	/// six degrees of freedom relative to parent
  	FLOATING
  };
  
  /// Interface class for calculating inverse dynamics for tree structured
  /// multibody systems
  ///
  /// Note on degrees of freedom
  /// The q vector contains the generalized coordinate set defining the tree's configuration.
  /// Every joint adds elements that define the corresponding link's frame pose relative to
  /// its parent. For the joint types that is:
  ///	- FIXED:	 none
  ///	- REVOLUTE:  angle of rotation [rad]
  ///	- PRISMATIC: displacement [m]
  ///	- FLOATING:  Euler x-y-z angles [rad] and displacement in body-fixed frame of parent [m]
  ///				 (in that order)
  /// The u vector contains the generalized speeds, which are
  ///	- FIXED:	 none
  ///	- REVOLUTE:  time derivative of angle of rotation [rad/s]
  ///	- PRISMATIC: time derivative of displacement [m/s]
  ///	- FLOATING:  angular velocity [rad/s] (*not* time derivative of rpy angles)
  ///				 and time derivative of displacement in parent frame [m/s]
  ///
  /// The q and u vectors are obtained by stacking contributions of all bodies in one
  /// vector in the order of body indices.
  ///
  /// Note on generalized forces: analogous to u, i.e.,
  ///	 - FIXED:	 none
  ///	 - REVOLUTE:  moment [Nm], about joint axis
  ///	 - PRISMATIC: force  [N], along joint axis
  ///	 - FLOATING:  moment vector [Nm] and force vector [N], both in body-fixed frame
  ///				  (in that order)
  ///
  /// TODO - force element interface (friction, springs, dampers, etc)
  ///	  - gears and motor inertia
  class MultiBodyTree {
  public:
          ID_DECLARE_ALIGNED_ALLOCATOR();
  	/// The contructor.
  	/// Initialization & allocation is via addBody and buildSystem calls.
  	MultiBodyTree();
  	/// the destructor. This also deallocates all memory
  	~MultiBodyTree();
  
  	/// Add body to the system. this allocates memory and not real-time safe.
  	/// This only adds the data to an initial cache. After all bodies have been
  	/// added,
  	/// the system is setup using the buildSystem call
  	/// @param body_index index of the body to be added. Must >=0, <number of bodies,
  	///		and index of parent must be < index of body
  	/// @param parent_index index of the parent body
  	///		The root of the tree has index 0 and its parent (the world frame)
  	///		is assigned index -1
  	///		the rotation and translation relative to the parent are taken as
  	///		pose of the root body relative to the world frame. Other parameters
  	///		are ignored
  	/// @param JointType type of joint connecting the body to the parent
  	/// @param mass the mass of the body
  	/// @param body_r_body_com the center of mass of the body relative to and
  	/// described in
  	///		the body fixed frame, which is located in the joint axis connecting
  	/// the body to its parent
  	/// @param body_I_body the moment of inertia of the body w.r.t the body-fixed
  	/// frame
  	///		(ie, the reference point is the origin of the body-fixed frame and
  	/// the matrix is written
  	///		 w.r.t. those unit vectors)
  	/// @param parent_r_parent_body_ref position of joint relative to the parent
  	/// body's reference frame
  	///		for q=0, written in the parent bodies reference frame
  	/// @param body_axis_of_motion translation/rotation axis in body-fixed frame.
  	///		Ignored for joints that are not revolute or prismatic.
  	///		must be a unit vector.
  	/// @param body_T_parent_ref transform matrix from parent to body reference
  	/// frame for q=0.
  	///		This is the matrix transforming a vector represented in the
  	/// parent's reference frame into one represented
  	///		in this body's reference frame.
  	///		ie, if parent_vec is a vector in R^3 whose components are w.r.t to
  	/// the parent's reference frame,
  	///		then the same vector written w.r.t. this body's frame (for q=0) is
  	/// given by
  	///		body_vec = parent_R_body_ref * parent_vec
  	/// @param user_ptr pointer to user data
  	/// @param user_int pointer to user integer
  	/// @return 0 on success, -1 on error
  	int addBody(int body_index, int parent_index, JointType joint_type,
  				const vec3& parent_r_parent_body_ref, const mat33& body_T_parent_ref,
  				const vec3& body_axis_of_motion, idScalar mass, const vec3& body_r_body_com,
  				const mat33& body_I_body, const int user_int, void* user_ptr);
  	/// set policy for invalid mass properties
  	/// @param flag if true, invalid mass properties are accepted,
  	///		the default is false
  	void setAcceptInvalidMassParameters(bool flag);
  	/// @return the mass properties policy flag
  	bool getAcceptInvalidMassProperties() const;
  	/// build internal data structures
  	/// call this after all bodies have been added via addBody
  	/// @return 0 on success, -1 on error
  	int finalize();
  	/// pretty print ascii description of tree to stdout
  	void printTree();
  	/// print tree data to stdout
  	void printTreeData();
  	/// Calculate joint forces for given generalized state & derivatives.
          /// This also updates kinematic terms computed in calculateKinematics.
          /// If gravity is not set to zero, acceleration terms will contain
          /// gravitational acceleration.
  	/// @param q generalized coordinates
  	/// @param u generalized velocities. In the general case, u=T(q)*dot(q) and dim(q)>=dim(u)
  	/// @param dot_u time derivative of u
  	/// @param joint_forces this is where the resulting joint forces will be
  	///		stored. dim(joint_forces) = dim(u)
  	/// @return 0 on success, -1 on error
  	int calculateInverseDynamics(const vecx& q, const vecx& u, const vecx& dot_u,
  								 vecx* joint_forces);
  	/// Calculate joint space mass matrix
  	/// @param q generalized coordinates
  	/// @param initialize_matrix if true, initialize mass matrix with zero.
  	///		If mass_matrix is initialized to zero externally and only used
  	///		for mass matrix computations for the same system, it is safe to
  	///		set this to false.
  	/// @param set_lower_triangular_matrix if true, the lower triangular section of mass_matrix
  	///		is also populated, otherwise not.
  	/// @param mass_matrix matrix for storing the output (should be dim(q)xdim(q))
  	/// @return -1 on error, 0 on success
  	int calculateMassMatrix(const vecx& q, const bool update_kinematics,
  							const bool initialize_matrix, const bool set_lower_triangular_matrix,
  							matxx* mass_matrix);
  
  	/// Calculate joint space mass matrix.
  	/// This version will update kinematics, initialize all mass_matrix elements to zero and
  	/// populate all mass matrix entries.
  	/// @param q generalized coordinates
  	/// @param mass_matrix matrix for storing the output (should be dim(q)xdim(q))
  	/// @return -1 on error, 0 on success
  	int calculateMassMatrix(const vecx& q, matxx* mass_matrix);
  
  
          /// Calculates kinematics also calculated in calculateInverseDynamics,
          /// but not dynamics.
          /// This function ensures that correct accelerations are computed that do not
          /// contain gravitational acceleration terms.
          /// Does not calculate Jacobians, but only vector quantities (positions, velocities & accelerations)
          int calculateKinematics(const vecx& q, const vecx& u, const vecx& dot_u);
          /// Calculate position kinematics
          int calculatePositionKinematics(const vecx& q);
           /// Calculate position and velocity kinematics
          int calculatePositionAndVelocityKinematics(const vecx& q, const vecx& u);
  
  #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS)
          /// Calculate Jacobians (dvel/du), as well as velocity-dependent accelearation components
          /// d(Jacobian)/dt*u
          /// This function assumes that calculateInverseDynamics was called, or calculateKinematics,
          /// or calculatePositionAndVelocityKinematics
          int calculateJacobians(const vecx& q, const vecx& u);
          /// Calculate Jacobians (dvel/du)
          /// This function assumes that calculateInverseDynamics was called, or
          /// one of the calculateKineamtics functions
          int calculateJacobians(const vecx& q);
  #endif // BT_ID_HAVE_MAT3X
  
  
  	/// set gravitational acceleration
  	/// the default is [0;0;-9.8] in the world frame
  	/// @param gravity the gravitational acceleration in world frame
  	/// @return 0 on success, -1 on error
  	int setGravityInWorldFrame(const vec3& gravity);
  	/// returns number of bodies in tree
  	int numBodies() const;
  	/// returns number of mechanical degrees of freedom (dimension of q-vector)
  	int numDoFs() const;
  	/// get origin of a body-fixed frame, represented in world frame
  	/// @param body_index index for frame/body
  	/// @param world_origin pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyOrigin(const int body_index, vec3* world_origin) const;
  	/// get center of mass of a body, represented in world frame
  	/// @param body_index index for frame/body
  	/// @param world_com pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyCoM(const int body_index, vec3* world_com) const;
  	/// get transform from of a body-fixed frame to the world frame
  	/// @param body_index index for frame/body
  	/// @param world_T_body pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyTransform(const int body_index, mat33* world_T_body) const;
  	/// get absolute angular velocity for a body, represented in the world frame
  	/// @param body_index index for frame/body
  	/// @param world_omega pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyAngularVelocity(const int body_index, vec3* world_omega) const;
  	/// get linear velocity of a body, represented in world frame
  	/// @param body_index index for frame/body
  	/// @param world_velocity pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyLinearVelocity(const int body_index, vec3* world_velocity) const;
  	/// get linear velocity of a body's CoM, represented in world frame
  	/// (not required for inverse dynamics, provided for convenience)
  	/// @param body_index index for frame/body
  	/// @param world_vel_com pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyLinearVelocityCoM(const int body_index, vec3* world_velocity) const;
  	/// get origin of a body-fixed frame, represented in world frame
  	/// @param body_index index for frame/body
  	/// @param world_origin pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyAngularAcceleration(const int body_index, vec3* world_dot_omega) const;
  	/// get origin of a body-fixed frame, represented in world frame
  	/// NOTE: this will include the gravitational acceleration, so the actual acceleration is
  	/// obtainened by setting gravitational acceleration to zero, or subtracting it.
  	/// @param body_index index for frame/body
  	/// @param world_origin pointer for return data
  	/// @return 0 on success, -1 on error
  	int getBodyLinearAcceleration(const int body_index, vec3* world_acceleration) const;
  
  #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS)
          // get translational jacobian, in world frame (dworld_velocity/du)
          int getBodyJacobianTrans(const int body_index, mat3x* world_jac_trans) const;
          // get rotational jacobian, in world frame (dworld_omega/du)
          int getBodyJacobianRot(const int body_index, mat3x* world_jac_rot) const;
          // get product of translational jacobian derivative * generatlized velocities
          int getBodyDotJacobianTransU(const int body_index, vec3* world_dot_jac_trans_u) const;
          // get product of rotational jacobian derivative * generatlized velocities
          int getBodyDotJacobianRotU(const int body_index, vec3* world_dot_jac_rot_u) const;
  #endif // BT_ID_HAVE_MAT3X
  
  	/// returns the (internal) index of body
  	/// @param body_index is the index of a body
  	/// @param parent_index pointer to where parent index will be stored
  	/// @return 0 on success, -1 on error
  	int getParentIndex(const int body_index, int* parent_index) const;
  	/// get joint type
  	/// @param body_index index of the body
  	/// @param joint_type the corresponding joint type
  	/// @return 0 on success, -1 on failure
  	int getJointType(const int body_index, JointType* joint_type) const;
  	/// get joint type as string
  	/// @param body_index index of the body
  	/// @param joint_type string naming the corresponding joint type
  	/// @return 0 on success, -1 on failure
  	int getJointTypeStr(const int body_index, const char** joint_type) const;
      	/// get offset translation to parent body (see addBody)
  	/// @param body_index index of the body
  	/// @param r the offset translation (see above)
  	/// @return 0 on success, -1 on failure
          int getParentRParentBodyRef(const int body_index, vec3* r) const;
  	/// get offset rotation to parent body (see addBody)
  	/// @param body_index index of the body
  	/// @param T the transform (see above)
  	/// @return 0 on success, -1 on failure
          int getBodyTParentRef(const int body_index, mat33* T) const;
  	/// get axis of motion (see addBody)
  	/// @param body_index index of the body
  	/// @param axis the axis (see above)
  	/// @return 0 on success, -1 on failure
          int getBodyAxisOfMotion(const int body_index, vec3* axis) const;
  	/// get offset for degrees of freedom of this body into the q-vector
  	/// @param body_index index of the body
  	/// @param q_offset offset the q vector
  	/// @return -1 on error, 0 on success
  	int getDoFOffset(const int body_index, int* q_offset) const;
  	/// get user integer. not used by the library.
  	/// @param body_index index of the body
  	/// @param user_int   the user integer
  	/// @return 0 on success, -1 on error
  	int getUserInt(const int body_index, int* user_int) const;
  	/// get user pointer. not used by the library.
  	/// @param body_index index of the body
  	/// @param user_ptr   the user pointer
  	/// @return 0 on success, -1 on error
  	int getUserPtr(const int body_index, void** user_ptr) const;
  	/// set user integer. not used by the library.
  	/// @param body_index index of the body
  	/// @param user_int   the user integer
  	/// @return 0 on success, -1 on error
  	int setUserInt(const int body_index, const int user_int);
  	/// set user pointer. not used by the library.
  	/// @param body_index index of the body
  	/// @param user_ptr   the user pointer
  	/// @return 0 on success, -1 on error
  	int setUserPtr(const int body_index, void* const user_ptr);
  	/// set mass for a body
  	/// @param body_index index of the body
  	/// @param mass the mass to set
  	/// @return 0 on success, -1 on failure
  	int setBodyMass(const int body_index, const idScalar mass);
  	/// set first moment of mass for a body
  	/// (mass * center of mass, in body fixed frame, relative to joint)
  	/// @param body_index index of the body
  	/// @param first_mass_moment the vector to set
  	/// @return 0 on success, -1 on failure
  	int setBodyFirstMassMoment(const int body_index, const vec3& first_mass_moment);
  	/// set second moment of mass for a body
  	/// (moment of inertia, in body fixed frame, relative to joint)
  	/// @param body_index index of the body
  	/// @param second_mass_moment the inertia matrix
  	/// @return 0 on success, -1 on failure
  	int setBodySecondMassMoment(const int body_index, const mat33& second_mass_moment);
  	/// get mass for a body
  	/// @param body_index index of the body
  	/// @param mass the mass
  	/// @return 0 on success, -1 on failure
  	int getBodyMass(const int body_index, idScalar* mass) const;
  	/// get first moment of mass for a body
  	/// (mass * center of mass, in body fixed frame, relative to joint)
  	/// @param body_index index of the body
  	/// @param first_moment the vector
  	/// @return 0 on success, -1 on failure
  	int getBodyFirstMassMoment(const int body_index, vec3* first_mass_moment) const;
  	/// get second moment of mass for a body
  	/// (moment of inertia, in body fixed frame, relative to joint)
  	/// @param body_index index of the body
  	/// @param second_mass_moment the inertia matrix
  	/// @return 0 on success, -1 on failure
  	int getBodySecondMassMoment(const int body_index, mat33* second_mass_moment) const;
  	/// set all user forces and moments to zero
  	void clearAllUserForcesAndMoments();
  	/// Add an external force to a body, acting at the origin of the body-fixed frame.
  	/// Calls to addUserForce are cumulative. Set the user force and moment to zero
  	/// via clearAllUserForcesAndMoments()
  	/// @param body_force the force represented in the body-fixed frame of reference
  	/// @return 0 on success, -1 on error
  	int addUserForce(const int body_index, const vec3& body_force);
  	/// Add an external moment to a body.
  	/// Calls to addUserMoment are cumulative. Set the user force and moment to zero
  	/// via clearAllUserForcesAndMoments()
  	/// @param body_moment the moment represented in the body-fixed frame of reference
  	/// @return 0 on success, -1 on error
  	int addUserMoment(const int body_index, const vec3& body_moment);
  
  private:
  	// flag indicating if system has been initialized
  	bool m_is_finalized;
  	// flag indicating if mass properties are physically valid
  	bool m_mass_parameters_are_valid;
  	// flag defining if unphysical mass parameters are accepted
  	bool m_accept_invalid_mass_parameters;
  	// This struct implements the inverse dynamics calculations
  	class MultiBodyImpl;
  	MultiBodyImpl* m_impl;
  	// cache data structure for initialization
  	class InitCache;
  	InitCache* m_init_cache;
  };
  }  // namespace btInverseDynamics
  #endif  // MULTIBODYTREE_HPP_
  