/*************************************************************************** frames.hpp `- description ------------------------- begin : June 2006 copyright : (C) 2006 Erwin Aertbelien email : firstname.lastname@mech.kuleuven.be History (only major changes)( AUTHOR-Description ) : *************************************************************************** * This library is free software; you can redistribute it and/or * * modify it under the terms of the GNU Lesser General Public * * License as published by the Free Software Foundation; either * * version 2.1 of the License, or (at your option) any later version. * * * * This library is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * * Lesser General Public License for more details. * * * * You should have received a copy of the GNU Lesser General Public * * License along with this library; if not, write to the Free Software * * Foundation, Inc., 59 Temple Place, * * Suite 330, Boston, MA 02111-1307 USA * * * ***************************************************************************/ /** * \file * \warning * Efficienty can be improved by writing p2 = A*(B*(C*p1))) instead of * p2=A*B*C*p1 * * \par PROPOSED NAMING CONVENTION FOR FRAME-like OBJECTS * * \verbatim * A naming convention of objects of the type defined in this file : * (1) Frame : F... * Rotation : R ... * (2) Twist : T ... * Wrench : W ... * Vector : V ... * This prefix is followed by : * for category (1) : * F_A_B : w.r.t. frame A, frame B expressed * ( each column of F_A_B corresponds to an axis of B, * expressed w.r.t. frame A ) * in mathematical convention : * A * F_A_B == F * B * * for category (2) : * V_B : a vector expressed w.r.t. frame B * * This can also be prepended by a name : * e.g. : temporaryV_B * * With this convention one can write : * * F_A_B = F_B_A.Inverse(); * F_A_C = F_A_B * F_B_C; * V_B = F_B_C * V_C; // both translation and rotation * V_B = R_B_C * V_C; // only rotation * \endverbatim * * \par CONVENTIONS FOR WHEN USED WITH ROBOTS : * * \verbatim * world : represents the frame ([1 0 0,0 1 0,0 0 1],[0 0 0]') * mp : represents mounting plate of a robot * (i.e. everything before MP is constructed by robot manufacturer * everything after MP is tool ) * tf : represents task frame of a robot * (i.e. frame in which motion and force control is expressed) * sf : represents sensor frame of a robot * (i.e. frame at which the forces measured by the force sensor * are expressed ) * * Frame F_world_mp=...; * Frame F_mp_sf(..) * Frame F_mp_tf(,.) * * Wrench are measured in sensor frame SF, so one could write : * Wrench_tf = F_mp_tf.Inverse()* ( F_mp_sf * Wrench_sf ); * \endverbatim * * \par CONVENTIONS REGARDING UNITS : * Any consistent series of units can be used, e.g. N,mm,Nmm,..mm/sec * * \par Twist and Wrench transformations * 3 different types of transformations do exist for the twists * and wrenches. * * \verbatim * 1) Frame * Twist or Frame * Wrench : * this transforms both the velocity/force reference point * and the basis to which the twist/wrench are expressed. * 2) Rotation * Twist or Rotation * Wrench : * this transforms the basis to which the twist/wrench are * expressed, but leaves the reference point intact. * 3) Twist.RefPoint(v_base_AB) or Wrench.RefPoint(v_base_AB) * this transforms only the reference point. v is expressed * in the same base as the twist/wrench and points from the * old reference point to the new reference point. * \endverbatim * * \par Complexity * Sometimes the amount of work is given in the documentation * e.g. 6M+3A means 6 multiplications and 3 additions. * * \author * Erwin Aertbelien, Div. PMA, Dep. of Mech. Eng., K.U.Leuven * ****************************************************************************/ #ifndef KDL_FRAMES_H #define KDL_FRAMES_H #include "utilities/kdl-config.h" #include "utilities/utility.h" ///////////////////////////////////////////////////////////// namespace KDL { class Vector; class Rotation; class Frame; class Wrench; class Twist; class Vector2; class Rotation2; class Frame2; /** * \brief A concrete implementation of a 3 dimensional vector class */ class Vector { public: double data[3]; //! Does not initialise the Vector to zero. use Vector::Zero() or SetToZero for that inline Vector() {data[0]=data[1]=data[2] = 0.0;} //! Constructs a vector out of the three values x, y and z inline Vector(double x,double y, double z); //! Constructs a vector out of an array of three values x, y and z inline Vector(double* xyz); //! Constructs a vector out of an array of three values x, y and z inline Vector(float* xyz); //! Assignment operator. The normal copy by value semantics. inline Vector(const Vector& arg); //! store vector components in array inline void GetValue(double* xyz) const; //! Assignment operator. The normal copy by value semantics. inline Vector& operator = ( const Vector& arg); //! Access to elements, range checked when NDEBUG is not set, from 0..2 inline double operator()(int index) const; //! Access to elements, range checked when NDEBUG is not set, from 0..2 inline double& operator() (int index); //! Equivalent to double operator()(int index) const double operator[] ( int index ) const { return this->operator() ( index ); } //! Equivalent to double& operator()(int index) double& operator[] ( int index ) { return this->operator() ( index ); } inline double x() const; inline double y() const; inline double z() const; inline void x(double); inline void y(double); inline void z(double); //! Reverses the sign of the Vector object itself inline void ReverseSign(); //! subtracts a vector from the Vector object itself inline Vector& operator-=(const Vector& arg); //! Adds a vector from the Vector object itself inline Vector& operator +=(const Vector& arg); //! Scalar multiplication is defined inline friend Vector operator*(const Vector& lhs,double rhs); //! Scalar multiplication is defined inline friend Vector operator*(double lhs,const Vector& rhs); //! Scalar division is defined inline friend Vector operator/(const Vector& lhs,double rhs); inline friend Vector operator+(const Vector& lhs,const Vector& rhs); inline friend Vector operator-(const Vector& lhs,const Vector& rhs); inline friend Vector operator*(const Vector& lhs,const Vector& rhs); inline friend Vector operator-(const Vector& arg); inline friend double dot(const Vector& lhs,const Vector& rhs); //! To have a uniform operator to put an element to zero, for scalar values //! and for objects. inline friend void SetToZero(Vector& v); //! @return a zero vector inline static Vector Zero(); /** Normalizes this vector and returns it norm * makes v a unitvector and returns the norm of v. * if v is smaller than eps, Vector(1,0,0) is returned with norm 0. * if this is not good, check the return value of this method. */ double Normalize(double eps=epsilon); //! @return the norm of the vector double Norm() const; //! a 3D vector where the 2D vector v is put in the XY plane inline void Set2DXY(const Vector2& v); //! a 3D vector where the 2D vector v is put in the YZ plane inline void Set2DYZ(const Vector2& v); //! a 3D vector where the 2D vector v is put in the ZX plane inline void Set2DZX(const Vector2& v); //! a 3D vector where the 2D vector v_XY is put in the XY plane of the frame F_someframe_XY. inline void Set2DPlane(const Frame& F_someframe_XY,const Vector2& v_XY); //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const Vector& a,const Vector& b,double eps=epsilon); //! return a normalized vector inline friend Vector Normalize(const Vector& a, double eps=epsilon); //! The literal equality operator==(), also identical. inline friend bool operator==(const Vector& a,const Vector& b); //! The literal inequality operator!=(). inline friend bool operator!=(const Vector& a,const Vector& b); friend class Rotation; friend class Frame; }; /** \brief represents rotations in 3 dimensional space. This class represents a rotation matrix with the following conventions : \verbatim Suppose V2 = R*V, (1) V is expressed in frame B V2 is expressed in frame A This matrix R consists of 3 collumns [ X,Y,Z ], X,Y, and Z contain the axes of frame B, expressed in frame A Because of linearity expr(1) is valid. \endverbatim This class only represents rotational_interpolation, not translation Two interpretations are possible for rotation angles. * if you rotate with angle around X frame A to have frame B, then the result of SetRotX is equal to frame B expressed wrt A. In code: \verbatim Rotation R; F_A_B = R.SetRotX(angle); \endverbatim * Secondly, if you take the following code : \verbatim Vector p,p2; Rotation R; R.SetRotX(angle); p2 = R*p; \endverbatim then the frame p2 is rotated around X axis with (-angle). Analogue reasonings can be applyd to SetRotY,SetRotZ,SetRot \par type Concrete implementation */ class Rotation { public: double data[9]; inline Rotation() { *this = Rotation::Identity(); } inline Rotation(double Xx,double Yx,double Zx, double Xy,double Yy,double Zy, double Xz,double Yz,double Zz); inline Rotation(const Vector& x,const Vector& y,const Vector& z); // default copy constructor is sufficient inline void setValue(float* oglmat); inline void getValue(float* oglmat) const; inline Rotation& operator=(const Rotation& arg); //! Defines a multiplication R*V between a Rotation R and a Vector V. //! Complexity : 9M+6A inline Vector operator*(const Vector& v) const; //! Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set inline double& operator()(int i,int j); //! Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set inline double operator() (int i,int j) const; friend Rotation operator *(const Rotation& lhs,const Rotation& rhs); //! Sets the value of *this to its inverse. inline void SetInverse(); //! Gives back the inverse rotation matrix of *this. inline Rotation Inverse() const; //! The same as R.Inverse()*v but more efficient. inline Vector Inverse(const Vector& v) const; //! The same as R.Inverse()*arg but more efficient. inline Wrench Inverse(const Wrench& arg) const; //! The same as R.Inverse()*arg but more efficient. inline Twist Inverse(const Twist& arg) const; //! Gives back an identity rotaton matrix inline static Rotation Identity(); // = Rotations //! The Rot... static functions give the value of the appropriate rotation matrix back. inline static Rotation RotX(double angle); //! The Rot... static functions give the value of the appropriate rotation matrix back. inline static Rotation RotY(double angle); //! The Rot... static functions give the value of the appropriate rotation matrix back. inline static Rotation RotZ(double angle); //! The DoRot... functions apply a rotation R to *this,such that *this = *this * Rot.. //! DoRot... functions are only defined when they can be executed more efficiently inline void DoRotX(double angle); //! The DoRot... functions apply a rotation R to *this,such that *this = *this * Rot.. //! DoRot... functions are only defined when they can be executed more efficiently inline void DoRotY(double angle); //! The DoRot... functions apply a rotation R to *this,such that *this = *this * Rot.. //! DoRot... functions are only defined when they can be executed more efficiently inline void DoRotZ(double angle); //! Along an arbitrary axes. It is not necessary to normalize rotaxis. //! returns identity rotation matrix in the case that the norm of rotaxis //! is to small to be used. // @see Rot2 if you want to handle this error in another way. static Rotation Rot(const Vector& rotaxis,double angle); //! Along an arbitrary axes. rotvec should be normalized. static Rotation Rot2(const Vector& rotvec,double angle); // make sure the matrix is a pure rotation (no scaling) void Ortho(); //! Returns a vector with the direction of the equiv. axis //! and its norm is angle Vector GetRot() const; //! Returns a 2D vector representing the equivalent rotation in the XZ plane that brings the //! Y axis onto the Matrix Y axis and its norm is angle Vector2 GetXZRot() const; /** Returns the rotation angle around the equiv. axis * @param axis the rotation axis is returned in this variable * @param eps : in the case of angle == 0 : rot axis is undefined and choosen * to be +/- Z-axis * in the case of angle == PI : 2 solutions, positive Z-component * of the axis is choosen. * @result returns the rotation angle (between [0..PI] ) */ double GetRotAngle(Vector& axis,double eps=epsilon) const; //! Gives back a rotation matrix specified with EulerZYZ convention : //! First rotate around Z with alfa, //! then around the new Y with beta, then around //! new Z with gamma. static Rotation EulerZYZ(double Alfa,double Beta,double Gamma); //! Gives back the EulerZYZ convention description of the rotation matrix : //! First rotate around Z with alfa, //! then around the new Y with beta, then around //! new Z with gamma. //! //! Variables are bound by //! (-PI <= alfa <= PI), //! (0 <= beta <= PI), //! (-PI <= alfa <= PI) void GetEulerZYZ(double& alfa,double& beta,double& gamma) const; //! Sets the value of this object to a rotation specified with RPY convention: //! first rotate around X with roll, then around the //! old Y with pitch, then around old Z with alfa static Rotation RPY(double roll,double pitch,double yaw); //! Gives back a vector in RPY coordinates, variables are bound by //! -PI <= roll <= PI //! -PI <= Yaw <= PI //! -PI/2 <= PITCH <= PI/2 //! //! convention : first rotate around X with roll, then around the //! old Y with pitch, then around old Z with alfa void GetRPY(double& roll,double& pitch,double& yaw) const; //! Gives back a rotation matrix specified with EulerZYX convention : //! First rotate around Z with alfa, //! then around the new Y with beta, then around //! new X with gamma. //! //! closely related to RPY-convention inline static Rotation EulerZYX(double Alfa,double Beta,double Gamma) { return RPY(Gamma,Beta,Alfa); } //! GetEulerZYX gets the euler ZYX parameters of a rotation : //! First rotate around Z with alfa, //! then around the new Y with beta, then around //! new X with gamma. //! //! Range of the results of GetEulerZYX : //! -PI <= alfa <= PI //! -PI <= gamma <= PI //! -PI/2 <= beta <= PI/2 //! //! Closely related to RPY-convention. inline void GetEulerZYX(double& Alfa,double& Beta,double& Gamma) const { GetRPY(Gamma,Beta,Alfa); } //! Transformation of the base to which the twist is expressed. //! Complexity : 18M+12A //! @see Frame*Twist for a transformation that also transforms //! the velocity reference point. inline Twist operator * (const Twist& arg) const; //! Transformation of the base to which the wrench is expressed. //! Complexity : 18M+12A //! @see Frame*Wrench for a transformation that also transforms //! the force reference point. inline Wrench operator * (const Wrench& arg) const; //! Access to the underlying unitvectors of the rotation matrix inline Vector UnitX() const { return Vector(data[0],data[3],data[6]); } //! Access to the underlying unitvectors of the rotation matrix inline void UnitX(const Vector& X) { data[0] = X(0); data[3] = X(1); data[6] = X(2); } //! Access to the underlying unitvectors of the rotation matrix inline Vector UnitY() const { return Vector(data[1],data[4],data[7]); } //! Access to the underlying unitvectors of the rotation matrix inline void UnitY(const Vector& X) { data[1] = X(0); data[4] = X(1); data[7] = X(2); } //! Access to the underlying unitvectors of the rotation matrix inline Vector UnitZ() const { return Vector(data[2],data[5],data[8]); } //! Access to the underlying unitvectors of the rotation matrix inline void UnitZ(const Vector& X) { data[2] = X(0); data[5] = X(1); data[8] = X(2); } //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval friend bool Equal(const Rotation& a,const Rotation& b,double eps=epsilon); //! The literal equality operator==(), also identical. friend bool operator==(const Rotation& a,const Rotation& b); //! The literal inequality operator!=() friend bool operator!=(const Rotation& a,const Rotation& b); friend class Frame; }; bool operator==(const Rotation& a,const Rotation& b); /** \brief represents a frame transformation in 3D space (rotation + translation) if V2 = Frame*V1 (V2 expressed in frame A, V1 expressed in frame B) then V2 = Frame.M*V1+Frame.p Frame.M contains columns that represent the axes of frame B wrt frame A Frame.p contains the origin of frame B expressed in frame A. */ class Frame { public: Vector p; //!< origine of the Frame Rotation M; //!< Orientation of the Frame public: inline Frame(const Rotation& R,const Vector& V); //! The rotation matrix defaults to identity explicit inline Frame(const Vector& V); //! The position matrix defaults to zero explicit inline Frame(const Rotation& R); inline void setValue(float* oglmat); inline void getValue(float* oglmat) const; inline Frame() {} //! The copy constructor. Normal copy by value semantics. inline Frame(const Frame& arg); //! Reads data from an double array //\TODO should be formulated as a constructor void Make4x4(double* d); //! Treats a frame as a 4x4 matrix and returns element i,j //! Access to elements 0..3,0..3, bounds are checked when NDEBUG is not set inline double operator()(int i,int j); //! Treats a frame as a 4x4 matrix and returns element i,j //! Access to elements 0..3,0..3, bounds are checked when NDEBUG is not set inline double operator() (int i,int j) const; // = Inverse //! Gives back inverse transformation of a Frame inline Frame Inverse() const; //! The same as p2=R.Inverse()*p but more efficient. inline Vector Inverse(const Vector& arg) const; //! The same as p2=R.Inverse()*p but more efficient. inline Wrench Inverse(const Wrench& arg) const; //! The same as p2=R.Inverse()*p but more efficient. inline Twist Inverse(const Twist& arg) const; //! Normal copy-by-value semantics. inline Frame& operator = (const Frame& arg); //! Transformation of the base to which the vector //! is expressed. inline Vector operator * (const Vector& arg) const; //! Transformation of both the force reference point //! and of the base to which the wrench is expressed. //! look at Rotation*Wrench operator for a transformation //! of only the base to which the twist is expressed. //! //! Complexity : 24M+18A inline Wrench operator * (const Wrench& arg) const; //! Transformation of both the velocity reference point //! and of the base to which the twist is expressed. //! look at Rotation*Twist for a transformation of only the //! base to which the twist is expressed. //! //! Complexity : 24M+18A inline Twist operator * (const Twist& arg) const; //! Composition of two frames. inline friend Frame operator *(const Frame& lhs,const Frame& rhs); //! @return the identity transformation Frame(Rotation::Identity(),Vector::Zero()). inline static Frame Identity(); //! The twist is expressed wrt the current //! frame. This frame is integrated into an updated frame with //! . Very simple first order integration rule. inline void Integrate(const Twist& t_this,double frequency); /* // DH_Craig1989 : constructs a transformationmatrix // T_link(i-1)_link(i) with the Denavit-Hartenberg convention as // described in the Craigs book: Craig, J. J.,Introduction to // Robotics: Mechanics and Control, Addison-Wesley, // isbn:0-201-10326-5, 1986. // // Note that the frame is a redundant way to express the information // in the DH-convention. // \verbatim // Parameters in full : a(i-1),alpha(i-1),d(i),theta(i) // // axis i-1 is connected by link i-1 to axis i numbering axis 1 // to axis n link 0 (immobile base) to link n // // link length a(i-1) length of the mutual perpendicular line // (normal) between the 2 axes. This normal runs from (i-1) to // (i) axis. // // link twist alpha(i-1): construct plane perpendicular to the // normal project axis(i-1) and axis(i) into plane angle from // (i-1) to (i) measured in the direction of the normal // // link offset d(i) signed distance between normal (i-1) to (i) // and normal (i) to (i+1) along axis i joint angle theta(i) // signed angle between normal (i-1) to (i) and normal (i) to // (i+1) along axis i // // First and last joints : a(0)= a(n) = 0 // alpha(0) = alpha(n) = 0 // // PRISMATIC : theta(1) = 0 d(1) arbitrarily // // REVOLUTE : theta(1) arbitrarily d(1) = 0 // // Not unique : if intersecting joint axis 2 choices for normal // Frame assignment of the DH convention : Z(i-1) follows axis // (i-1) X(i-1) is the normal between axis(i-1) and axis(i) // Y(i-1) follows out of Z(i-1) and X(i-1) // // a(i-1) = distance from Z(i-1) to Z(i) along X(i-1) // alpha(i-1) = angle between Z(i-1) to Z(i) along X(i-1) // d(i) = distance from X(i-1) to X(i) along Z(i) // theta(i) = angle between X(i-1) to X(i) along X(i) // \endverbatim */ static Frame DH_Craig1989(double a,double alpha,double d,double theta); // DH : constructs a transformationmatrix T_link(i-1)_link(i) with // the Denavit-Hartenberg convention as described in the original // publictation: Denavit, J. and Hartenberg, R. S., A kinematic // notation for lower-pair mechanisms based on matrices, ASME // Journal of Applied Mechanics, 23:215-221, 1955. static Frame DH(double a,double alpha,double d,double theta); //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const Frame& a,const Frame& b,double eps=epsilon); //! The literal equality operator==(), also identical. inline friend bool operator==(const Frame& a,const Frame& b); //! The literal inequality operator!=(). inline friend bool operator!=(const Frame& a,const Frame& b); }; /** * \brief represents both translational and rotational velocities. * * This class represents a twist. A twist is the combination of translational * velocity and rotational velocity applied at one point. */ class Twist { public: Vector vel; //!< The velocity of that point Vector rot; //!< The rotational velocity of that point. public: //! The default constructor initialises to Zero via the constructor of Vector. Twist():vel(),rot() {}; Twist(const Vector& _vel,const Vector& _rot):vel(_vel),rot(_rot) {}; inline Twist& operator-=(const Twist& arg); inline Twist& operator+=(const Twist& arg); //! index-based access to components, first vel(0..2), then rot(3..5) inline double& operator()(int i); //! index-based access to components, first vel(0..2), then rot(3..5) //! For use with a const Twist inline double operator()(int i) const; double operator[] ( int index ) const { return this->operator() ( index ); } double& operator[] ( int index ) { return this->operator() ( index ); } inline friend Twist operator*(const Twist& lhs,double rhs); inline friend Twist operator*(double lhs,const Twist& rhs); inline friend Twist operator/(const Twist& lhs,double rhs); inline friend Twist operator+(const Twist& lhs,const Twist& rhs); inline friend Twist operator-(const Twist& lhs,const Twist& rhs); inline friend Twist operator-(const Twist& arg); inline friend double dot(const Twist& lhs,const Wrench& rhs); inline friend double dot(const Wrench& rhs,const Twist& lhs); inline friend void SetToZero(Twist& v); //! @return a zero Twist : Twist(Vector::Zero(),Vector::Zero()) static inline Twist Zero(); //! Reverses the sign of the twist inline void ReverseSign(); //! Changes the reference point of the twist. //! The vector v_base_AB is expressed in the same base as the twist //! The vector v_base_AB is a vector from the old point to //! the new point. //! //! Complexity : 6M+6A inline Twist RefPoint(const Vector& v_base_AB) const; //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const Twist& a,const Twist& b,double eps=epsilon); //! The literal equality operator==(), also identical. inline friend bool operator==(const Twist& a,const Twist& b); //! The literal inequality operator!=(). inline friend bool operator!=(const Twist& a,const Twist& b); // = Friends friend class Rotation; friend class Frame; }; /** * \brief represents both translational and rotational acceleration. * * This class represents an acceleration twist. A acceleration twist is * the combination of translational * acceleration and rotational acceleration applied at one point. */ /* class AccelerationTwist { public: Vector trans; //!< The translational acceleration of that point Vector rot; //!< The rotational acceleration of that point. public: //! The default constructor initialises to Zero via the constructor of Vector. AccelerationTwist():trans(),rot() {}; AccelerationTwist(const Vector& _trans,const Vector& _rot):trans(_trans),rot(_rot) {}; inline AccelerationTwist& operator-=(const AccelerationTwist& arg); inline AccelerationTwist& operator+=(const AccelerationTwist& arg); //! index-based access to components, first vel(0..2), then rot(3..5) inline double& operator()(int i); //! index-based access to components, first vel(0..2), then rot(3..5) //! For use with a const AccelerationTwist inline double operator()(int i) const; double operator[] ( int index ) const { return this->operator() ( index ); } double& operator[] ( int index ) { return this->operator() ( index ); } inline friend AccelerationTwist operator*(const AccelerationTwist& lhs,double rhs); inline friend AccelerationTwist operator*(double lhs,const AccelerationTwist& rhs); inline friend AccelerationTwist operator/(const AccelerationTwist& lhs,double rhs); inline friend AccelerationTwist operator+(const AccelerationTwist& lhs,const AccelerationTwist& rhs); inline friend AccelerationTwist operator-(const AccelerationTwist& lhs,const AccelerationTwist& rhs); inline friend AccelerationTwist operator-(const AccelerationTwist& arg); //inline friend double dot(const AccelerationTwist& lhs,const Wrench& rhs); //inline friend double dot(const Wrench& rhs,const AccelerationTwist& lhs); inline friend void SetToZero(AccelerationTwist& v); //! @return a zero AccelerationTwist : AccelerationTwist(Vector::Zero(),Vector::Zero()) static inline AccelerationTwist Zero(); //! Reverses the sign of the AccelerationTwist inline void ReverseSign(); //! Changes the reference point of the AccelerationTwist. //! The vector v_base_AB is expressed in the same base as the AccelerationTwist //! The vector v_base_AB is a vector from the old point to //! the new point. //! //! Complexity : 6M+6A inline AccelerationTwist RefPoint(const Vector& v_base_AB) const; //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const AccelerationTwist& a,const AccelerationTwist& b,double eps=epsilon); //! The literal equality operator==(), also identical. inline friend bool operator==(const AccelerationTwist& a,const AccelerationTwist& b); //! The literal inequality operator!=(). inline friend bool operator!=(const AccelerationTwist& a,const AccelerationTwist& b); // = Friends friend class Rotation; friend class Frame; }; */ /** * \brief represents the combination of a force and a torque. * * This class represents a Wrench. A Wrench is the force and torque applied at a point */ class Wrench { public: Vector force; //!< Force that is applied at the origin of the current ref frame Vector torque; //!< Torque that is applied at the origin of the current ref frame public: //! Does initialise force and torque to zero via the underlying constructor of Vector Wrench():force(),torque() {}; Wrench(const Vector& _force,const Vector& _torque):force(_force),torque(_torque) {}; // = Operators inline Wrench& operator-=(const Wrench& arg); inline Wrench& operator+=(const Wrench& arg); //! index-based access to components, first force(0..2), then torque(3..5) inline double& operator()(int i); //! index-based access to components, first force(0..2), then torque(3..5) //! for use with a const Wrench inline double operator()(int i) const; double operator[] ( int index ) const { return this->operator() ( index ); } double& operator[] ( int index ) { return this->operator() ( index ); } //! Scalar multiplication inline friend Wrench operator*(const Wrench& lhs,double rhs); //! Scalar multiplication inline friend Wrench operator*(double lhs,const Wrench& rhs); //! Scalar division inline friend Wrench operator/(const Wrench& lhs,double rhs); inline friend Wrench operator+(const Wrench& lhs,const Wrench& rhs); inline friend Wrench operator-(const Wrench& lhs,const Wrench& rhs); //! An unary - operator inline friend Wrench operator-(const Wrench& arg); //! Sets the Wrench to Zero, to have a uniform function that sets an object or //! double to zero. inline friend void SetToZero(Wrench& v); //! @return a zero Wrench static inline Wrench Zero(); //! Reverses the sign of the current Wrench inline void ReverseSign(); //! Changes the reference point of the wrench. //! The vector v_base_AB is expressed in the same base as the twist //! The vector v_base_AB is a vector from the old point to //! the new point. //! //! Complexity : 6M+6A inline Wrench RefPoint(const Vector& v_base_AB) const; //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const Wrench& a,const Wrench& b,double eps=epsilon); //! The literal equality operator==(), also identical. inline friend bool operator==(const Wrench& a,const Wrench& b); //! The literal inequality operator!=(). inline friend bool operator!=(const Wrench& a,const Wrench& b); friend class Rotation; friend class Frame; }; //! 2D version of Vector class Vector2 { double data[2]; public: //! Does not initialise to Zero(). Vector2() {data[0]=data[1] = 0.0;} inline Vector2(double x,double y); inline Vector2(const Vector2& arg); inline Vector2(double* xyz); inline Vector2(float* xyz); inline Vector2& operator = ( const Vector2& arg); //! Access to elements, range checked when NDEBUG is not set, from 0..1 inline double operator()(int index) const; //! Access to elements, range checked when NDEBUG is not set, from 0..1 inline double& operator() (int index); //! store vector components in array inline void GetValue(double* xy) const; inline void ReverseSign(); inline Vector2& operator-=(const Vector2& arg); inline Vector2& operator +=(const Vector2& arg); inline friend Vector2 operator*(const Vector2& lhs,double rhs); inline friend Vector2 operator*(double lhs,const Vector2& rhs); inline friend Vector2 operator/(const Vector2& lhs,double rhs); inline friend Vector2 operator+(const Vector2& lhs,const Vector2& rhs); inline friend Vector2 operator-(const Vector2& lhs,const Vector2& rhs); inline friend Vector2 operator*(const Vector2& lhs,const Vector2& rhs); inline friend Vector2 operator-(const Vector2& arg); inline friend void SetToZero(Vector2& v); //! @return a zero 2D vector. inline static Vector2 Zero(); /** Normalizes this vector and returns it norm * makes v a unitvector and returns the norm of v. * if v is smaller than eps, Vector(1,0,0) is returned with norm 0. * if this is not good, check the return value of this method. */ double Normalize(double eps=epsilon); //! @return the norm of the vector inline double Norm() const; //! projects v in its XY plane, and sets *this to these values inline void Set3DXY(const Vector& v); //! projects v in its YZ plane, and sets *this to these values inline void Set3DYZ(const Vector& v); //! projects v in its ZX plane, and sets *this to these values inline void Set3DZX(const Vector& v); //! projects v_someframe in the XY plane of F_someframe_XY, //! and sets *this to these values //! expressed wrt someframe. inline void Set3DPlane(const Frame& F_someframe_XY,const Vector& v_someframe); //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const Vector2& a,const Vector2& b,double eps=epsilon); friend class Rotation2; }; //! A 2D Rotation class, for conventions see Rotation. For further documentation //! of the methods see Rotation class. class Rotation2 { double s,c; //! c,s represent cos(angle), sin(angle), this also represents first col. of rot matrix //! from outside, this class behaves as if it would store the complete 2x2 matrix. public: //! Default constructor does NOT initialise to Zero(). Rotation2() {c=1.0;s=0.0;} explicit Rotation2(double angle_rad):s(sin(angle_rad)),c(cos(angle_rad)) {} Rotation2(double ca,double sa):s(sa),c(ca){} inline Rotation2& operator=(const Rotation2& arg); inline Vector2 operator*(const Vector2& v) const; //! Access to elements 0..1,0..1, bounds are checked when NDEBUG is not set inline double operator() (int i,int j) const; inline friend Rotation2 operator *(const Rotation2& lhs,const Rotation2& rhs); inline void SetInverse(); inline Rotation2 Inverse() const; inline Vector2 Inverse(const Vector2& v) const; inline void SetIdentity(); inline static Rotation2 Identity(); //! The SetRot.. functions set the value of *this to the appropriate rotation matrix. inline void SetRot(double angle); //! The Rot... static functions give the value of the appropriate rotation matrix bac inline static Rotation2 Rot(double angle); //! Gets the angle (in radians) inline double GetRot() const; //! do not use operator == because the definition of Equal(.,.) is slightly //! different. It compares whether the 2 arguments are equal in an eps-interval inline friend bool Equal(const Rotation2& a,const Rotation2& b,double eps=epsilon); }; //! A 2D frame class, for further documentation see the Frames class //! for methods with unchanged semantics. class Frame2 { public: Vector2 p; //!< origine of the Frame Rotation2 M; //!< Orientation of the Frame public: inline Frame2(const Rotation2& R,const Vector2& V); explicit inline Frame2(const Vector2& V); explicit inline Frame2(const Rotation2& R); inline Frame2(void); inline Frame2(const Frame2& arg); inline void Make4x4(double* d); //! Treats a frame as a 3x3 matrix and returns element i,j //! Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set inline double operator()(int i,int j); //! Treats a frame as a 4x4 matrix and returns element i,j //! Access to elements 0..3,0..3, bounds are checked when NDEBUG is not set inline double operator() (int i,int j) const; inline void SetInverse(); inline Frame2 Inverse() const; inline Vector2 Inverse(const Vector2& arg) const; inline Frame2& operator = (const Frame2& arg); inline Vector2 operator * (const Vector2& arg); inline friend Frame2 operator *(const Frame2& lhs,const Frame2& rhs); inline void SetIdentity(); inline void Integrate(const Twist& t_this,double frequency); inline static Frame2 Identity() { Frame2 tmp; tmp.SetIdentity(); return tmp; } inline friend bool Equal(const Frame2& a,const Frame2& b,double eps=epsilon); }; IMETHOD Vector diff(const Vector& a,const Vector& b,double dt=1); IMETHOD Vector diff(const Rotation& R_a_b1,const Rotation& R_a_b2,double dt=1); IMETHOD Twist diff(const Frame& F_a_b1,const Frame& F_a_b2,double dt=1); IMETHOD Twist diff(const Twist& a,const Twist& b,double dt=1); IMETHOD Wrench diff(const Wrench& W_a_p1,const Wrench& W_a_p2,double dt=1); IMETHOD Vector addDelta(const Vector& a,const Vector&da,double dt=1); IMETHOD Rotation addDelta(const Rotation& a,const Vector&da,double dt=1); IMETHOD Frame addDelta(const Frame& a,const Twist& da,double dt=1); IMETHOD Twist addDelta(const Twist& a,const Twist&da,double dt=1); IMETHOD Wrench addDelta(const Wrench& a,const Wrench&da,double dt=1); #ifdef KDL_INLINE // #include "vector.inl" // #include "wrench.inl" //#include "rotation.inl" //#include "frame.inl" //#include "twist.inl" //#include "vector2.inl" //#include "rotation2.inl" //#include "frame2.inl" #include "frames.inl" #endif } #endif