frames.hpp File Reference

#include "utilities/kdl-config.h"
#include "utilities/utility.h"
#include "frames.inl"

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Classes
class	KDL::Frame
	represents a frame transformation in 3D space (rotation + translation) More...
class	KDL::Frame2
class	KDL::Rotation
	represents rotations in 3 dimensional space. More...
class	KDL::Rotation2
class	KDL::Twist
	represents both translational and rotational velocities. More...
class	KDL::Vector
	A concrete implementation of a 3 dimensional vector class. More...
class	KDL::Vector2
	2D version of Vector More...
class	KDL::Wrench
	represents both translational and rotational acceleration. More...

Namespaces
	KDL

Functions
IMETHOD Vector	KDL::addDelta (const Vector &p_w_a, const Vector &p_w_da, double dt=1)
	adds vector da to vector a. see also the corresponding diff() routine. More...
IMETHOD Rotation	KDL::addDelta (const Rotation &R_w_a, const Vector &da_w, double dt=1)
IMETHOD Frame	KDL::addDelta (const Frame &F_w_a, const Twist &da_w, double dt=1)
IMETHOD Twist	KDL::addDelta (const Twist &a, const Twist &da, double dt=1)
	adds the twist da to the twist a. see also the corresponding diff() routine. More...
IMETHOD Wrench	KDL::addDelta (const Wrench &a, const Wrench &da, double dt=1)
	adds the wrench da to the wrench w. see also the corresponding diff() routine. see also the corresponding diff() routine. More...
IMETHOD Vector	KDL::diff (const Vector &p_w_a, const Vector &p_w_b, double dt=1)
IMETHOD Vector	KDL::diff (const Rotation &R_a_b1, const Rotation &R_a_b2, double dt=1)
IMETHOD Twist	KDL::diff (const Frame &F_a_b1, const Frame &F_a_b2, double dt=1)
IMETHOD Twist	KDL::diff (const Twist &a, const Twist &b, double dt=1)
IMETHOD Wrench	KDL::diff (const Wrench &W_a_p1, const Wrench &W_a_p2, double dt=1)
IMETHOD double	KDL::dot (const Vector &lhs, const Vector &rhs)
IMETHOD double	KDL::dot (const Twist &lhs, const Wrench &rhs)
IMETHOD double	KDL::dot (const Wrench &rhs, const Twist &lhs)
bool	KDL::Equal (const Vector &a, const Vector &b, double eps=epsilon)
bool	KDL::Equal (const Frame &a, const Frame &b, double eps=epsilon)
bool	KDL::Equal (const Twist &a, const Twist &b, double eps=epsilon)
bool	KDL::Equal (const Wrench &a, const Wrench &b, double eps=epsilon)
bool	KDL::Equal (const Vector2 &a, const Vector2 &b, double eps=epsilon)
bool	KDL::Equal (const Rotation2 &a, const Rotation2 &b, double eps=epsilon)
bool	KDL::Equal (const Frame2 &a, const Frame2 &b, double eps=epsilon)
bool	KDL::Equal (const Rotation &a, const Rotation &b, double eps)
IMETHOD bool	KDL::operator!= (const Frame &a, const Frame &b)
IMETHOD bool	KDL::operator!= (const Vector &a, const Vector &b)
IMETHOD bool	KDL::operator!= (const Twist &a, const Twist &b)
IMETHOD bool	KDL::operator!= (const Wrench &a, const Wrench &b)
IMETHOD bool	KDL::operator!= (const Rotation &a, const Rotation &b)
IMETHOD bool	KDL::operator!= (const Vector2 &a, const Vector2 &b)
Vector	KDL::operator* (const Vector &lhs, double rhs)
Vector	KDL::operator* (double lhs, const Vector &rhs)
Vector	KDL::operator* (const Vector &lhs, const Vector &rhs)
Wrench	KDL::operator* (const Wrench &lhs, double rhs)
Wrench	KDL::operator* (double lhs, const Wrench &rhs)
Twist	KDL::operator* (const Twist &lhs, double rhs)
Twist	KDL::operator* (double lhs, const Twist &rhs)
Twist	KDL::operator* (const Twist &lhs, const Twist &rhs)
Wrench	KDL::operator* (const Twist &lhs, const Wrench &rhs)
Frame	KDL::operator* (const Frame &lhs, const Frame &rhs)
IMETHOD Vector2	KDL::operator* (const Vector2 &lhs, double rhs)
IMETHOD Vector2	KDL::operator* (double lhs, const Vector2 &rhs)
IMETHOD Rotation2	KDL::operator* (const Rotation2 &lhs, const Rotation2 &rhs)
IMETHOD Frame2	KDL::operator* (const Frame2 &lhs, const Frame2 &rhs)
IMETHOD Vector	KDL::operator+ (const Vector &lhs, const Vector &rhs)
Wrench	KDL::operator+ (const Wrench &lhs, const Wrench &rhs)
Twist	KDL::operator+ (const Twist &lhs, const Twist &rhs)
IMETHOD Vector2	KDL::operator+ (const Vector2 &lhs, const Vector2 &rhs)
IMETHOD Vector	KDL::operator- (const Vector &lhs, const Vector &rhs)
Wrench	KDL::operator- (const Wrench &lhs, const Wrench &rhs)
Wrench	KDL::operator- (const Wrench &arg)
Twist	KDL::operator- (const Twist &lhs, const Twist &rhs)
Twist	KDL::operator- (const Twist &arg)
Vector	KDL::operator- (const Vector &arg)
IMETHOD Vector2	KDL::operator- (const Vector2 &lhs, const Vector2 &rhs)
IMETHOD Vector2	KDL::operator- (const Vector2 &arg)
Vector	KDL::operator/ (const Vector &lhs, double rhs)
Wrench	KDL::operator/ (const Wrench &lhs, double rhs)
Twist	KDL::operator/ (const Twist &lhs, double rhs)
IMETHOD Vector2	KDL::operator/ (const Vector2 &lhs, double rhs)
bool	KDL::operator== (const Rotation &a, const Rotation &b)
IMETHOD bool	KDL::operator== (const Frame &a, const Frame &b)
IMETHOD bool	KDL::operator== (const Vector &a, const Vector &b)
IMETHOD bool	KDL::operator== (const Twist &a, const Twist &b)
IMETHOD bool	KDL::operator== (const Wrench &a, const Wrench &b)
IMETHOD bool	KDL::operator== (const Vector2 &a, const Vector2 &b)
IMETHOD void	KDL::posrandom (Vector &a)
IMETHOD void	KDL::posrandom (Twist &a)
IMETHOD void	KDL::posrandom (Wrench &a)
IMETHOD void	KDL::posrandom (Rotation &R)
IMETHOD void	KDL::posrandom (Frame &F)
IMETHOD void	KDL::random (Vector &a)
	addDelta operator for displacement rotational velocity. More...
IMETHOD void	KDL::random (Twist &a)
IMETHOD void	KDL::random (Wrench &a)
IMETHOD void	KDL::random (Rotation &R)
IMETHOD void	KDL::random (Frame &F)
IMETHOD Rotation	KDL::Rot (const Vector &axis_a_b)
IMETHOD void	KDL::SetToZero (Vector &v)
IMETHOD void	KDL::SetToZero (Twist &v)
IMETHOD void	KDL::SetToZero (Wrench &v)
IMETHOD void	KDL::SetToZero (Vector2 &v)

Detailed Description

Warning

Efficienty can be improved by writing p2 = A*(B*(C*p1))) instead of p2=A*B*C*p1

PROPOSED NAMING CONVENTION FOR FRAME-like OBJECTS

*      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
* 

CONVENTIONS FOR WHEN USED WITH ROBOTS :

*       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 );
* 

CONVENTIONS REGARDING UNITS :

Any consistent series of units can be used, e.g. N,mm,Nmm,..mm/sec

Twist and Wrench transformations

3 different types of transformations do exist for the twists and wrenches.

*      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.
* 

Spatial cross products

Let m be a 6D motion vector (Twist) and f be a 6D force vector (Wrench) attached to a rigid body moving with a certain velocity v (Twist). Then

*     1) m_dot = v cross m or Twist=Twist*Twist
*     2) f_dot = v cross f or Wrench=Twist*Wrench
*

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

Definition in file frames.hpp.