orocos_kdl: frames.hpp File Reference

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

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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
namespace	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.
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.
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.
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)
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)
bool	KDL::operator== (const Rotation &a, const Rotation &b)

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.

Classes

Namespaces

Functions

Detailed Description