Geometric Primitives

Introduction

Geometric primitives are represented by the following classes.

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.
 *

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 :: Typically we use the standard S.I. units: N, m, sec.