Element Coordination/Global Coordinates

Global Coordinates Concept

For working with robots of different point type's global coordinates concept has been defined. This allows giving robot position in one common unique format for independently how many axes the robot has. The key property used here is the robot's base transformation as described in:Robot_Working_Frames

BASE

There are two cartesian coordinate system associated with a robot: World Frame and Base Frame

World Frame

Having a robot in a pose defined by q = (q₁,q₂,q₃, .... , q_n) where n is the NDOF of the robot. The world frame coordinates are defined by:

p_world = Inverse Kinematics (q)

where p can be: p = (x,y,z, yaw, pitch,roll) depending on robot kinematics.

	NOTE
	For the sake of simplicity of this discussion we assume the tool is included in Inverse Kinematics calculation. Frames of WorkPiece and MachineTable are omitted here.

Base Frame

Base Frame is the World Frame moved by the robot.base propert:

p_base = base:p_world

where : is the compound operator.

Global Coordinates

All user inputs (target points of motion commands , moving frame coordinates, etc.) are given in base coordinate system. However thse systems can differe from robot to robot (e.g. R1 has XYZR and R2 has XYZYPR). Therefore we assume one common (global) base coordinate system that will transform all robots into one system by:

p¹_global = R1.glbalbase:R1.base:R1.InverseKinemaitcs(R1.pcmd)
p²_global = R2.glbalbase:R2.base:R2.InverseKinemaitcs(R2.pcmd)
p³_global = R3.glbalbase:R3.base:R3.InverseKinemaitcs(R3.pcmd)
... p^m_global = Rm.glbalbase:Rm.base:Rm.InverseKinemaitcs(Rm.pcmd)

Assuming system of m-robots.

This is achieved by adding <robot>.glbalbase location that is always, indepandetly from the actual robot point type, given in XYZYPR system.