Element Coordination/Global Coordinates

Universal Coordinates Concept

For working with robots of different point type's universal 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.

Universal 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 base coordinate system that will transform all robots into one system by:

p¹_base = R1.base:R1.InverseKinemaitcs(R1.pcmd)
p²_base = R2.base:R2.InverseKinemaitcs(R2.pcmd)
p³_base = R3.base:R3.InverseKinemaitcs(R3.pcmd)
... p^m_base = Rm.base:Rm.InverseKinemaitcs(Rm.pcmd)

Assuming system of m-robots.

This is achieved by: <robot>.base can assigned in two ways:

• classical assignment by location of same point type: R1.base = #{100,200,0}
• universal coordinates - assignment by location of XYZYPR point type R1.base = #{100,200,0,0,180,0}

In both cases the <robot>.base coordinate will be kept internally as XYZYPR point.

Also all IverseKinemaitcs(.) function results will be embedded into universal coordinates (i.e. XYZYPR) by adding zeros on cartesian coordinates that are not included in robot kinematics.