Defining Cartesian Groups

Introduction

Cartesian groups are enhancements of groups. Like groups, they are a collection of axes that can be moved together. In addition, they have a predefined Cartesian model for defining the roll of each axis in the Cartesian space.

Creating a Cartesian Group

Cartesian groups are defined similar to ordinary groups, either in configuration file or as a terminal input. The only difference is that at the end the type of the group is defined by : model=1 of <point type>, where <point type> is a string that defines the actual Cartesian model, which can be one of the following:

mnemonic constant used in CASTPOINT	numerical value used in CASTPOINT function	<point type> string	explanation
NO_ROBOT	0	NONE	List-of-coordinates, uninitialized generic points
TYPE_X	1	X	X coordinate only
TYPE_XY	2	XY	X Y table
TYPE_XYZ	3	XYZ	X Y Z
TYPE_XYZU	4	XYZU
TYPE_XYZUV	5	XYZUV
TYPE_XYZUVW	6	XYZUVW
TYPE_XYR	7	XYR	X Y Roll
TYPE_XYRZ	8	XYRZ
TYPE_XYRZU	9	XYRZU
TYPE_XYRZUV	10	XYRZUV
TYPE_XYZR	11	XYZR	X Y Z Roll
TYPE_XYZRU	12	XYZRU
TYPE_XYZRUV	13	XYZRUV
TYPE_XYZURV	14	XYZURV
TYPE_XYZUR	15	XYZUR
TYPE_XYZRPU	16	XYZRPU
TYPE_XYZRP	17	XYZRP	X Y Z Roll Pitch
TYPE_XYRURV	18	XYZRURV
TYPE_XYRUR	19	XYRUR
TYPE_XYRP	20	XYRP	X Y Roll Pitch
TYPE_XYRPU	21	XYRPU
TYPE_XYRPUV	22	XYRPUV
TYPE_XYRPUQ	23	XYRPUQ
TYPE_XYZYPR	24	XYZYPR	X Y Z Yaw Pitch Roll
TYPE_XYZPR	36		User defined point
TYPE_XYZA	37	XYZA	X Y Z A-angle
TYPE_XYZAB	38	XYZAB	X Y Z A-angle B-angle
TYPE_YPR	50	YPR	Yaw Pitch Roll
TYPE_PR	51	PR	Pitch Roll
TYPE_R	52	R	Roll

For example, the following defines a Cartesian group called GXYZ:

common shared GXYZ   as group Axnm = a1 Axnm = a2 Axnm = a3 model=1  of xyz

Usage

Cartesian groups implement robot models with 1-1 Inverse and Direct kinematics functions. For example, an XY Cartesian group is defined by following mapping:

J1 ←→ X
J2 ←→ Y

This means that coordinates of <group.setpoint and <group>.pcmd will have equal values.

Translation vs. Rotation

The greatest difference between ordinary groups and Cartesian groups is the separation of translational and rotational movements. This further means that axis type must mach the Cartesian model:

For example, in XYR group (X, Y and Roll) axistype must be set as:

Common Shared GXYR as Group of A1 A2 A3 model = 1 of XYR
...
a1.axistype = 1
a2.axistype = 1
a3.axistype = 1
ConfigGroup GXYR

If axis type is not properly set, ConfigGroup command will return an error. When such a group is properly set it allows setting physical kinematics values of velocity, acceleration and jerk separated into translational and rotational parts in the same way it is done in robot models:

MoveS GXYR #{100,100,90} VelTran=100 VelRot=20

This will move the GXYR to the target point (X=100mm, Y=100mm, R = 90deg) with 100 mm/sec or 20 deg/sec, depending on which values dominates (takes more time).

Motion

The following motion interpolation types are defined in Cartesian groups:

• Move - joint interpolations, used Vcruise, Vfinal in non-physical user units.
  
• MoveS - "straight-line" interpolation with separated kinematics parameters (Vtra/Vrot, Atran/Arot, Jtran/Jrot) defined in physical units for rotation and translation.
  
• Circle - circular/helycal interpolation in XYZ space with proportional change of additional rotation axes with separated kinematics parameters (Vtra/Vrot, Atran/Arot, Jtran/Jrot) defined in physical units for rotation and translation.
  

	NOTE
	There is no difference in the path of Move and Moves interpolation, except for how the time derivatives are determined.