2.2. Configuration Vector

The configuration vector selects which joint solution the voraus Robot Control uses when it converts a Cartesian pose into joint positions (inverse kinematics).

2.2.1. Definition and Physical Meaning

A Cartesian pose does not describe the state of a robot completely: the inverse kinematics is ambiguous. Several joint configurations, i.e., several postures of the arm (for example with the elbow pointing upwards or downwards), lead to the same Cartesian pose. These configurations are separated from each other by singularities of the kinematics (for example the shoulder, elbow and wrist singularity of a six-axis robot arm): within one configuration the joint positions change continuously with the Cartesian pose, while switching to another configuration always requires passing through the corresponding singularity.

The configuration vector resolves this ambiguity. It is an array in which every element is a flag with the value +1 or -1 that selects one of the two configurations separated by one singularity of the kinematics. A kinematics with \(n\) flags therefore has up to \(2^{n}\) different joint solutions for the same Cartesian pose. A solution is only usable if all resulting joint positions lie within the configured axis position limits (see Limitations).

Note

The configuration vector is only relevant for poses that are specified in a Cartesian coordinate system. A target that is specified in the Joint CS (JOINT_CS) already defines the joint positions unambiguously, so no inverse kinematics and therefore no configuration vector is needed.

2.2.2. Number of Elements

The number of flags is fixed for a given robot; it is determined by the KinematicsType entry of the robot configuration file (see Robot Config File). Table 4 lists the number of flags of all supported kinematics types.

Table 4 Number of Configuration Vector Elements per Kinematics Type

KinematicsType	Elements	Resolved singularities	Typical robots
CrossedWrist6R / CrossedShifted6R_3	3	Shoulder, elbow, wrist	Six-axis robot arms with spherical wrist (with or without offset)
ParallelWrist6R-1 / ParallelWrist6R-2	3	Shoulder, elbow, wrist	Six-axis robot arms with no spherical wrist
DoubleParallelogram_4R	2	Shoulder, elbow	Four-axis palletizing robots with a double parallelogram structure
ScaraRRPR	1	Elbow	SCARA robots
Gantry_XYZ_3P	0	—	Gantry (portal) robots

Note

The OPC UA interface transports the configuration vector as an array of up to six elements, independently of the connected robot: elements beyond the number of flags required by the robot’s kinematics are ignored on input and set to 1 on output. An input array with fewer elements than required is rejected as invalid.

2.2.3. Specifying a Configuration

Cartesian Motion Targets

The PTP command accepts an optional configuration vector via its ConfigVector parameter, see the ConfigVector entry in Table 79. It is evaluated when the target is specified in a Cartesian coordinate system:

• If the configuration vector contains only zeros or is empty, no configuration is requested. The motion planner then determines the target configuration on its own, primarily by keeping the current configuration of the robot, see Target Coordinates.

• If at least one element is non-zero, the configuration vector is applied. All flags required by the robot’s kinematics must then be provided and each of them must be either +1 or -1, otherwise the command is rejected.

The LIN and CIRC commands do not accept a configuration vector: a Cartesian path is always executed in the configuration that the robot has at the start of the command, because changing it would require moving through a singularity. A configuration is therefore always changed by a PTP motion.

Kinematic Transformations

The InverseKinematic function of the OPC UA interface takes a configuration vector as an input argument in order to select the joint solution to be calculated. If an empty array is submitted, the currently commanded configuration of the robot is used instead, see Inverse Kinematic.

The configuration of a given joint pose can also be read back, which is the recommended way to determine the flag values of a specific arm configuration:

• The ForwardKinematic function of the OPC UA interface returns, next to the Cartesian pose, the configuration vector of the submitted joint positions, see Forward Kinematic.

• The currently commanded configuration of the robot is published cyclically as RobotCommandedConfiguration on the OPC UA interface.

Both functions are described in the section Kinematic Transformations.

2.2.4. Example: Six-Axis Robot Arm with Three Flags

A six-axis robot arm of the kinematics type CrossedWrist6R (e.g., a KUKA robot) has three flags, so the same Cartesian pose of the Tool CS can be reached with up to eight different sets of joint positions. Each flag switches between two configurations without changing the pose of the Tool CS. Which of the eight combinations can actually be used depends on the axis position limits of the specific robot.

The first flag selects the configuration of the shoulder (axis 1), i.e., whether the arm points towards the wrist or reaches backwards over its own base, see Fig. 6.

Fig. 6 Shoulder configuration: the arm points towards the wrist (left) or reaches backwards over its own base (right)

The second flag selects the configuration of the elbow, i.e., whether the elbow points upwards or downwards, see Fig. 7.

Fig. 7 Elbow configuration: elbow above (left) or below (right) the connecting line between shoulder and wrist

The third flag selects the configuration of the wrist. Both configurations lead to the same flange orientation, but axis 5 is rotated in the opposite direction and axes 4 and 6 differ by 180°, see Fig. 8.

Fig. 8 Wrist configuration: the two wrist configurations that lead to the same flange orientation

2.2.5. Configuration Flags of the Supported Kinematics

The following sections list, for every kinematics type, which singularity and axis each of its flags resolves.

Note

Which of the two configurations a flag value selects depends on the axis convention of the robot (see Axes). The figures in this section and in Example: Six-Axis Robot Arm with Three Flags show the assignment for the respective kinematics; for a specific robot, the values of a known pose can be read back as described in Specifying a Configuration.

Six-Axis Robot Arms with Spherical Wrist

Kinematics type CrossedShifted6R_3, see Table 5.

Table 5 Configuration Flags of CrossedWrist6R and CrossedShifted6R_3

Element	Axis	Selected configuration
ConfigVector[0]	Axis 1	Shoulder: +1 turns axis 1 such that the arm points towards the wrist, -1 turns it by 180° so that the arm reaches backwards over its own base.
ConfigVector[1]	Axis 3	Elbow: the two solutions of axis 3, i.e., elbow above or below the connecting line between shoulder and wrist.
ConfigVector[2]	Axis 5	Wrist: +1 selects a negative angle of axis 5, -1 a positive angle.

Examples of configuration for a robot with spherical wrist are shown in Fig. 6, Fig. 7, and Fig. 8. A robot with spherical wrist and offset (kinematics type CrossedShifted6R_3 ) is shown in Fig. 9.

Fig. 9 Shoulder [-1, 1, 1], elbow [-1, -1, 1] and wrist [1, 1, -1] configurations of a six-axis robot arm with a crossed and shifted wrist

Six-Axis Robot Arms with no Spherical Wrist

Kinematics types ParallelWrist6R-1 and ParallelWrist6R-2, see Table 6 and Fig. 10.

Table 6 Configuration Flags of ParallelWrist6R-1 and ParallelWrist6R-2

Element	Axis	Selected configuration
ConfigVector[0]	Axis 1	Shoulder: the two solutions of axis 1, i.e., the shoulder is turned to the left or to the right of the wrist.
ConfigVector[1]	Axis 3	Elbow: +1 selects a positive angle of axis 3, -1 a negative one.
ConfigVector[2]	Axis 5	Wrist: +1 selects a positive angle of axis 5, -1 a negative one.

Fig. 10 Shoulder [-1, 1, 1], elbow [1, -1, 1] and wrist [1, 1, -1] configurations of a robot arm with a parallel wrist

Four-Axis Palletizing Robots

Kinematics type DoubleParallelogram_4R. Palletizing robots can only reach a restricted set of tool orientations: the tool always points downwards and only the rotation about the vertical axis is free. The wrist, therefore, has no ambiguity and only two flags remain, see Table 7.

Table 7 Configuration Flags of DoubleParallelogram_4R

Element	Axis	Selected configuration
ConfigVector[0]	Axis 1	Shoulder: +1 turns axis 1 such that the arm points towards the wrist, -1 turns it by 180° so that the arm reaches backwards over its own base.
ConfigVector[1]	Axis 3	Elbow: +1 selects a positive angle of axis 3, -1 a negative one.

SCARA Robots

Kinematics type ScaraRRPR. A SCARA robot has a single flag, which selects the configuration of the elbow, see Table 8 and Fig. 11.

Table 8 Configuration Flags of ScaraRRPR

Element	Axis	Selected configuration
ConfigVector[0]	Axis 2	Elbow: +1 selects a positive angle of axis 2, -1 a negative one. The two configurations are commonly referred to as left-handed and right-handed.

Fig. 11 Left-handed and right-handed elbow configuration of a SCARA robot

Gantry Robots

Kinematics type Gantry_XYZ_3P. The three prismatic axes of a gantry robot reach every pose within the workspace with exactly one set of joint positions, and the tool orientation is fixed (see voraus Conventions). The inverse kinematics is therefore unambiguous and the configuration vector is empty.