Hand-eye calibration¶
For applications, in which the camera is integrated into one or more robot systems, it needs to be calibrated w.r.t. some robot reference frames. For this purpose, the rc_cube is shipped with an on-board calibration routine called the hand-eye calibration module. It is a base module which is available on every rc_cube.
Note
The implemented calibration routine is completely agnostic about the user-defined robot frame to which the camera is calibrated. It might be a robot’s end-effector (e.g., flange or tool center point) or any point on the robot structure. The method’s only requirement is that the pose (i.e., translation and rotation) of this robot frame w.r.t. a user-defined external reference frame (e.g., world or robot mounting point) is exactly observable by the robot controller and can be reported to the calibration module.
The Calibration routine itself is an easy-to-use three-step procedure using a calibration grid which can be obtained from Roboception.
Calibration interfaces¶
The following two interfaces are offered to conduct hand-eye calibration:
All services and parameters of this module required to conduct the hand-eye calibration programmatically are exposed by the rc_cube’s REST-API interface. The respective node name of this module is
rc_hand_eye_calibration
and the respective service calls are documented Services.Note
The described approach requires a network connection between the rc_cube and the robot controller to pass robot poses from the controller to the rc_cube’s calibration module.
For use cases where robot poses cannot be passed programmatically to the rc_cube’s hand-eye calibration module, the Web GUI’s Hand-Eye Calibration page under the Configuration tab offers a guided process to conduct the calibration routine manually.
Note
During the process, the described approach requires the user to manually enter into the Web GUI robot poses, which need to be accessed from the respective robot-teaching or handheld device.
Camera mounting¶
As illustrated in Fig. 23 and Fig. 25, two different use cases w.r.t. to the mounting of the camera generally have to be considered:
- The camera is mounted on the robot, i.e., it is mechanically fixed to a robot link (e.g., at its flange or a flange-mounted tool), and hence moves with the robot.
- The camera is not mounted on the robot but is fixed to a table or other place in the robot’s vicinity and remains at a static position w.r.t. the robot.
While the general Calibration routine is very similar in both use cases, the calibration process’s output, i.e., the resulting calibration transform, will be semantically different, and the fixture of the calibration grid will also differ.
- Calibration with a robot-mounted camera
When calibrating a robot-mounted camera with the robot, the calibration grid has to be secured in a static position w.r.t. the robot, e.g., on a table or some other fixed-base coordinate system as sketched in Fig. 23.
Warning
It is extremely important that the calibration grid does not move during step 2 of the Calibration routine. Securely fixing its position to prevent unintended movements such as those caused by vibrations, moving cables, or the like is therefore strongly recommended.
The result of the calibration (step 3 of the Calibration routine) is a pose \(\mathbf{T}^{\text{robot}}_{\text{camera}}\) describing the (previoulsy unknown) relative positional and rotational transformation from the camera frame into the user-selected robot frame such that
(3)¶\[\mathbf{p}_{\text{robot}} = \mathbf{R}^{\text{robot}}_{\text{camera}} \cdot \mathbf{p}_{\text{camera}} + \mathbf{t}^{\text{robot}}_{\text{camera}} \:,\]where \(\mathbf{p}_{\text{robot}} = (x,y,z)^T\) is a 3D point with its coordinates expressed in the robot frame, \(\mathbf{p}_{\text{camera}}\) is the same point represented in the camera coordinate frame, and \(\mathbf{R}^{\text{robot}}_{\text{camera}}\) as well as \(\mathbf{t}^{\text{robot}}_{\text{camera}}\) are the corresponding \(3\times 3\) rotation matrix and \(3\times 1\) translation vector of the pose \(\mathbf{T}^{\text{robot}}_{\text{camera}}\), respectively. In practice, in the calibration result and in the provided robot poses, the rotation is defined by Euler angles or as quaternion instead of a rotation matrix (see Pose formats).
Additional user input is required if the movement of the robot is constrained and the robot can rotate the Tool Center Point (TCP) only around one axis. This is typically the case for robots with four Degrees Of Freedom (4DOF) that are often used for palletizing tasks. In this case, the user must specify which axis of the robot frame is the rotation axis of the TCP. Further, the signed offset from the TCP to the camera coordinate system along the TCP rotation axis has to be provided. Fig. 24 illustrates the situation.
For rc_visard, the camera coordinate system is located in the optical center of the left camera. The approximate location is given in section Coordinate Frames.
- Calibration with a statically-mounted camera
In use cases where the camera is positioned statically w.r.t. the robot, the calibration grid needs to be mounted to the robot as shown for example in Fig. 25 and Fig. 26.
Note
The hand-eye calibration module is completely agnostic about the exact mounting and positioning of the calibration grid w.r.t. the user-defined robot frame. That means, the relative positioning of the calibration grid to that frame neither needs to be known, nor it is relevant for the calibration routine, as shown in Fig. 26.
Warning
It is extremely important that the calibration grid is attached securely to the robot such that it does not change its relative position w.r.t. the user-defined robot frame during step 2 of the Calibration routine.
In this use case, the result of the calibration (step 3 of the Calibration routine) is the pose \(\mathbf{T}^{\text{ext}}_{\text{camera}}\) describing the (previoulsy unknown) relative positional and rotational transformation between the camera frame and the user-selected external reference frame ext such that
(4)¶\[\mathbf{p}_{\text{ext}} = \mathbf{R}^{\text{ext}}_{\text{camera}} \cdot \mathbf{p}_{\text{camera}} + \mathbf{t}^{\text{ext}}_{\text{camera}} \:,\]where \(\mathbf{p}_{\text{ext}} = (x,y,z)^T\) is a 3D point with its coordinates expressed in the external reference frame ext, \(\mathbf{p}_{\text{camera}}\) is the same point represented in the camera coordinate frame, and \(\mathbf{R}^{\text{ext}}_{\text{camera}}\) as well as \(\mathbf{t}^{\text{ext}}_{\text{camera}}\) are the corresponding \(3\times 3\) rotation matrix and \(3\times 1\) translation vector of the pose \(\mathbf{T}^{\text{ext}}_{\text{camera}}\), respectively. In practice, in the calibration result and in the provided robot poses, the rotation is defined by Euler angles or as quaternion instead of a rotation matrix (see Pose formats).
Additional user input is required if the movement of the robot is constrained and the robot can rotate the Tool Center Point (TCP) only around one axis. This is typically the case for robots with four Degrees Of Freedom (4DOF) that are often used for palletizing tasks. In this case, the user must specify which axis of the robot frame is the rotation axis of the TCP. Further, the signed offset from the TCP to the visible surface of the calibration grid along the TCP rotation axis has to be provided. The grid must be mounted such that the TCP rotation axis is orthogonal to the grid. Fig. 27 illustrates the situation.
Calibration routine¶
The general hand-eye calibration routine consists of three steps, which are illustrated in Fig. 28. These three steps are also represented in the Web GUI’s guided hand-eye-calibration process.
Step 1: Setting parameters¶
Before starting the actual calibration routine, the grid and mounting parameters have to be set to the module. As for the REST-API, the respective parameters are listed in Parameters.
- Web GUI example:
The Web GUI offers an interface for entering these parameters during the first step of the calibration routine as shown in Fig. 29. In addition to grid size and camera mounting, the Web GUI also offers settings for calibrating 4DOF robots. In this case, the rotation axis, as well as the offset from the TCP to the camera coordinate system (robot-mounted camera) or grid surface (statically mounted camera) must be given. Finally, the pose format can be chosen, which is used for setting poses in the upcoming step 2 of the calibration process. It can be set to either XYZABC for positions and Euler angles, or XYZ+quaternion for positions plus quaternions for representing rotations. See Pose formats for the exact definitions.
Note
The Pose parameter is added to the Web GUI as a convenience option only. For reporting poses programmatically via REST-API, the XYZ+quaternion format is mandatory.
Step 2: Selecting and reporting robot calibration positions¶
In this step (2a.), the user defines several calibration positions for the robot to approach. These positions must each ensure that the calibration grid is completely visible in the left camera image. Furthermore, the robot positions need to be selected properly to achieve a variety of different perspectives for the camera to perceive the calibration grid. Fig. 30 shows a schematic recommendation of four different grid positions which should be recorded from a close and a far point of view, resulting in eight images for the calibration.
Warning
Calibration quality, i.e., the accuracy of the calculated calibration result, depends on the calibration-grid views provided. The more diverse the perspectives are, the better is the calibration. Choosing very similar views, i.e., varying the robot positions only slightly between different repetitions of step 2a., may lead to inaccurate estimation of the desired calibration transformation.
After the robot reaches each calibration position, the corresponding pose \(\mathbf{T}^{\text{ext}}_{\text{robot}}\) of the user-defined robot frame in the user-defined external reference frame ext needs to be reported to the hand-eye calibration module (2b.). For this purpose, the module offers different slots to store the reported poses and the corresponding left camera images. All filled slots will then be used to calculate the desired calibration transformation between the camera frame and either the user-defined robot frame (robot-mounted camera) or the user-defined external reference frame ext (static camera).
Note
To successfully calculate the hand-eye calibration transformation, at least three different robot calibration poses need to be reported and stored in slots. However, to prevent errors induced by possible inaccurate measurements, at least eight calibration poses are recommended.
To transmit the poses programmatically, the module’s REST-API
offers the set_pose
service call (see
Services).
- Web GUI example:
After completing the calibration settings in step 1 and clicking Next, the Web GUI offers eight different slots (Close View 1, Close View 2, etc.) for the user to fill manually with robot poses. At the very top, a live stream from the camera is shown indicating whether the calibration grid is currently detected or not. Next to each slot, a figure suggests a respective dedicated viewpoint on the grid. For each slot, the robot must be operated to achieve the suggested view.
Once the suggested view is achieved, the user-defined robot frame’s pose needs to be entered manually into the respective text fields, and the corresponding camera image is captured using the Take Picture to Proceed button.
Note
The user’s acquisition of robot pose data depends on the robot model and manufacturer – it might be read from a teaching or handheld device, which is shipped with the robot.
Warning
Please be careful to correctly and accurately enter the values; even small variations or typos may lead to calibration-process failure.
This procedure is repeated eight times in total. Complying to the suggestions to observe the grid from close and far distance from different viewing angles as sketched in Fig. 30, in this example the following corresponding camera images have been sent to the hand-eye calibration module with their associated robot pose:
Step 3: Calculating and saving the calibration transformation¶
The final step in the hand-eye calibration routine consists of issuing the
desired calibration transformation to be computed from the collected
poses and camera images. The REST-API offers this functionality via the
calibrate
service call
(see Services).
Depending on the way
the camera is mounted, this service computes and returns the
transformation (i.e., the pose) between the camera frame and
either the user-defined
robot frame (robot-mounted camera)
or the user-defined external reference frame ext
(statically mounted camera); see
Camera mounting.
To enable users to judge the quality of the resulting calibration transformation, the module also reports the translational and rotational calibration errors, which are computed from the variance of the calibration result.
- Web GUI example:
The Web GUI automatically triggers computation of the calibration result after taking the last of the eight pictures. The user just needs to click the Next button to proceed to the result. The user has the possibility to specify or correct settings related to calibration of 4DOF robots if required. After changing any settings, the recompute button needs to be pressed.
In the example that is shown in Fig. 33, 4DOF is turned off and the camera is mounted statically. The resulting output is the pose of the left camera in the external coordinate system of the robot. The reported translational error is 0.67 mm and the rotational error is 0.83 deg.
Parameters¶
The hand-eye calibration module is called rc_hand_eye_calibration
in the REST-API and is
represented by the Hand-Eye Calibration page under the Configuration tab in the
Web GUI.
The user can change the calibration parameters there or use the
REST-API interface.
Parameter overview¶
This module offers the following run-time parameters:
Name | Type | Min | Max | Default | Description |
---|---|---|---|---|---|
grid_height |
float64 | 0.0 | 10.0 | 0.0 | The height of the calibration pattern in meters |
grid_width |
float64 | 0.0 | 10.0 | 0.0 | The width of the calibration pattern in meters |
robot_mounted |
bool | false | true | true | Whether the camera is mounted on the robot |
tcp_offset |
float64 | -10.0 | 10.0 | 0.0 | Offset from TCP along tcp_rotation_axis |
tcp_rotation_axis |
int32 | -1 | 2 | -1 | -1 for off, 0 for x, 1 for y, 2 for z |
Description of run-time parameters¶
The parameter descriptions are given with the corresponding Web GUI names in brackets.
grid_width
(Grid Width (m))¶
Width of the calibration grid in meters. The width should be given with a very high accuracy, preferably with sub-millimeter accuracy.
Via the REST-API, this parameter can be set as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/parameters?grid_width=<value>
grid_height
(Grid Height (m))¶
Height of the calibration grid in meters. The height should be given with a very high accuracy, preferably with sub-millimeter accuracy.
Via the REST-API, this parameter can be set as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/parameters?grid_height=<value>
robot_mounted
(Camera Mounting)¶
If set to true, the camera is mounted on the robot. If set to false, the camera is mounted statically and the calibration grid is mounted on the robot.
Via the REST-API, this parameter can be set as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/parameters?robot_mounted=<value>
tcp_offset
(TCP Offset)¶
The signed offset from the TCP to the camera coordinate system (robot-mounted sensor) or the visible surface of the calibration grid (statically mounted sensor) along the TCP rotation axis in meters. This is required if the robot’s movement is constrained and it can rotate its TCP only around one axis (e.g., 4DOF robot).
Via the REST-API, this parameter can be set as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/parameters?tcp_offset=<value>
tcp_rotation_axis
(TCP Rotation Axis)¶
The axis of the robot frame around which the robot can rotate its TCP. 0 is used for X, 1 for Y and 2 for the Z axis. This is required if the robot’s movement is constrained and it can rotate its TCP only around one axis (e.g., 4DOF robot). -1 means that the robot can rotate its TCP around two independent rotation axes.
tcp_offset
is ignored in this case.Via the REST-API, this parameter can be set as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/parameters?tcp_rotation_axis=<value>
(Pose)¶
For convenience, the user can choose in the Web GUI between calibration in XYZABC format or in XYZ+quaternion format (see Pose formats). When calibrating using the REST-API, the calibration result will always be given in XYZ+quaternion.
Services¶
The REST-API service calls offered to programmatically conduct the hand-eye calibration and to store or restore this module’s parameters are explained below.
save_parameters
¶
With this service call, the current parameter settings of the hand-eye calibration module are persisted to the rc_cube. That means, these values are applied even after reboot.
This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/save_parametersThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "save_parameters", "response": { "return_code": { "message": "string", "value": "int16" } } }
reset_defaults
¶
restores and applies the default values for this module’s parameters (“factory reset”). Does not affect the calibration result itself or any of the
slots
saved during calibration. Only parameters such as the grid dimensions and the mount type will be reset.Warning
By calling this service, the current parameter settings for this module are irrecoverably lost.
This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/reset_defaultsThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "reset_defaults", "response": { "return_code": { "message": "string", "value": "int16" } } }
reset_calibration
¶
deletes all previously provided poses and corresponding images. The last saved calibration result is reloaded. This service might be used to (re-)start the hand-eye calibration from scratch.
This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/reset_calibrationThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "reset_calibration", "response": { "message": "string", "status": "int32", "success": "bool" } }
set_pose
¶
provides a robot pose as calibration pose to the hand-eye calibration routine.
The
slot
argument is used to assign numbers to the different calibration poses. At each instant whenset_pose
is called, an image is recorded. This service call fails if the grid was undetectable in the current image.This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/set_poseThe definition for the request arguments with corresponding datatypes is:
{ "args": { "pose": { "orientation": { "w": "float64", "x": "float64", "y": "float64", "z": "float64" }, "position": { "x": "float64", "y": "float64", "z": "float64" } }, "slot": "int32" } }The definition for the response with corresponding datatypes is:
{ "name": "set_pose", "response": { "message": "string", "status": "int32", "success": "bool" } }
¶ status
success
Description 1 true
pose stored successfully 3 true
pose stored successfully; collected enough poses for calibration, i.e., ready to calibrate 4 false
calibration grid was not detected, e.g., not fully visible in camera image 8 false
no image data available 12 false
given orientation values are invalid
calibrate
¶
calculates and returns the hand-eye calibration transformation with the robot poses configured by the
set_pose
service.save_calibration
must be called to make the calibration available for other modules via theget_calibration
service call and to store it persistently.Note
For calculating the hand-eye calibration transformation at least three robot calibration poses are required (see
set_pose
service). However, eight calibration poses are recommended.This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/calibrateThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "calibrate", "response": { "error": "float64", "message": "string", "pose": { "orientation": { "w": "float64", "x": "float64", "y": "float64", "z": "float64" }, "position": { "x": "float64", "y": "float64", "z": "float64" } }, "robot_mounted": "bool", "rotation_error_degree": "float64", "status": "int32", "success": "bool", "translation_error_meter": "float64" } }The field
error
gives the calibration error in pixels which is computed from the translational errortranslation_error_meter
and the rotational errorrotation_error_degree
. This value is only given for compatibility with older versions. The translational and rotational errors should be preferred.
¶ status
success
Description 0 true
calibration successful, returned calibration result 1 false
not enough poses to perform calibration 2 false
calibration result is invalid, please verify the input data 3 false
given calibration grid dimensions are not valid 4 false
insufficient rotation, tcp_offset
andtcp_rotation_axis
must be specified5 false
sufficient rotation available, tcp_rotation_axis
must be set to -16 false
poses are not distinct enough from each other
set_calibration
¶
sets the hand-eye calibration transformation with arguments of this call. The calibration transformation is expected in the same format as returned by the
calibrate
andget_calibration
calls. The given calibration information is also stored persistently on the sensor by internally callingsave_calibration
.This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/set_calibrationThe definition for the request arguments with corresponding datatypes is:
{ "args": { "pose": { "orientation": { "w": "float64", "x": "float64", "y": "float64", "z": "float64" }, "position": { "x": "float64", "y": "float64", "z": "float64" } }, "robot_mounted": "bool" } }The definition for the response with corresponding datatypes is:
{ "name": "set_calibration", "response": { "message": "string", "status": "int32", "success": "bool" } }
¶ status
success
Description 0 true
setting the calibration transformation was successful 12 false
given orientation values are invalid
save_calibration
¶
persistently saves the result of hand-eye calibration to the rc_cube and overwrites the existing one. The stored result can be retrieved any time by the
get_calibration
service.This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/save_calibrationThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "save_calibration", "response": { "message": "string", "status": "int32", "success": "bool" } }
¶ status
success
Description 0 true
calibration saved successfully 1 false
could not save calibration file 2 false
calibration result is not available
remove_calibration
¶
removes the persistent hand-eye calibration on the rc_cube. After this call the
get_calibration
service reports again that no hand-eye calibration is available.This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/remove_calibrationThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "remove_calibration", "response": { "message": "string", "status": "int32", "success": "bool" } }
¶ status
success
Description 0 true
removed persistent calibration, device reports as uncalibrated 1 true
no persistent calibration found, device reports as uncalibrated 2 false
could not remove persistent calibration
get_calibration
¶
returns the hand-eye calibration currently stored on the rc_cube.
This service can be called as follows.
PUT http://<host>/api/v1/nodes/rc_hand_eye_calibration/services/get_calibrationThis service has no arguments.
The definition for the response with corresponding datatypes is:
{ "name": "get_calibration", "response": { "error": "float64", "message": "string", "pose": { "orientation": { "w": "float64", "x": "float64", "y": "float64", "z": "float64" }, "position": { "x": "float64", "y": "float64", "z": "float64" } }, "robot_mounted": "bool", "rotation_error_degree": "float64", "status": "int32", "success": "bool", "translation_error_meter": "float64" } }The field
error
gives the calibration error in pixels which is computed from the translational errortranslation_error_meter
and the rotational errorrotation_error_degree
. This value is only given for compatibility with older versions. The translational and rotational errors should be preferred.
¶ status
success
Description 0 true
returned valid calibration pose 2 false
calibration result is not available