Hand-Eye Calibration Process
To gather the data required to perform the calibration involves a robot making a series of planned movements (10 to 20 are recommended), either human-operated or automatically. At the end of each movement, the camera takes an image of the calibration object. The calibration object pose is extracted from the image, and the robot pose is registered from the controller. To achieve good calibration quality, the robot poses used when the camera takes images of the calibration object should be:
sufficiently distinct
using all the robot joints
This results in a diversity of perspectives with different viewing angles. The images below illustrate the required diversity of imaging poses for eye-to-hand and eye-in-hand systems. At the same time, the calibration object should be fully visible in the field of view of the camera.
Note
If using ArUco markers as calibration objects, not all the markers need to be fully visible in the field of view of the camera for each robot pose.
The task is then to solve homogeneous transformation equations to estimate the rotational and translational components of the locations of the calibration object and those of the hand-eye transformation.
Hand-eye calibration process steps:
Tip
It is recommended to Warm-up the camera and run Infield Correction before running hand-eye calibration. Use the same capture cycle during warmup, infield correction, and hand-eye calibration as in your application. To further reduce the impact of temperature dependent performance factors, enable Thermal Stabilization.
Move the robot to a new posture
Register the end-effector pose
Image the calibration object (obtain its pose)
Repeat steps 1-3 multiple times, e.g. 10 - 20
Compute hand-eye transform
To learn how to integrate hand-eye calibration into your solution, check out our interactive code samples:
/*
Perform Hand-Eye calibration.
*/
#include <Zivid/Application.h>
#include <Zivid/Calibration/Detector.h>
#include <Zivid/Calibration/HandEye.h>
#include <Zivid/Calibration/Pose.h>
#include <Zivid/Exception.h>
#include <Zivid/Zivid.h>
#include <iostream>
namespace
{
enum class CommandType
{
AddPose,
Calibrate,
Unknown
};
std::string getInput()
{
std::string command;
std::getline(std::cin, command);
return command;
}
CommandType enterCommand()
{
std::cout << "Enter command, p (to add robot pose) or c (to perform calibration): ";
const auto command = getInput();
if(command == "P" || command == "p")
{
return CommandType::AddPose;
}
if(command == "C" || command == "c")
{
return CommandType::Calibrate;
}
return CommandType::Unknown;
}
Zivid::Calibration::Pose enterRobotPose(size_t index)
{
std::cout << "Enter pose with id (a line with 16 space separated values describing 4x4 row-major matrix) : "
<< index << std::endl;
std::stringstream input(getInput());
float element{ 0 };
std::vector<float> transformElements;
for(size_t i = 0; i < 16 && input >> element; ++i)
{
transformElements.emplace_back(element);
}
const auto robotPose{ Zivid::Matrix4x4{ transformElements.cbegin(), transformElements.cend() } };
std::cout << "The following pose was entered: \n" << robotPose << std::endl;
return robotPose;
}
Zivid::Frame assistedCapture(Zivid::Camera &camera)
{
const auto parameters = Zivid::CaptureAssistant::SuggestSettingsParameters{
Zivid::CaptureAssistant::SuggestSettingsParameters::AmbientLightFrequency::none,
Zivid::CaptureAssistant::SuggestSettingsParameters::MaxCaptureTime{ std::chrono::milliseconds{ 800 } }
};
const auto settings = Zivid::CaptureAssistant::suggestSettings(camera, parameters);
return camera.capture(settings);
}
std::string markersToString(const std::vector<int> &markerIds)
{
std::ostringstream oss;
for(const auto &id : markerIds)
{
oss << id << " ";
}
return oss.str();
}
void handleAddPose(
size_t ¤tPoseId,
std::vector<Zivid::Calibration::HandEyeInput> &handEyeInput,
Zivid::Camera &camera,
const std::string &calibrationObject)
{
const auto robotPose = enterRobotPose(currentPoseId);
std::cout << "Detecting calibration object in point cloud" << std::endl;
if(calibrationObject == "c")
{
const auto frame = Zivid::Calibration::captureCalibrationBoard(camera);
const auto detectionResult = Zivid::Calibration::detectCalibrationBoard(frame);
if(detectionResult.valid())
{
std::cout << "Calibration board detected " << std::endl;
handEyeInput.emplace_back(robotPose, detectionResult);
currentPoseId++;
}
else
{
std::cout
<< "Failed to detect calibration board, ensure that the entire board is in the view of the camera"
<< std::endl;
}
}
else if(calibrationObject == "m")
{
const auto frame = assistedCapture(camera);
auto markerDictionary = Zivid::Calibration::MarkerDictionary::aruco4x4_50;
std::vector<int> markerIds = { 1, 2, 3 };
std::cout << "Detecting arUco marker IDs " << markersToString(markerIds) << "from the dictionary "
<< markerDictionary << std::endl;
auto detectionResult = Zivid::Calibration::detectMarkers(frame, markerIds, markerDictionary);
if(detectionResult.valid())
{
std::cout << "ArUco marker(s) detected: " << detectionResult.detectedMarkers().size() << std::endl;
handEyeInput.emplace_back(robotPose, detectionResult);
currentPoseId++;
}
else
{
std::cout
<< "Failed to detect any ArUco markers, ensure that at least one ArUco marker is in the view of the camera"
<< std::endl;
}
}
}
std::vector<Zivid::Calibration::HandEyeInput> readHandEyeInputs(Zivid::Camera &camera)
{
size_t currentPoseId{ 0 };
bool calibrate{ false };
std::string calibrationObject;
while(true)
{
std::cout
<< "Enter calibration object you are using, m (for ArUco marker(s)) or c (for Zivid checkerboard): "
<< std::endl;
calibrationObject = getInput();
if(calibrationObject == "m" || calibrationObject == "c")
{
break;
}
}
std::cout << "Zivid primarily operates with a (4x4) transformation matrix. To convert" << std::endl;
std::cout << "from axis-angle, rotation vector, roll-pitch-yaw, or quaternion, check out" << std::endl;
std::cout << "our PoseConversions sample." << std::endl;
std::vector<Zivid::Calibration::HandEyeInput> handEyeInput;
do
{
switch(enterCommand())
{
case CommandType::AddPose:
{
try
{
handleAddPose(currentPoseId, handEyeInput, camera, calibrationObject);
}
catch(const std::exception &e)
{
std::cout << "Error: " << Zivid::toString(e) << std::endl;
continue;
}
break;
}
case CommandType::Calibrate:
{
calibrate = true;
break;
}
case CommandType::Unknown:
{
std::cout << "Error: Unknown command" << std::endl;
break;
}
}
} while(!calibrate);
return handEyeInput;
}
Zivid::Calibration::HandEyeOutput performCalibration(
const std::vector<Zivid::Calibration::HandEyeInput> &handEyeInput)
{
while(true)
{
std::cout << "Enter type of calibration, eth (for eye-to-hand) or eih (for eye-in-hand): ";
const auto calibrationType = getInput();
if(calibrationType == "eth" || calibrationType == "ETH")
{
std::cout << "Performing eye-to-hand calibration with " << handEyeInput.size() << " dataset pairs"
<< std::endl;
std::cout << "The resulting transform is the camera pose in robot base frame" << std::endl;
return Zivid::Calibration::calibrateEyeToHand(handEyeInput);
}
if(calibrationType == "eih" || calibrationType == "EIH")
{
std::cout << "Performing eye-in-hand calibration with " << handEyeInput.size() << " dataset pairs"
<< std::endl;
std::cout << "The resulting transform is the camera pose in flange (end-effector) frame" << std::endl;
return Zivid::Calibration::calibrateEyeInHand(handEyeInput);
}
std::cout << "Entered uknown method" << std::endl;
}
}
} // namespace
int main()
{
try
{
Zivid::Application zivid;
std::cout << "Connecting to camera" << std::endl;
auto camera{ zivid.connectCamera() };
const auto handEyeInput{ readHandEyeInputs(camera) };
const auto calibrationResult{ performCalibration(handEyeInput) };
std::cout << "Zivid primarily operates with a (4x4) transformation matrix. To convert" << std::endl;
std::cout << "to axis-angle, rotation vector, roll-pitch-yaw, or quaternion, check out" << std::endl;
std::cout << "our PoseConversions sample." << std::endl;
if(calibrationResult.valid())
{
std::cout << "Hand-Eye calibration OK\n"
<< "Result:\n"
<< calibrationResult << std::endl;
}
else
{
std::cout << "Hand-Eye calibration FAILED" << std::endl;
return EXIT_FAILURE;
}
}
catch(const std::exception &e)
{
std::cerr << "\nError: " << Zivid::toString(e) << std::endl;
std::cout << "Press enter to exit." << std::endl;
std::cin.get();
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
/*
Perform Hand-Eye calibration.
*/
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using Zivid.NET.Calibration;
using Duration = Zivid.NET.Duration;
class Program
{
static int Main()
{
try
{
var zivid = new Zivid.NET.Application();
Console.WriteLine("Connecting to camera");
var camera = zivid.ConnectCamera();
var handEyeInput = readHandEyeInputs(camera);
var calibrationResult = performCalibration(handEyeInput);
Console.WriteLine("Zivid primarily operates with a (4x4) transformation matrix. To convert");
Console.WriteLine("to axis-angle, rotation vector, roll-pitch-yaw, or quaternion, check out");
Console.WriteLine("our PoseConversions sample.");
if (calibrationResult.Valid())
{
Console.WriteLine("{0}\n{1}\n{2}", "Hand-Eye calibration OK", "Result: ", calibrationResult);
}
else
{
Console.WriteLine("Hand-Eye calibration FAILED");
return 1;
}
}
catch (Exception ex)
{
Console.WriteLine("Error: {0}", ex.Message);
return 1;
}
return 0;
}
static List<HandEyeInput> readHandEyeInputs(Zivid.NET.Camera camera)
{
var handEyeInput = new List<HandEyeInput>();
var currentPoseId = 0U;
var beingInput = true;
var calibrationObject = "";
while (true)
{
Console.WriteLine("Enter calibration object you are using, m (for ArUco marker(s)) or c (for Zivid checkerboard): ");
calibrationObject = Console.ReadLine();
if (calibrationObject.Equals("m", StringComparison.CurrentCultureIgnoreCase) ||
calibrationObject.Equals("c", StringComparison.CurrentCultureIgnoreCase))
{
break;
}
}
Interaction.ExtendInputBuffer(2048);
Console.WriteLine("Zivid primarily operates with a (4x4) transformation matrix. To convert");
Console.WriteLine("from axis-angle, rotation vector, roll-pitch-yaw, or quaternion, check out");
Console.WriteLine("our PoseConversions sample.");
do
{
switch (Interaction.EnterCommand())
{
case CommandType.AddPose:
try
{
HandleAddPose(ref currentPoseId, ref handEyeInput, camera, calibrationObject);
}
catch (Exception ex)
{
Console.WriteLine("Error: {0}", ex.Message);
continue;
}
break;
case CommandType.Calibrate: beingInput = false; break;
case CommandType.Unknown: Console.WriteLine("Error: Unknown command"); break;
}
} while (beingInput);
return handEyeInput;
}
public static void HandleAddPose(ref uint currentPoseId, ref List<HandEyeInput> handEyeInput, Zivid.NET.Camera camera, string calibrationObject)
{
var robotPose = Interaction.EnterRobotPose(currentPoseId);
Console.Write("Detecting calibration object in point cloud");
if (calibrationObject.Equals("c", StringComparison.CurrentCultureIgnoreCase))
{
var frame = Zivid.NET.Calibration.Detector.CaptureCalibrationBoard(camera);
var detectionResult = Detector.DetectCalibrationBoard(frame);
if (detectionResult.Valid())
{
Console.WriteLine("Calibration board detected");
handEyeInput.Add(new HandEyeInput(robotPose, detectionResult));
++currentPoseId;
}
else
{
Console.WriteLine("Failed to detect calibration board, ensure that the entire board is in the view of the camera");
}
}
else if (calibrationObject.Equals("m", StringComparison.CurrentCultureIgnoreCase))
{
var frame = AssistedCapture(camera);
var markerDictionary = Zivid.NET.MarkerDictionary.Aruco4x4_50;
var markerIds = new List<int> { 1, 2, 3 };
Console.WriteLine("Detecting arUco marker IDs " + string.Join(", ", markerIds));
var detectionResult = Detector.DetectMarkers(frame, markerIds, markerDictionary);
if (detectionResult.Valid())
{
Console.WriteLine("ArUco marker(s) detected: " + detectionResult.DetectedMarkers().Length);
handEyeInput.Add(new HandEyeInput(robotPose, detectionResult));
++currentPoseId;
}
else
{
Console.WriteLine("Failed to detect any ArUco markers, ensure that at least one ArUco marker is in the view of the camera");
}
}
}
static Zivid.NET.Calibration.HandEyeOutput performCalibration(List<HandEyeInput> handEyeInput)
{
while (true)
{
Console.WriteLine("Enter type of calibration, eth (for eye-to-hand) or eih (for eye-in-hand): ");
var calibrationType = Console.ReadLine();
if (calibrationType.Equals("eth", StringComparison.CurrentCultureIgnoreCase))
{
Console.WriteLine("Performing eye-to-hand calibration with " + handEyeInput.Count + " dataset pairs");
Console.WriteLine("The resulting transform is the camera pose in robot base frame");
return Calibrator.CalibrateEyeToHand(handEyeInput);
}
if (calibrationType.Equals("eih", StringComparison.CurrentCultureIgnoreCase))
{
Console.WriteLine("Performing eye-in-hand calibration with " + handEyeInput.Count + " dataset pairs");
Console.WriteLine("The resulting transform is the camera pose in flange (end-effector) frame");
return Calibrator.CalibrateEyeInHand(handEyeInput);
}
Console.WriteLine("Entered unknown method");
}
}
public static Zivid.NET.Frame AssistedCapture(Zivid.NET.Camera camera)
{
var suggestSettingsParameters = new Zivid.NET.CaptureAssistant.SuggestSettingsParameters
{
AmbientLightFrequency =
Zivid.NET.CaptureAssistant.SuggestSettingsParameters.AmbientLightFrequencyOption.none,
MaxCaptureTime = Duration.FromMilliseconds(800)
};
var settings = Zivid.NET.CaptureAssistant.Assistant.SuggestSettings(camera, suggestSettingsParameters);
return camera.Capture(settings);
}
}
enum CommandType
{
AddPose,
Calibrate,
Unknown
}
class Interaction
{
// Console.ReadLine only supports reading 256 characters, by default. This limit is modified
// by calling ExtendInputBuffer with the maximum length of characters to be read.
public static void ExtendInputBuffer(int size)
{
Console.SetIn(new StreamReader(Console.OpenStandardInput(), Console.InputEncoding, false, size));
}
public static CommandType EnterCommand()
{
Console.Write("Enter command, p (to add robot pose) or c (to perform calibration): ");
var command = Console.ReadLine().ToLower();
switch (command)
{
case "p": return CommandType.AddPose;
case "c": return CommandType.Calibrate;
default: return CommandType.Unknown;
}
}
public static Pose EnterRobotPose(ulong index)
{
var elementCount = 16;
Console.WriteLine(
"Enter pose with id (a line with {0} space separated values describing 4x4 row-major matrix) : {1}",
elementCount,
index);
var input = Console.ReadLine();
var elements = input.Split().Where(x => !string.IsNullOrEmpty(x.Trim())).Select(x => float.Parse(x)).ToArray();
var robotPose = new Pose(elements); Console.WriteLine("The following pose was entered: \n{0}", robotPose);
return robotPose;
}
}
"""
Perform Hand-Eye calibration.
"""
import datetime
from pathlib import Path
from typing import List, Tuple
import numpy as np
import zivid
from zividsamples.save_load_matrix import assert_affine_matrix_and_save
def _enter_robot_pose(index: int) -> zivid.calibration.Pose:
"""Robot pose user input.
Args:
index: Robot pose ID
Returns:
robot_pose: Robot pose
"""
inputted = input(
f"Enter pose with id={index} (a line with 16 space separated values describing 4x4 row-major matrix): "
)
elements = inputted.split(maxsplit=15)
data = np.array(elements, dtype=np.float64).reshape((4, 4))
robot_pose = zivid.calibration.Pose(data)
print(f"The following pose was entered:\n{robot_pose}")
return robot_pose
def _perform_calibration(hand_eye_input: List[zivid.calibration.HandEyeInput]) -> zivid.calibration.HandEyeOutput:
"""Hand-Eye calibration type user input.
Args:
hand_eye_input: Hand-Eye calibration input
Returns:
hand_eye_output: Hand-Eye calibration result
"""
while True:
calibration_type = input("Enter type of calibration, eth (for eye-to-hand) or eih (for eye-in-hand): ").strip()
if calibration_type.lower() == "eth":
print(f"Performing eye-to-hand calibration with {len(hand_eye_input)} dataset pairs")
print("The resulting transform is the camera pose in robot base frame")
hand_eye_output = zivid.calibration.calibrate_eye_to_hand(hand_eye_input)
return hand_eye_output
if calibration_type.lower() == "eih":
print(f"Performing eye-in-hand calibration with {len(hand_eye_input)} dataset pairs")
print("The resulting transform is the camera pose in flange (end-effector) frame")
hand_eye_output = zivid.calibration.calibrate_eye_in_hand(hand_eye_input)
return hand_eye_output
print(f"Unknown calibration type: '{calibration_type}'")
def _assisted_capture(camera: zivid.Camera) -> zivid.Frame:
"""Acquire frame with capture assistant.
Args:
camera: Zivid camera
Returns:
frame: Zivid frame
"""
suggest_settings_parameters = zivid.capture_assistant.SuggestSettingsParameters(
max_capture_time=datetime.timedelta(milliseconds=800),
ambient_light_frequency=zivid.capture_assistant.SuggestSettingsParameters.AmbientLightFrequency.none,
)
settings = zivid.capture_assistant.suggest_settings(camera, suggest_settings_parameters)
return camera.capture(settings)
def _handle_add_pose(
current_pose_id: int, hand_eye_input: List, camera: zivid.Camera, calibration_object: str
) -> Tuple[int, List]:
"""Acquire frame with capture assistant.
Args:
current_pose_id: Counter of the current pose in the hand-eye calibration dataset
hand_eye_input: List of hand-eye calibration dataset pairs (poses and point clouds)
camera: Zivid camera
calibration_object: m (for ArUco marker(s)) or c (for Zivid checkerboard)
Returns:
Tuple[int, List]: Updated current_pose_id and hand_eye_input
"""
robot_pose = _enter_robot_pose(current_pose_id)
print("Detecting calibration object in point cloud")
if calibration_object == "c":
frame = zivid.calibration.capture_calibration_board(camera)
detection_result = zivid.calibration.detect_calibration_board(frame)
if detection_result.valid():
print("Calibration board detected")
hand_eye_input.append(zivid.calibration.HandEyeInput(robot_pose, detection_result))
current_pose_id += 1
else:
print("Failed to detect calibration board, ensure that the entire board is in the view of the camera")
elif calibration_object == "m":
frame = _assisted_capture(camera)
marker_dictionary = zivid.calibration.MarkerDictionary.aruco4x4_50
marker_ids = [1, 2, 3]
print(f"Detecting arUco marker IDs {marker_ids} from the dictionary {marker_dictionary}")
detection_result = zivid.calibration.detect_markers(frame, marker_ids, marker_dictionary)
if detection_result.valid():
print(f"ArUco marker(s) detected: {len(detection_result.detected_markers())}")
hand_eye_input.append(zivid.calibration.HandEyeInput(robot_pose, detection_result))
current_pose_id += 1
else:
print(
"Failed to detect any ArUco markers, ensure that at least one ArUco marker is in the view of the camera"
)
return current_pose_id, hand_eye_input
def _main() -> None:
app = zivid.Application()
print("Connecting to camera")
camera = app.connect_camera()
current_pose_id = 0
hand_eye_input = []
calibrate = False
while True:
calibration_object = input(
"Enter calibration object you are using, m (for ArUco marker(s)) or c (for Zivid checkerboard): "
).strip()
if calibration_object.lower() == "m" or calibration_object.lower() == "c":
break
print(
"Zivid primarily operates with a (4x4) transformation matrix. To convert\n"
"from axis-angle, rotation vector, roll-pitch-yaw, or quaternion, check out\n"
"our pose_conversions sample."
)
while not calibrate:
command = input("Enter command, p (to add robot pose) or c (to perform calibration): ").strip()
if command == "p":
try:
current_pose_id, hand_eye_input = _handle_add_pose(
current_pose_id, hand_eye_input, camera, calibration_object
)
except ValueError as ex:
print(ex)
elif command == "c":
calibrate = True
else:
print(f"Unknown command '{command}'")
calibration_result = _perform_calibration(hand_eye_input)
transform = calibration_result.transform()
transform_file_path = Path(Path(__file__).parent / "transform.yaml")
assert_affine_matrix_and_save(transform, transform_file_path)
print(
"Zivid primarily operates with a (4x4) transformation matrix. To convert\n"
"to axis-angle, rotation vector, roll-pitch-yaw, or quaternion, check out\n"
"our pose_conversions sample."
)
if calibration_result.valid():
print("Hand-Eye calibration OK")
print(f"Result:\n{calibration_result}")
else:
print("Hand-Eye calibration FAILED")
if __name__ == "__main__":
_main()
We have code samples that enable performing hand-eye calibration easily:
UR5 Robot + Python: Generate Dataset and perform Hand-Eye Calibration
Any Robot + RoboDK + Python: Generate Dataset and Perform Hand-Eye Calibration
Alternatively, computing hand-eye transform can be done using a CLI tool:
This Command-Line Interface enables the user to specify the dataset collected in steps 1-3 to compute the transformation matrix and residuals. These results are saved in user-specified files. This CLI tool is experimental and it will eventually be replaced by a GUI.
Continue reading about hand-eye calibration Cautions And Recommendations.