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We are in the process of publishing our software for multi-DOF kinematic calibration. While the software is basically usable, it may still have some rough edges in the documentation. Please give us a couple of days to sort those out.


This software allows the accurate calibration of geometric/kinematic transformation hierarchies from sensor data. It is possible to calibrate/estimate

  • unknown robot locations,
  • unknown relative poses within the transformation hierarchy (for example the relative pose between two cameras),
  • and unknown 1-DOF hinge joints, including the rotational axes as well as a mapping from raw encoder values to angles.

Prior to optimization, hierarchies have to be modeled in a simple JSON file format, which is passed to the optimizer. The latter will then try to optimize the problem my minimizing reprojection errors to known configurations of markers, or point-to-plane metrical errors of laser points to (planar) marker surfaces.

For both, the calibration of cameras and the calibration of laser range finders, known 3D reference geometry is required. We establish this reference making use of our visual_marker_mapping toolkit. It allows the accurate estimation of the 3D poses of configurations of optical markers given a set of camera images (from a DSLR camera for example). It uses AprilTags by Olson, that can simply be printed out and attached to walls or objects. To perform the reconstruction, you need a calibrated camera with a fixed focal length (no auto focus). The camera needs to be calibrated using the typical OpenCV camera calibration model.



In Ubuntu, the first three dependencies can be installed using the command

  • apt-get install libceres-dev libsuitesparse-dev libopencv-dev libeigen3-dev libboost-dev libboost-filesystem-dev libboost-program-options-dev libboost-system-dev python-pip

In Arch Linux, use:

  • pacman -S eigen opencv boost python-pip

  • Ceres is available as an AUR package called ceres-solver.

The visual_marker_mapping dependency is automatically pulled in as a git submodule.


You need at least

If you are using Ubuntu, this means that you need at least Ubuntu 14.04.


  1. Install flep:
git clone
pip install --user ./flep
  1. Install multi_dof_kinematic calibration and deps:
mkdir flep_ws && cd flep_ws && flep init
cd src
git clone
flep get_deps
flep cmake -DCMAKE_BUILD_TYPE=Release
flep make -j5

In order to get easy access to the built binaries, we provide a ROS-style file, that adds the flep_ws/build/bin directory to your PATH environment variable. Use

source flep_ws/build/

to run it. If you prefer not to do this step, you obviously need to provide the full path to the binaries, when running the applications.


It should be possible to build our software on Windows, given that we do not use any platform specific features, but so far we have not attempted to build it there. Please let us know if you run into problems doing this.



Our software works on project paths. A project path typically has a layout similar to to this:

  • The file reconstruction.json contains the marker-based 3D reference geometry. It needs to be created using the visual_marker_mapping tool. Please refer to the README file in that project for information about this process.
  • The file calibration_data.json is the main file that describes the calibration problem to be solved. We provide a number of examples that show how to create this one.
  • The folders my_camera and my_laser depend on the concrete sensor setup that is being optimized. The given folder- and file names only serve as an example.
  • After completion, our tool write out two files: calibration_result.json and calibration_result_visualization.json. The first one contains the actual calibration results. The second one contains special information that is read by our visualization tool to visualize the results.


Our software consists of a command-line tool called multi_dof_kinematic_calibration located in the build/bin folder, and a python script that can optionally be used to visualize the results in 3D.


  • --help: Shows a help text.
  • --project-path: Path to the aforementioned project directory.

For visualization of the results in 3D, we also include a Python (2.7/3.0) script called "". It is based on pygame, OpenGL, GLU, GLUT, numpy, and you may need to install the corresponding Python packages for your distribution in order to be able to run it.

The tools only parameter is the project path. The camera can be controlled using W, S, A, D. The mouse can be used to look around by holding the left mouse button. The camera speed can be increased by holding space.


We provide a test dataset, that you can use to test our tools. It is available here.

Use the following steps to perform the marker detection and 3D reconstruction (assuming you are in the root folder of this repository):

cd ptu_d47_w_xtion_ir_WRT_calibration_room_1
visual_marker_detection --project_path ir_cam/ --marker_width 0.1285 --marker_height 0.1295
multi_dof_kinematic_calibration --project_path .

As an alternative, the dataset includes a Makefile that performs the necessary steps. Use

cd ptu_d47_w_xtion_ir_WRT_calibration_room_1

to run it. For this to work, you need to have to have sourced the build/ file, as explained in the Building section.


Solving full optimization problem...
    Full optimization returned termination type 0
    Full training reprojection error RMS: 0.840787 px
Solving full optimization problem...done!

Resulting Parameters:
    Tick2Rad for all joints:
        pan_joint:0.000895116, tilt_joint:0.000919349, 
    Joint poses:
        pan_joint:    1.10492          0          0    0.78117  0.0077221 -0.0024885  -0.624265
        tilt_joint:   1.29675         0         0  0.550994 -0.439112 -0.557578  0.438968
        ir_cam_joint:  0.00844504   0.0594558 -0.00874979    0.515369    0.489033    0.505573    0.489529
Test Reprojection Error RMS: 2.51105 px
Test Reprojection Error RMS for camera 1: 2.51105 px

The tool prints the estimated transformations for all of the joints/transformations. All poses transform from a joint's parent to joint space. Poses a given in the order x, y, z, qw, qx, qy, qz.

If you want to visualize the results, simply run:

python .


The sample contains a calibration_data.json file, which looks as follows:

  "world_reference" : "calibration_room_1/reconstruction.json",
  "hierarchy" : [
      "name" : "pan_joint",
      "type" : "1_dof_joint",
      "ticks_to_rad" : 0.00089760538,
      "angular_noise_std_dev" : 0.00089760538,
      "parent_to_joint_pose_guess" : [0, 0, 0, 1, 0, 0, 0],
      "parent" : "base"
      "name" : "tilt_joint",
      "type" : "1_dof_joint",
      "ticks_to_rad" : 0.00091879199999999998,
      "angular_noise_std_dev" : 0.00091879199999999998,
      "parent_to_joint_pose_guess" : [0, 0, 0, 1, 0, 0, 0],
      "parent" : "pan_joint"
      "name" : "ir_cam_joint",
      "type" : "pose",
      "parent_to_joint_pose_guess" : [0, 0, 0, 1, 0, 0, 0],
      "parent" : "tilt_joint"
  "sensors" : [
      "sensor_id" : "1",
      "sensor_type" : "camera",
      "parent_joint" : "ir_cam_joint",
      "camera_path" : "ir_cam"
  "calibration_frames" : [
      "location_id" : -1,
      "camera_image_path_1" : "images/img_0.png",
      "pan_joint_ticks" : "-1783",
      "tilt_joint_ticks" : "613"
      "location_id" : -1,
      "camera_image_path_1" : "images/img_1.png",
      "pan_joint_ticks" : "-1640",
      "tilt_joint_ticks" : "613"

TODO: Add more detailed description here.

All poses transform from a joint's parent to joint space. Poses a given in the order x, y, z, qw, qx, qy, qz. The local coordinate systems are defined as follows:

  • A cameras x-axis points to the right, y-axis down, and the z-axis in viewing direction.

More examples

We provide a number additional examples that can be used to understand the capabilities of the system.

Synthetic Dataset with Ground Truth

In order to evaluate our approach, we created a synthetic dataset with simulated robotic arms with 3 and 4 DOF. We simulate varying amounts of noises (0 deg, 0.025 deg, 0.05 deg, 0.1 deg and 1 deg) on the actuator positioning, and render a 3D marker configuration from the simulated camera's pose.

We provide two variants of our dataset:

  • This one contains all of the mentioned data, including the actual renderings.
  • In this one, markers have already been extracted from the camera images using our visual_marker_detection tool. The images itself are not included.

To run our software on any of the datasets, you can proceed in exactly the same way as it is done in the previous example. Each dataset in the archive contains a Makefile that performs the processing.


  • Frank Neuhaus (
  • Stephan Manthe

Copyright and License

GPL 3.0


If you use our work, please cite us:

Practical Calibration of Actuated Multi-DOF Camera Systems. International Conference on Pattern Recognition Systems (ICPRS-17), 2017, IET. Juli 2017


Ed Olson, AprilTag: A robust and flexible visual fiducial system, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2011


Multi Sensor, Multi Actuator Extrinsic Calibration Toolkit







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