Given a bagfile of calibration_msgs/RobotMeasurement collected using the pr2_calibration_executive package (or similar), pr2_calibration_estimation uses this data along with several configuration configuration files to estimate various parameters for the PR2.

Technical Explanation: This is a multi-step nonlinear optimizer that uses scipy's levenberg-marquardt optimizer, scipy.optimize.leastsq, to estimate various parameters of the PR2 using a bundle adjustment like framework.


This package is still unstable, and does not have a released API.


This stack is still very experimental, and we have not standardized (let alone even reviewed) many of the internal APIs in this stack. However, it seems that many people are still interested in porting this unstable code to other robot platforms. We are providing the information below to help others port this stack to their robots, even though it is an unstable stack.

Launching the Estimator

The main goal of the pr2_calibration_estimation package is to provide a reconfigurable nonlinear optimizer for estimating calibration parameters for some defined robot. For the PR2, the estimator is launched using pr2_calibration_launch/estimate_params/config_pr2_beta/estimate_pr2_beta.launch. This launch file loads the estimation configuration onto the parameter server and then launches the estimator (

Estimator Command Line Usage [bagfile] [target_dir]

  • [bagfile] - Path to the bag that contains calibration samples. These messages must be of type calibration_msgs/RobotMeasurement under the topic “/robot_measurement”

  • [target_dir] - Directory at which to store intermediate data files after each calibration step

Estimation Configuration (Parameter Server)

The estimator looks for it's configuration in the /calibration_config namespace. The PR2's configuration is stored in pr2_calibration_launch/estimate_params/head_then_arms_params.launch

  • initial_system - yaml blob that defines all of the robot's primitives

  • sensors - Every parameter in this namespace must be a yaml blob that defines sensors on the robot.

  • cal_steps - Defines each of the calibration steps. Each step is defined by a namespace within cal_steps, and the steps are executed in alphabetical order by namespace names.

    • use_cov (bool) - Specify whether or not to use measurement covariances during this step. If True, then covariances are used

    • free_params - yaml blob that defines which parameters are being estimated during this step

    • sensors - list of sensor_ids that defines which sensors to use during this calibration step. Any sensor specified must have a full definition in the higher level sensors namespace.

  • output_filename - Identifier for the results of this calibration step. This name is prepended to the step's results, and stored in the estimator's previously defined [target_dir]

The Calibration Bagfile

The estimator relies on calibration samples in the specified bagfile in order to run the calibration. These messages must be of type calibration_msgs/RobotMeasurement under the topic /robot_measurement. Below is a description of all of the fields, and what they mean:

  • sample_id - This simply a string identifier to help the user understand where this calibration sample came from. It doesn't even have to be unique across samples

  • target_id - Specifies which target the sensors in the sample are looking at. This must correspond to the name of a checkerboard primitive. For the PR2, this can be either small_cb_4x5 or large_cb_7x6.

  • M_cam - Stores data from a single camera measurement

    • header - Not Used

    • sensor_id - Name of the camera sensor. This must correspond to a camera primitive defined for the robot. (See #Rectified_Cameras)

    • image_points - Stores the corners of the detected checkerboard target. This list is ordered, and must correspond to the same ordering of corners as openCV's checkerboard detector would detect the checkerboard specified in target_id.

    • cam_info - Store the intrinsics for this camera

  • M_laser - Stores data for a tilting laser sensor

    • header - Not used

    • laser_id - Name of the tilting laser. Must correspond to a tilting laser primitive defined for the robot. See #Tilting_Lasers-1.

    • joint_points - Each joint point corresponds to a tilt, bearing, and range for a single detected corner.

  • M_chain - Stores data for a specific kinematic chain

    • header - Not used

    • chain_id - Name of the chain. Must correspond to a chain primitive defined for the robot. See #DH_Chains

    • chain_state - Store the state of the joints that are a part of this chain. Must be ordered from root to tip of the chain and cannot have any joints that don't correspond to this chain

Defining the Robot's Primitives

The calibration estimator relies on a yaml file that stores the configuration of the robot's various kinematic and sensor primitives that we may want to estimate. For the PR2, this file is pr2_calibration_launch/estimate_params/config_pr2_beta/system.yaml. The currently support primitives are dh_chains, tilting_lasers, transforms, and rectified cameras. Although not necessarily a "robot primitive", checkerboard intrinsics are also defined in this file.

DH Chains

A DH Chain primitive is used to represent a kinematic linkage using Denavit-Hartenberg parameters. Each DH Chain primitive must be included as a dictionary element under the dh_chains section of the config file. The parameters defined below are used in pr2_calibration_estimation/


   - [   0,  -pi/2, .1, 0      ]    # r_shoulder_pan_joint
   - [ pi/2,  pi/2,  0, 0      ]    # r_shoulder_lift_joint
   - [   0,  -pi/2,  0, .4     ]    # r_upper_arm_joint
   - [   0,   pi/2,  0, 0      ]    # r_elbow_flex_joint
   - [   0,  -pi/2,  0, .321   ]    # r_forearm_roll_joint
   - [   0,   pi/2,  0, 0      ]    # r_wrist_flex_joint
   - [   0,    0,    0, 0      ]    # r_wrist_roll_joint
     joint_angles: [0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001]
   gearing: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
  • dh - Each list item under dh stores the 4 DH parameters for a link. They are ordered as [theta, alpha, a, d]. In the example above, there are 7 links.

  • cov/joint_angles - Defines a standard deviation (in radians) for each joint angle. This list must be the same length as the dh parameter list.

  • gearing - Defines a prescalar for each joint angle, before applying forward kinematics. This list must be the same length as the dh parameter list. In general, these values are known extremely well (since you can count the gear teeth in the transmission). However, it is important to estimate these parameters when dealing with belts and drums.

Note that we have not defined where this kinematic chain is rooted on the robot. This is done later, when defining sensors.


A transform primitive is a full 6 dof transformation in a robot system. As defined here, it is very unclear where and how these transforms attach to actual robot frames. Later, when we define sensors, we can attach these transforms before and after dh chains.

6 Examples:

  head_plate_frame_joint:    [   .0232, .0, .0645, 0, 0, 0]
  double_stereo_frame_joint: [ 0, 0, .003, 0, 0, 0]
  wide_stereo_frame_joint:   [ 0, .03, .0305, 0, 0, 0  ]
  narrow_stereo_frame_joint: [ 0, .06, .0305, 0, 0, 0  ]
  wide_stereo_optical_frame_joint:    [0, 0, 0, -1.20919, 1.20919, -1.20919]
  narrow_stereo_optical_frame_joint:  [0, 0, 0, -1.20919, 1.20919, -1.20919]

Each transform is defined by a list with 6 elements:

  • Elements 0:2 - Translation terms. Elements 0,1,2 correspond to an x,y,z translation vector

  • Elements 3:5 - Rotation terms. Elements 3,4,5 correspond to an x,y,z rotation vector. The direction of the vector is the axis of rotation, and the magnitude of the rotation vector is the rotation angle. See Wikipedia: Rotation Representation

    • Why are we using this rotation representation? We could very well have used rotation matrices or quaternions. Both of these representations introduce constraints on the system, which we were hoping to avoid. Ideally, we would completely avoid optimizing in a specific rotation space, and instead, operate directly on the rotations themselves, using incremental rotations. See Skew Parameters

Tilting Lasers

The tilting laser primitive is used to represent a laser rangefinder (such as the UTM-30lx) that is actuated.


    before_joint: [ .09893, 0,  .227, 0, 0, 0]
    after_joint:  [  0, 0,  .03,  0, 0, 0]
    gearing: 1.0
      bearing: 0.0005
      range: 0.005
      tilt: 0.0005


  • before_joint - Transform from the system origin to the joint axis of the tilting platform. The tilting platform rotates around the y-axis of the resulting frame

  • after_joint - Transform from the rotating axis on the tilting platform to the optical center of the laser rangefinder. We assume that a a 0 degree bearing measurement from the laser rangefinder is along the x axis of the resulting frame, and a 90 degress bearing measurement is along the y axis of the resulting frame.

  • gearing - Prescalar for the tilting joint, before applying forward kinematics. Similar to the gearing element in the dh chain, except we only have 1 joint, and thus don't need a list.

  • cov

    • bearing - StDev for the bearing angle for the tilting laser (in radians)

    • range - StDev for range measurement for the tilting laser (in radians)

    • tilt - StDev for tilting angle for the tilting laser platform (in radians)

Rectified Cameras

The recified camera primitive is used to represent a monocular camera that has already been rectified. We assume that the distortion correction is perfect, and we only have estimate parameters associated with the pinhole camera model.


    baseline_shift: 0.0
    f_shift: 0.0
    cx_shift: 0.0
    cy_shift: 0.0
    cov: {u: 0.125, v: 0.125}
  • baseline_shift - Value to add to the -baseline*Tx term in the projection matrix (camera_info.P[3])

  • f_shift - Value to add to the focal length term in the projetion matrix (camera_info.P[0] & camera_info.P[5])

  • cx_shift - Value to add to the cx term in the projetion matrix (camera_info.P[2])

  • cy_shift - Value to add to the cy term in the projetion matrix (camera_info.P[6])

  • cov

    • u - StDev of uncertainty along u axis of the image (in pixels)

    • v - StDev of uncertainty along v axis of the image (in pixels)


Although the checkerboards themselves aren't really a part of the robot, they still have parameters that need to be defined and could be estimated. Thus this file becomes a convenient location to define them.

2 Examples:

    corners_x: 4
    corners_y: 5
    spacing_x: .025
    spacing_y: .025
    corners_x: 7
    corners_y: 6
    spacing_x: .108
    spacing_y: .108
  • corners_x - Number of corners along the x-axis of the checkerboard. This is an integer parameter, and will not be changed by the estimator.

  • spacing_x - The x-axis spacing between checkerboard corners.

corners_y and spacing_y have the same semantics as corners_x and spacing_x

Defining the Robot's Sensors

Once we have a set of primitives defined for the robot, we need to define a set of sensors that are attached to the robot. The sensors simply string various primitives together into actual measurement models. There currently are three types of sensors: camera_chains, tilting_lasers, chains.

The sensors used in the PR2 estimation are defined at pr2_calibration_launch/estimate_params/config_pr2_beta/sensors.yaml. This is a yaml file broken down by sensor type. For each sensor type, there is a list of sensors.

Camera Chain

This sensor is used to define a camera that is attached to an actuated linkage. The standard example of this is a camera on a pan-tilt platform:

  - camera_id: forearm_right_rect
    sensor_id: forearm_right_rect
      before_chain: [r_shoulder_pan_joint]
      chain_id:     right_arm_chain
      after_chain:  [r_forearm_roll_adj, r_forearm_cam_frame_joint,
      dh_link_num:  4
  • sensor_id - Unique identifier for this sensor

  • camera_id - Monocular camera being used for this sensor. Must match a rectified camera primitive

  • chain - (Collectively define the linkage that the camera is attached to)

    • before_chain - Ordered list of transforms to apply before attaching DH Chain. Must all be transform primitives

    • chain_id - DH chain primitive to attach to the end of the before chain tranforms.

    • dh_link_num - Define how many DH links to use. In many cases, we don't want to use the entire DH Chain. In this example, the forearm camera is attached to the DH link indexed at 4 (which is the forearm_roll_link).

    • after_chain - Transforms to apply after applying the DH chain. The camera is then attached to the end of these transforms. We are assuming a “Z Forward, X Right, Y Down” camera

This sensor will only be used with a sample (calibration_msgs/RobotMeasurement) with the following requirements:

  • The message must have a CameraMeasurement that matches the sensor's camera_id

  • The message must have a ChainMeasurement that matches sensor's chain_id


A chain sensor is a sensor that can hold a checkerboard.


  - sensor_id:    left_arm_chain
    before_chain: [l_shoulder_pan_joint]
    chain_id:     left_arm_chain
    after_chain:  [left_arm_tip_adj, left_arm_cb]
    dh_link_num:  6
  • sensor_id - Unique identifier for this sensor

  • The before_chain, chain_id, and after_chain have the same meaning as in the camera_chain. The checkerboard target is attached the the kinematic chain after after_chain transforms.

This sensor will only be used with a sample (calibration_msgs/RobotMeasurement) with the following requirements:

  • The message must have a ChainMeasurement that matches sensor's chain_id

  • The message's chain_id must match the sensor's chain_id. This ensures that the target is in fact being held with the specified chain.

Tilting Lasers

All the information that we need about a tilting laser is already in robot primitive definitions. Thus, all we need to do is specify the name of the tilting laser primitive, along with a unique sensor_id.


    - sensor_id: tilt_laser
      laser_id:  tilt_laser

This sensor will only be used with a sample (calibration_msgs/RobotMeasurement) with the following requirements:

  • The message must have a LaserMeasurement that matches sensor's laser_id

Defining Which Parameters to Estimate

For each estimation step, we need to specify which parameters we want to estimate. This is done using a yaml file that looks extremely to the primitives definition file, except that instead of having values for all the parameters, it is filled with 0s and 1s. All parameters with 1s will be estimated. These are defined for the pr2 as pr2_calibration_launch/estimate_params/config_pr2_beta/free_*.yaml.

How the estimation works

The main thing that the package does is take all of these previously specified configuration files and generate a Jacobian based on the measurements in the previously collected calibration bagfile (cal_measurements.bag). The following diagram gives an overview of what this Jacobian looks like:



There is one blockrow for each calibration_msgs/RobotMeasurement on the robot_measurement topic. Each of the messages is called a sample. For each sample, there are multiple sensor measurements inside, where each sensor is its own sub-blockrow. Each sensor has multiple rows, where the number of rows is determined based on the number of feature points detected, and the type of measurement. For instance, a tilting laser has 3 rows per feature point (cartesian x,y,z) and a camera has 2 rows per feature point (image u,v).


The columns are separated into two sections: system parameters and checkerboard poses.

  • System parameters

    • This section is based off of the system.yaml file passed into the estimation. This contains all of various parameters that define the robot system: transforms, dh parameters, tilting laser kinematics, stereo baselines, etc. These columns answer the question of "If I change parameter X in my system, how does the error residual of my samples change?".

  • Checkerboard Poses

    • This section defines a checkerboard pose for each robot measurement. This answers the question of "If I move checkerboard J, how does the error residual of my samples change?" Note that this part of the Jacobian is block diagonal. That is, altering the 1st checkerboard pose does not affect the 2nd sample.

Wiki: pr2_calibration_estimation (last edited 2011-05-31 21:06:34 by VijayPradeep)