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Abstract—With the increasing miniaturization of robotic devices, some actuators are not provided with absolute position sensing, thus making the state of the system unknown at startup. In this paper we present a vision based method for the automatic calibration of serial pan-tilt kinematic struc-tures with a perspective camera on the end-effector. Examples of such systems are surveillance cameras and humanoid robot heads. The method is based on prospective motions of one joint in the kinematic chain to induce image motion in the camera. The analysis of the induced homography allows the computation of the angle of the other joint. The method can be iterated on more axes to calibrate longer serial chains composed of rotational joints. The method requires calibrated cameras, but runs completely automatic. We have implemented and validated the method in a small humanoid 21950
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robot head.
I. INTRODUCTION
Whenever the motors in robotic system are not provided
with absolute sensors, it is not possible to know the state
of the robot at startup. This happens frequently because
most motors are equipped with incremental encoders as the
main feedback sensor, lacking absolute position sensing.
Therefore, a procedure is necessary to set the robot to a
known initial state, also dented its home, or zero position.
To address this problem, it is usual to equip the robot
with limit switches, or homing switches, that detect when
the axes are in particular angular positions. However, due
to miniaturization constrains, it may not be possible to
install such sensors in the robot. Another possibility is to
drive the axes to a mechanical stop and monitor the motor
current. When the current exceeds a certain value, then
the motor has reach the mechanical limit, whose angle
can be known a priori. However, this procedure adds a
source of physical stress in the system and may damage
the mechanical components in the long term.
Even when the above strategies are feasible, they require
the careful placement of limit and home switches, and a
precise measurement of the mechanical limits. Addition-
ally, when attaching the cameras to the end-effector, there
are always some misalignments that may degrade the initial
calibration procedure.
In this paper we propose a solution to this problem.
We present a self-calibration procedure, at start time, that
does not require absolute sensors or the need to drive the
system to mechanical hard stops. Instead, it performs small
prospective motions in the robot joints and observes the
This work was supported by the European Commission, Project IST-
004370 RobotCub, and by the Portuguese Government - Fundac¸ ˜ ao
para a Ciˆ encia e Tecnologia (ISR/IST plurianual funding) through the
POS Conhecimento Program that includes FEDER funds, and through
project BIO-LOOK, PTDC / EEA-ACR / 71032 / 2006.
B. Tworek is with Faculty of Electrical Engineering, Automatics,
Computer Science and Electronics, AGH University of Technology and
Science, Krakow, Poland bartosz.tworek@gmail.com
A. Bernardino and J. Santos-Victor are with the Institute for
Systems and Robotics, Instituto Superior T´ ecnico, Lisboa, Portugal
falex,jasvg@isr.ist.utl.ptimage motion induced in the camera. If the scene is static
and scene objects are sufficiently distant from the camera,
the induced image motion only depends on the prospective
rotation and the angle between the camera’s optical axis
and the rotation axis. By iterating this procedure in the
several robot axes, it is therefore possible to automatically
determine the wake-up state of the system.
We address explicitly the case of pan-tilt kinematic
structures because they are very common both on surveil-
lance cameras and in robot heads. We implement the