Modelling an arm's spatially correlated biases: an application to camera calibration for teleoperation

Calibration of the extrinsic and intrinsic parameters of cameras viewing the workspace of a teleoperated robot arm is a necessary step in the recovery of metric information for transmission to the operator. In this paper, we develop an algorithm that uses the robot slave manipulator to generate the calibration pattern of points in three dimensions which define the world frame. These points are used, along with their associated image positions, as measurements in a maximum likelihood estimation of the calibration parameters. However, the algorithm does not assume that the robot generates perfect world positions. Instead they are optimised using a model for covariance which respects the physical attributes of the robot arm and its linkages. Errors in world positions are actually correlated biases rather than stochastic noise, and so they are assigned a covariance that is a function of position and that encodes a coherence length over which relative position measurements are accurate. Experiments are presented which compare the calibration results with the camera parameters obtained using a conventional calibration grid, and which validate the proposed covariance model.