Scale-invariant isotropy of an optical mouse array for mobile robot velocity estimation

This paper presents the scale-invariant isotropy analysis of an optical mouse array for the mobile robot velocity estimation. First, with the characteristic length introduced, the velocity kinematics of a mobile robot with optical mice is described. Then, the uncertainty ellipsoid is obtained to represent the error characteristics of the optical mouse based mobile robot velocity estimation, and the isotropy index is defined as the closeness of the uncertainty ellipsoid to a sphere. Next, using the defined isotropy index, the conditions for the anisotropic, isotropic, and regular optical mouse arrays are derived in terms of the installation positions of optical mice, along with the corresponding characteristic lengths.