Systematic robustness analysis of least squares mobile robot velocity estimation using a regular polygonal optical mouse array

Abstract

This paper presents the robust velocity estimation of an omnidirectional mobile robot using a regular polygonal array of optical mice that are installed at the bottom of a mobile robot. First, the velocity kinematics from a mobile robot to an array of optical mice is derived, from which the least squares estimation of the mobile robot velocity is obtained as the simple average of the optical mouse velocity readings. Second, it is shown that a redundant number of optical mice contributes to the robustness of the least squares mobile robot velocity estimation against both measurement noises and partial malfunction of optical mice. Third, the sensitivity analysis of the least squares mobile robot velocity estimation to imprecise installation of optical mice is made, from which a practical method of optical mouse position calibration is devised. Finally, some experimental results using commercial optical mice are given to demonstrate the validity and performance of the proposed mobile robot velocity estimation.

Isotropic Optical Mouse Placement for Mobile Robot Velocity Estimation

“…From (2) and (3), the velocity kinematics of a mobile robot with an array of N optical mice can be obtained by [1, 4–6, 14, 16, 17]…”

Optimal optical mouse placement for mobile robot velocity estimation

“…For smaller value of        , the geometrical center of  optical mice needs to be closer to the center . Without restriction on installation,  optical mice should be placed in a regular polygonal array centered at the center , and the size of a regular polygon should be made large as much as possible [6].…”

“…Considerable efforts have been made to use optical mice for the velocity estimation of a mobile robot [3][4][5][6][7][8][9][10][11]. Optical mice installed at the bottom of a mobile robot are free from aforementioned problems of typical sensors, such as wheel slippage, line of sight, and heavy computation.…”

“…The positions of two optical mice were determined to minimize the sum of the maximum absolute errors of the mobile robot velocity estimation, caused by the noisy velocity measurements of optical mice [3]. A regular polygonal array of optical mice was proposed, for which the mobile robot velocity estimation can be obtained as the component-wise average of the velocity measurements of optical mice [6]. With possible structural restriction in installation, an analytic treatment for the optimal placement of optical mice was presented [11].…”

Passive Location Using TDOA Measurements from Compass Satellite Illuminators

“…Recently, by exploiting a least-squares (LS) principle [3], several closed form algorithms have been proposed for the TDOA based location system [4,5]. In those algorithms, the location problem has been reformulated mathematically as a set of linear equations in matrix form Ax = b, where the system matrix A and data vector b are the given data, and x is unknown.…”