Non-Parametric Calibration of the Inverse Kinematic Matrix of a Three-Wheeled Omnidirectional Mobile Robot Based on Genetic Algorithms

Abstract

Odometry is a computation method that provides a periodic estimation of the relative displacements performed by a mobile robot based on its inverse kinematic matrix, its previous orientation and position, and the estimation of the angular rotational velocity of its driving wheels. Odometry is cumulatively updated from tens to hundreds of times per second, so any inaccuracy in the definition of the inverse kinematic matrix of a robot leads to systematic trajectory errors. This paper proposes a non-parametric calibration of the inverse kinematic (IK) matrix of a three-wheeled omnidirectional mobile robot based on the use of genetic algorithms (GA) to minimize the positioning error registered in a set of calibration trajectories. The application of this non-parametric procedure has provided an average improvement of 82% in the estimation of the final position and orientation of the mobile robot. This is similar to the improvement achieved with analogous parametric methods. The advantage of this non-parametric approach is that it covers a larger search space because it eliminates the need to define feasible physical limits to the search performed to calibrate the inverse kinematic matrix of the mobile robot.