The inverse kinematics of mobile manipulators is a challenging problem due to the high degree of kinematic redundancy added by the coupling of the mobile platform and the manipulator. Some different approaches have been proposed to solve this problem, but most of them are either complex in terms of modelling and matrix calculation, with high computational cost and even with singularity problems, or slow in terms of convergence. This paper proposes a new approach for inverse kinematics of mobile manipulators based on the algorithm FABRIK. This new method, named M-FABRIK, has as main advantages the simplicity to implement, a fast convergence and a low computational cost, allowing real-time applications. Furthermore, this solution allows the robot to be positioned according to various criteria, such as decreasing convergence time, avoiding contact with obstacles, avoiding joint angle limits, increasing robot manipulability or even decreasing joint effort, besides avoiding matrix inversion and being robust to singularities. The proposed approach is illustrated by simulation considering a 5 DOF manipulator mounted on an omnidirectional base for a path-tracking task in different environments, including obstacles. A comparison between the proposed approach and classical methods is also presented.
