Linear Algebra Applied to Kinematic Control of Mobile Manipulators

This paper is focused in linear algebra theory applied to control of mobile manipulator robots. In order to design the control algorithm, the kinematic system is approximated using numerical methods. Then, the optimal control actions are obtained through linear algebra approach. The structure of the controller consists in two solutions; a particular solution that allow following the desired trajectory and a homogeneous solution that allow performing secondary objectives as maximum manipulability and avoid static obstacles. In addition, the stability analysis is demonstrated through linear algebra concepts where it is shown that the tracking error tends asymptotically to zero. Finally, experimental results show the effective of proposed control algorithm over the mobile manipulator robot AKASHA.