LQR Control Methods for Trajectory Execution in Omnidirectional Mobile Robots

Abstract

Omnidirectional mobile robots present the advantage of being able to move in any direction without having to rotate around the vertical axis first. While simple straight-line paths are relatively easy to achieve on this kind of robots, in many highly dynamic applications straight-line paths might just not be a feasible solution. This may be the case because of two main reasons: (1) there may be static and moving obstacles between the initial and desired final position of the robot, and (2) the dynamic effects of the inertia of the robot may force it to execute a curved path. This chapter will address these two situations and present a segment-wise optimal solution for the path execution problem which is based on a Linear-Quadratic Regulator. It must be emphasized that, rather than attempting to perform an exact path tracking, the approach presented here deals with the problem of visiting a sequence of target circular regions without specifying the path that will connect them. The freedom given to the connecting paths brings the opportunity for optimization. In fact, the path that the robot will take from one circular region to the next will emerge as the solution of an optimal control problem, hence the term segment-wise optimal solution. Omnidirectional wheels have the property of sliding laterally with almost zero force while providing full traction in the rolling direction. This effect is achieved by adding a set of smaller wheels around the periphery of the main wheel, as depicted in Fig. 1.