Application of a Time-Varying Linear Quadratic Controller for Trajectory Tracking of a Four-Wheel Mobile Robot with Independent Steering and Drive

This paper is concerned with the design of a controller for trajectory tracking of a mobile robot with four steerable and four independently driven wheels (4WIS4WID). Taking into account the appropriate assumptions, the kinematic equations of the robot are converted into three-input, two-chain, single-generator chained form. After that, for a small perturbations around the reference trajectory, an approximate linearization of the chained form is performed. This procedure led to the form of a time-varying system suitable for the synthesis of a time-varying linear control law according to the quadratic optimality criterion. The version of the control law which gives the best results is determined by computer simulations in a mathematical software package MATLAB (MathWorks, Natick, MA, USA). The obtained control law is applied to the experimental set-up of a mobile robot developed at the Regional Center of Excellence for Robotic Technology (CRTA). The controller is implemented using Robot Operating System (ROS) and experimental measurements are performed using the OptiTrack system.