Optimal Control-Based Algorithm Design and Application for Trajectory Tracking of a Mobile Robot with Four Independently Steered and Four Independently Actuated Wheels

Abstract

This paper deals with the synthesis and implementation of a controller for asymptotic tracking of the desired trajectory of a mobile robot. The mobile robot used for the experimental validation has eight motors with an inner control loop. Four steering actuators are controlled using position controllers and four driving actuators are controlled using velocity controllers. A complex robot kinematic model is converted into a control-oriented linear time-varying system, which is then used to design a time-varying control law that minimizes the quadratic optimality criterion. In contrast to conventional methodologies for solving the corresponding Riccati differential equations, a computational approach that explicitly determines the time-varying controller matrix by employing recurrent matrix computations is proposed. Mobile robot control inputs (linear velocity, steering angles and steering velocities) are forwarded to the steering and driving actuators with properly tuned position and velocity controllers using an inverse kinematic model of the mobile robot. The obtained control law is evaluated on an experimental set-up of a real mobile robot system. The controller is implemented using the Robot Operating System.

Keywords

• four-wheel steered and actuated mobile robot
• time-varying linear quadratic control
• recursive matrix relations
• experimental validation