Implementation of Linear Quadratic Regulator Algorithm for Path Tracking on Holonomic Service Robot

A navigation system is a crucial part of the autonomous service robot technology. Navigation system using holonomic drives on the omnidirectional wheels improves robot maneuver to achieve full planar mobility without changing its orientation. However, a drawback of this type of drive exists due to the different speed vector resultant that degrades the robot movement efficiency. To tackle this problem, it is necessary to design optimal path tracking control system to improve efficiency of the robot movement. The path tracking approach in our study is determined by waypoints (a set of multiple waypoints). Our proposed control system consists of a pure pursuit algorithm as a reference point selection, a Linear Quadratic Regulator (LQR) as a position controller, and a Proportional-Integral-Derivative (PID) controller as the motor speed controller. This method has been tested under various cases representing the robot task as a service robot (point-to-point movement and path tracking with various trajectories). Moreover, the system has been evaluated with different control parameters. Based on the simulation and implementation results, LQR for path tracking performs well to solve the service robot task. A promising result is presented with the path length of 19.33 m. The RMSE, maximum error, and steady-state error are 2.52 $\text{cm}, 6.13 ~\text{cm}$, and 4.72 cm respectively. Also, our results demonstrate the efficiency of LQR controller which are 33.94% and 18.20% more efficient than the PD controller and PID controller respectively.