Application of Iterative LQR on a Mobile Robot With Simple Dynamics

TL;DR

The paper tackles trajectory tracking for a differential-drive mobile robot with nonholonomic constraints using optimal control. It contrasts the classic LQR with the iterative iLQR, formulating a quadratic-cost framework and applying forward-backward passes to handle nonlinear dynamics. Through Matlab/Simulink simulations, it shows that iLQR can achieve stable trajectories with slightly reduced tracking error compared to LQR, while highlighting sensitivity to initialization and waypoint density. The work demonstrates the applicability of iLQR to simple mobile robot dynamics and suggests future work on update-rate refinements and continuous-time comparisons.

Abstract

The aim in this paper is to apply the iLQR, iterative Linear Quadratic Regulator, to control the movement of a mobile robot following an already defined trajectory. This control strategy has proven its utility for nonlinear systems. As follows up, this work intends to concertize this statement and to evaluate the extent to which the performance is comparatively improved against the ordinary, non-iterative LQR. The method is applied to a differential robot with non-holonomic constraints. The mathematical equations, resulting description and the implementation of this method are explicitly explained, and the simulation studies are conducted in the Matlab and Simulink environment.

Figures (5)

• Figure 1: Differential Mobile Robot Parameters, courtesy of Yacine Ahmine's paper [6].
• Figure 2: Schematisation of the iLQR Working Principle.
• Figure 3: Schematizing of the LQR approach.
• Figure 4: Resulting Path with LQR approach.
• Figure 5: Resulting Path with iLQR approach.