Design of a Linear Optimal Controller for Mobile Robots Using Distance Normalization Factor

Abstract

Precise and reliable trajectory planning of mobile robots remains a fundamental challenge due to distance-dependent gain sensitivity, dynamic constraints, and nonlinearities in real environments. Conventional kinematic controllers and fixed-reference distance ANN approaches often degrade in performance when initial conditions (initial position and posture) vary, resulting in excessive travel time or violations of velocity and angular velocity limits. To address this limitation, this paper proposes a Distance Normalization Factor-based Artificial Neural Network (DNF-ANN) trajectory-planning controller that generalizes quasi-optimal control gains across arbitrary initial positions and postures. In particular, the proposed controller aims to compute quasi-optimal gains immediately at the start of motion while satisfying physical velocity and angular-velocity constraints. The method introduces a distance normalization factor to transform gains optimized at a reference distance(ρref), combined with a nonlinear compensation scheme to prevent angular velocity constraint violations. A genetic algorithm generates optimal gain datasets, which an ANN learns for real-time inference before the robot starts moving. Simulation results demonstrate that the proposed DNF-ANN strictly satisfies dynamic constraints and achieves benchmark-level performance comparable to GA re-optimization under identical initial conditions, with only a 0.26 s average difference in travel time. These findings confirm that the proposed controller ensures stable and quasi-optimal operation under diverse initial conditions. The DNF-ANN framework is suitable for mobile robot applications that require near-real-time gain computation during the pre-departure planning stage, such as logistics, service robotics, and industrial automation.