Trajectory Tracking Control of Autonomous Mobile Robots via Linearized Model Predictive Control: Theory and Simulation Validation

Abstract

Accurate trajectory tracking is a fundamental requirement for autonomous mobile robots (AMRs) operating in complex environments. This paper addresses the tracking control problem for AMRs subject to kinematic constraints. A linearized model predictive control (LMPC) framework is proposed to effectively reduce trajectory tracking errors while ensuring smooth control inputs and high computational efficiency. First, the nonlinear kinematic model of the robot is derived and linearized around the reference trajectory using Taylor series expansion to obtain a discrete-time linear error dynamic model. Second, the tracking problem is formulated as a constrained finite-horizon optimization problem, which is transformed into a standard quadratic programming (QP) form to guarantee computational efficiency. Extensive simulations are conducted using a complex butterfly-shaped trajectory characterized by continuous curvature variations. The results demonstrate that the proposed controller achieves high tracking accuracy with centimeter-level position errors and generates feasible control inputs that strictly satisfy constraints, thereby demonstrating the robustness and effectiveness of the proposed controller.