Nonlinear Model Predictive Control-Based Reverse Path-Planning and Path-Tracking Control of a Vehicle with Trailer System

Reverse parking of a vehicle with trailer is a challenging task to complete for human drivers due to its articulated structure, unstable reverse-motion behaviors and unintuitive steering responses. This paper proposes a compact, trailer-centric nonlinear model predictive control (NMPC)-based automation routine that integrates local motion generation and feedback control into a single receding-horizon framework, without requiring a separately planned reference path or a dedicated path-tracking controller. The trailer unit is represented as a virtual standalone vehicle, and its motion requirements are mapped to the vehicle unit inputs via inverse kinematics. This allows trajectory prediction and tracking objective to be represented only with trailer states, hence reducing the dimensions of the horizon-stacked state and weighting matrices compared to using the full vehicle-trailer formulation. The proposed controller is implemented as a single-shooting nonlinear program (NLP) and supports a three-staged maneuver sequence to obtain an improved final parking configuration. Simulation results demonstrate successful vehicle-trailer parking maneuvers, while hardware-in-the-loop (HIL) results further illustrate that online NMPC computation times can remain within the real-time sampling deadline, indicating that the proposed NMPC framework can offer a practical receding-horizon automation routine for vehicle-trailer reverse parking tasks.