ENMPC Trajectory Tracking Method for Orchard Wheeled Robots Based on Disturbance compensation

Autonomous wheeled robots operating in orchard and forestry environments are required to achieve accurate trajectory tracking under complex and uncertain working conditions. In practical agricultural scenarios, external disturbances and model parameter uncertainties caused by uneven terrain, soft soil, and frequent steering maneuvers significantly degrade control performance, particularly when wheel slip and steering-induced slip occur. To address these challenges, this paper proposes a prediction-accuracy-enhanced explicit nonlinear model predictive control (ENMPC) algorithm integrated with a nonlinear disturbance observer (NDOB) for autonomous orchard wheeled robots. An extended kinematic model is first established by incorporating typical disturbance effects in agricultural field environments, including wheel slip and steering slip, into an ideal kinematic framework. Based on this model, the trajectory tracking error dynamics over a finite receding horizon are approximated using a Taylor series expansion. Under the assumption that external disturbances are measurable, an explicit analytical control law of the ENMPC is derived offline, eliminating the need for online nonlinear optimization. As a result, the proposed controller significantly reduces computational complexity and ensures deterministic real-time performance, which is critical for embedded agricultural robotic systems with limited computing resources. To enhance robustness against time-varying disturbances and modeling uncertainties, a nonlinear disturbance observer is designed to estimate and compensate for external disturbances in real time. Unlike conventional feedforward compensation strategies, where disturbance estimates are treated as additional corrective inputs, the proposed approach directly integrates the disturbance estimation into the output prediction model of the ENMPC. This unified formulation enables the predicted system outputs to explicitly account for disturbance effects within the prediction horizon, thereby achieving zero steady-state offset in trajectory tracking. The closed-loop stability of the resulting NDOB-ENMPC controller is rigorously analyzed, and stability is formally guaranteed under bounded disturbance conditions. Simulation studies are conducted to evaluate the performance of the proposed method under multiple disturbance scenarios, including constant disturbances, time-varying disturbances, and combined slip effects. The results demonstrate that the NDOB-ENMPC algorithm effectively suppresses disturbance influences and achieves superior trajectory tracking accuracy and robustness compared with conventional nonlinear model predictive control schemes. Field experiments are further performed using an autonomous orchard wheeled robot operating in a forest grassland environment. Experimental results show that, compared with a standard NMPC algorithm, the proposed NDOB-ENMPC reduces the maximum absolute lateral and longitudinal tracking errors by 39.42% and 49.01%, respectively, while the corresponding mean absolute errors are reduced by 29.45% and 44.01%. In addition, the average computation time is reduced by 97.47%. Compared with a feedforward-compensated NMPC algorithm, the proposed approach reduces the maximum absolute lateral and longitudinal errors by 17.86% and 37.64%, respectively, and the mean absolute errors by 16.41% and 20.59%, while achieving a 97.57% reduction in average computation time. These results indicate that the proposed NDOB-ENMPC algorithm satisfies the stringent requirements of real-time implementation, high tracking accuracy, and robustness for autonomous navigation of wheeled robots in complex orchard environments. The proposed method provides an effective and computationally efficient solution for deploying optimal control strategies on low-cost agricultural robotic platforms and offers strong potential for practical applications in intelligent orchard and forestry operations.