Dynamic Modelling and Coordinated Control for Autonomous Path Tracking of Agricultural Wide-Span Implement Carriers

Abstract

Agricultural wide-span implement carriers (WSICs) are controlled traffic farming platforms that reduce soil compaction and improve field-operation efficiency through the coordinated motion of two supporting vehicles connected by a long-span truss. This research presents an original, applied systems-engineering integration of vehicle-truss dynamic modelling, control design, adjoint-curve-based leader-follower synchronization, simulation, and experimental evaluation for this configuration. A dynamic model was formulated for the supporting vehicles of the coupled vehicle-truss system, incorporating longitudinal and lateral motion, yaw dynamics, tire-ground interaction, and loads transmitted quasi-statically through the truss and implement. The model served as the basis for a combined control strategy using incremental model predictive control (MPC) for steering, with adaptive weighting evaluated in simulation, and proportional-integral-derivative (PID) control for longitudinal velocity. Inter-vehicle coordination was achieved through a follower synchronization controller based on offset-error regulation, with first-order error dynamics and a Lyapunov-based stability analysis. The strategy was evaluated through MATLAB/Simulink and CarSim co-simulations and experimentally validated on a small-scale WSIC platform equipped with real-time kinematic Global Positioning System (RTK-GPS) receivers, inertial measurement units, and wireless communication modules.

The dynamic-model-based strategy was compared with a kinematic approach under demanding simulated conditions, including curved and reverse motion, higher speeds, implement resistance, and initial offset errors, with differences assessed against sensor-based thresholds and application-specific error bounds. On curved paths, the strategy reduced steady-state lateral error from ±0.20 m to ±0.12 m, meeting the ±0.15 m criterion, and reduced distance-based integral absolute error (IAE) for lateral tracking and offset by approximately 46% and 50%, respectively. In curved reverse motion, lateral-error IAE decreased by 34-36%. In straight-line simulations, the principal differences between the controllers were in offset regulation and recovery from a large initial offset. The combined MPC-PID strategy also reduced lateral-error IAE by about 28% relative to unified MPC during curved tracking. Small-scale experiments with fixed MPC weights demonstrated the strategy's feasibility: in two-vehicle cooperation, steady-state lateral errors were 0.02-0.03 m lower than those obtained with the kinematic controller. On sinusoidal paths, offset-error and separation-error IAEs decreased by 33-35%, while steady-state orientation error was approximately 0.02 rad larger. Experimental tracking errors exceeded simulated errors, owing mainly to the slower measured response of the follower velocity loop, together with unmodelled hardware nonlinearities, GPS fluctuations, and surface irregularities. Overall, incorporating vehicle dynamics, predictive steering, and explicit synchronization design provides an effective, experimentally validated foundation for WSIC guidance and future full-scale development.