Cooperative control model for hybrid rice seed production pollination drone swarm based on PINN-DMPC

A cooperative operation can often be required for the accurate synchronization and pollination in the mechanical rope-impact pollination for hybrid rice seed production. In this study, a cooperative pollination control was proposed for the machine group using the Physics-Informed Neural Network (PINN). Each vehicle was equipped in the pollination unit with an independent Distributed Model Predictive Controller (DMPC). The independence and flexibility of each vehicle were realized to reduce the complex and nonlinear constraints of the system during operation in farmland scenarios. Kinematic information was integrated into the PINN network in the form of partial differential equations. The actual motion states and physical movement of vehicles were also learned to combine the data-driven PINN and physical law constraints in the real world. The state quantities of the PINN network were predicted in the next time step by inputting the current time, current state quantities, and current control quantities. The self-circulation strategy was combined to enhance the solution efficiency and real-time performance of the predictive control in the nonlinear systems, fully meeting the computational requirements of the DMPC for the future state quantities. Finally, the state quantities were input into the DMPC for the rolling optimization. A cost function was constructed for evaluation, including tracking accuracy, control stability, and terminal stability error. The optimal control quantities were obtained for the next moment under the physical performance constraints of the vehicles. The precise tracking of the target position was realized for the formation coordination of the pollination unit during operation. Simulation, ground tests, and field experiments were carried out to verify the tracking accuracy, formation coordination, and actual operation adaptability. The simulation results show that the PINN-DMPC algorithm also exhibited better performance in the tracking error and asymptotic convergence, compared with the Adaptive-PID and Pure-Pursuit algorithms. The tracking error was within ±0.032 m with a standard deviation of 0.0098 m, indicating highly precise and stable path tracking. The yaw angle error was stabilized within 0.022 rad, providing a reliable directional reference for the position tracking. In terms of the solution efficiency, the average single-step solution time of PINN-DMPC was 0.011 s, which was 54.2% less than that of the original DMPC. The real-time response of the controller was significantly improved to reduce the performance and cost requirements for the control equipment. In the ground test, the effective operation range of the actual simulation also covered 84% of the entire road section, in terms of the ground formation coordination performance. The rapid adjustment was also achieved in the case of position deviation. The longitudinal distance error of the formation was controlled within 0.1 m. The stability of formation coordination was obtained with the included angle between the unit and the rice parental rows of less than 9°. This finding can provide a set of cooperative control algorithms suitable for the pollination in hybrid rice seed production. The precise path tracking and cooperative operation can also lay a foundation in modern agriculture.