Event-triggered MPC-PID based trajectory tracking control for differential drive mobile robots

Periodic model predictive control (MPC) for differential-drive mobile robots requires online optimization at every sampling instant, which can be redundant during near-steady tracking. This study develops an event-triggered hierarchical MPC–PID framework, termed ET–MPC–PID, to reduce the outer-loop optimization burden while accounting for actuator-side execution effects. The outer MPC updates the velocity setpoint only when a normalized event condition is satisfied or the maximum holding interval is reached. A fixed-period PID-form velocity servo with conditional integration regulates the actuator channel under lag and saturation. The formulation distinguishes holding-induced decision discrepancy from actuator-side mismatch and provides a local practical boundedness characterization. Simulations on double lane-change and figure-eight trajectories compare periodic PID, periodic MPC, periodic MPC–PID, an external variable-horizon ET–MPC reference, and event-triggered ablations. ET–MPC–PID reduces the QP call rate to 16.9% and 22.3% of periodic MPC while outperforming the no-PID event-triggered variant. Sensitivity, Pareto, runtime, and 100-trial Monte Carlo analyses further demonstrate the accuracy–computation trade-off and empirical robustness under sampled execution uncertainty.