REAL-TIME INTELLIGENT CONTROL OF MULTIVARIABLE MOBILE ROBOT SYSTEMS: CONSTRAINED MODEL PREDICTIVE CONTROL WITH AN ADAPTIVE MODEL-CORRECTION LAYER

Background: A mobile robot must compute constrained control actions within a fixed sampling interval, yet predictive control, model correction and solver timing are rarely studied together. Objective: To study constrained model predictive control (MPC) of a multivariable differential-drive robot as a real-time problem. Methods: A five-state, two-input torque model is analysed with the relative gain array. A linear time-varying MPC with input, rate and softened state constraints is solved as a sparse quadratic program with OSQP, with bounded recursive-least-squares gain-and-bias correction, a safeguard and a deadline fallback. Twelve simulated conditions (30 seeds each; gain 0.7 to 1.2, bias, disturbances, delay, 0 to 10 % packet loss) compared the MPC with a decoupled cascaded PID. Results: In the disturbed conditions the MPC lowered the position RMS error by 2.0 cm (95 % CI 2.0 to 2.1) and the residual after 5 s from 2.5 to 1.1 cm, but used 1.4 times the torque effort. The adaptive layer removed a further 0.21 cm of the residual (19 %) without detectable harm at ten times the sensor noise. In Python on a personal computer, a horizon of 20 samples needed 1.1 ms per sample (mean; 99th percentile 2.9 ms); at a 20 ms period the deadline was missed in at most 0.04 % of the samples for horizons up to 40. Conclusions: With a terminal weight, short-horizon constrained MPC fits these sampling rates and outperforms the PID at the price of rougher actuation. All results are simulations; hardware and embedded timing remain untested.