Neural-Augmented Sliding Mode Control for Omnidirectional Mobile Robots: A Lyapunov-Guided Hybrid Architecture with Statistical Validation
الكلمات المفتاحية:
Sliding-mode control، neural networks، omnidirectional mobile robots، Lyapunov stability، hybrid control, trajectory tracking، Monte Carloالملخص
This paper develops a Lyapunov-guided hybrid control architecture combining sliding-mode control (SMC) with neural network residual learning for trajectory tracking of four-wheeled omnidirectional mobile robots (FOMRs). We conduct n=100 Monte Carlo simulations for three trajectories (circle, lemniscate, square) and four noise levels (σ=0,0.005,0.01,0.02) with paired t-tests and Cohen's deffect sizes. The proposed neural-network-augmented SMC (NN-SMC) achieves statistical parity with SMC on the challenging square trajectory under low noise (p=0.5499, d=0.06) and significantly outperforms SMC under high noise (p<0.001, d=0.69). In contrast, pure neural network control fails catastrophically—degrading by a factor of 1.76× under high noise—revealing a critical disturbance-rejection failure mode. Lyapunov stability verification confirms that the theoretical guaranteed uniform ultimate boundedness (GUUB) bound holds across all 12 test conditions. The quadratic convergence margin of 17.4 guarantees rapid error decay in the large-error regime. These results demonstrate that the proposed architecture provides certifiable robustness while leveraging learned residual corrections for performance improvement.
المراجع
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