Parameter-Dependent LMI Synthesis for Semi-Global Differential ISS Trajectory Tracking of Nonholonomic Mobile Robots Under Multiplicative Wheel Slip
This work addresses trajectory tracking for nonholonomic mobile robots operating on highly variable terrain where severe multiplicative wheel slip significantly degrades performance. The authors propose a control approach based on parameter-dependent linear matrix inequalities (LMIs), which explicitly constructs an additive disturbance upper bound for multiplicative wheel slip within the Kanayama error coordinates—a first in the literature. By integrating affine parameterized gains with a nonlinear storage function, the method synergistically combines physical modeling insights with convex optimization. It further incorporates sampled convexification, variational contraction analysis, forward invariance, and dissipativity-based trajectory reconstruction to guarantee semi-global differential input-to-state stability with a prescribed exponential decay rate. Experimental results demonstrate that, over complex terrain featuring six segments with bidirectional ±50% slip, the proposed controller reduces peak tracking error by 12% and 49% compared to fixed-gain LMI and hand-tuned baselines, respectively, while satisfying certified envelope constraints in all 100 Monte Carlo trials.