New LMI robot controller cuts tracking error 49% under wheel slip

Mohammad Sabouri's new paper on arXiv (eess.SY 2608.08049) tackles a longstanding challenge in mobile robotics: precise trajectory tracking when wheels slip unpredictably on variable terrain. The proposed framework uses parameter-dependent linear matrix inequalities (LMIs) to synthesize a feedback controller that maintains stability and tracking performance even with multiplicative wheel slip ratios reaching ±50%. A key contribution is an explicit upper bound on slip-induced disturbances mapped into Kanayama error coordinates, bridging the physical slip mechanism with a convex optimization framework. The controller is validated across 100 Monte-Carlo simulations, six reference trajectories, six disturbance classes, and a 60-second variable-terrain scenario with six severe slip patches.

Numerical results show substantial gains over existing approaches: peak tracking error drops 12% compared to a fixed-gain LMI baseline and 49% versus a manually tuned baseline, while the constant-gain LMI baseline becomes infeasible at the prescribed decay rate. The design also factors in actuator limits, Gaussian sensor noise, and embedded-platform feasibility, making it practical for real-time deployment. By formalizing semi-global differential input-to-state stability (ISS) with regional pole placement and exponential decay, the method provides certified bounds on trajectory containment—a level of assurance rarely seen in slip-affected robot control. This work offers a rigorous, computationally tractable path toward safer and more reliable autonomous navigation in outdoor and industrial settings.