Data-driven discovery of performance boundaries in robotic systems through extreme quantile estimation

Characterizing the performance limits of physical systems from experimental data is essential for engineering decision-making, design optimization, and reliability analysis, yet conventional regression models estimate average behavior rather than the boundary of what is achievable. This paper develops a data-driven methodology for discovering nonlinear performance boundaries from experimental observations. The problem is formulated as extreme conditional quantile estimation. A nonparametric binned percentile estimator recovers low-quantile boundary points, and the Bayesian Information Criterion selects an interpretable closed-form law from a library of physically motivated families. Non-asymptotic guarantees are stated in the fixed-design regime the experiments occupy. The method is validated on two real robotic datasets. For UR10e trajectory tracking (30,600 observations), it discovers a saturation boundary E = 7 . 7 4 ( 1 − e − 1 3 . 2 7 S ) mm ( R 2 = 0 . 9 6 2 ; bootstrap 95% CI for E max of [7.05, 9.10] mm) and separates it from a steady-state envelope obeying the lag law e = t lag · v with t lag = 6 5 ms (