Friction-Aware Safe Formation Control of Car-like Mobile Robots on Variable-Friction Roads

Car-like robot formations on variable-friction roads experience slip-induced model mismatch and changing avoidance capability. This paper presents a friction-aware formation-control architecture combining a longitudinal–lateral error model, three disturbance-observation channels, Gaussian-process (GP) inference of an equivalent friction indicator, and adaptive high-order control barrier functions (HOCBFs). The two-power observer is analyzed as a Filippov bi-power super-twisting system: under exact continuous-time measurements and bounded disturbance derivatives it has a fixed settling-time bound, whereas its sampled noisy realization is assessed through finite-horizon practical estimation behavior. Safety constraints are derived from ground acceleration and allocated between neighboring robots, while a control Lyapunov function–HOCBF quadratic program balances tracking and avoidance under explicit feasibility assumptions. In 30 paired closed-loop trials on a simplified variable-friction plant, the proposed GP-assisted method produced no collisions, reduced mean formation RMSE from 9.929 m for fixed HOCBF to 8.920 m, and reduced the mean rejected-update fraction from 0.89% to 0.77%. A compact held-out test at two friction levels not used for training reports equivalent-coefficient RMSEs of 0.1225 and 0.1072.