{'fraction_non_alphanumeric': 0.024185068349106203, 'fraction_numerical': 0.0, 'mean_word_length': 6.051851851851852, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Output Multiformation Tracking of Networked Heterogeneous Robotic Systems via Finite-Time Hierarchical Control

This article investigates the finite-time output multiformation tracking (OMFT) problem of networked heterogeneous robotic systems (NHRSs), where each robot model involves external disturbances, parametric uncertainties, and possible kinematic redundancy. Besides, the interactions among robotic systems are described as a directed graph with an acyclic partition. Then, several novel practical finite-time hierarchical control (FTHC) algorithms are designed. The convergence analysis of the closed-loop dynamics is extremely difficult due to the lack of effective analysis methods. Based on the mathematics induction and reductio ad absurdum, a new nonsmooth Lyapunov function is proposed to derive the sufficient conditions and settling time functions. Finally, numerical simulations are performed on the NHRS to verify the main results.