Featured Application: The presented control design can enrich the multi-robot technologies and can benefit the coordination of multi-robot systems.Abstract: This paper investigates the formation problem of multiple robots based on the leader-follower mechanism. At first, the dynamics of such a leader-follower framework are modeled. The input-output equations are depicted by calculating the relative degree of a leader-follower formation system. Furthermore, the derivative and integral terminal sliding mode controller is designed based on the relative degree. Since the formation system suffers from uncertainties, the nonlinear disturbance observer is adopted to deal with the uncertainties. The stability of the closed-loop control system is proven in the sense of Lyapunov. Finally, some numerical simulations are displayed to verify the feasibility and effectiveness by the designed controller and observer.

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In recent years, Xi'an metro construction has been progressing rapidly, becoming the primary mode of urban green public transportation. Since the ridership of the metro is closely linked to the characteristics of its surrounding built environment, a key problem in promoting the benign development between the two is to explore the spatiotemporal distributional difference in ridership and its influencing factors. In this study, the "5D" characteristics of built environment are described by density, diversity, design, destination and distance variables. The spatiotemporal distribution characteristics of ridership are analyzed via Arc GIS and Python, while the nonlinear relationships between ridership and built environment of 106 metro stations of downtown Xi'an, as well as relevant threshold effects are revealed via Shapley additive explanations  with gradient boosted decision tree (GBDT-SHAP). The results show that: (1) Xi'an metro travel presents a medium-short spatiotemporal distribution, and the ridership network is characterized by strong center-spillover. (2) The nonlinear relationship between built environment and ridership is ubiquitous and presents a threshold effect. The impact threshold of bus stop density on ridership is 4-6 pcs/km2, the impact threshold of road network density is roughly 4-5 km/km2, and the effective threshold of building density does not exceed 20%. (3) The positive impact of POI facility density on peak ridership is stronger than that at flat hours. Variables like land use mixture, population density and distance from downtown have a time-driven effect on the ridership, whose importance and influence change with time. This study provides a better understanding of the spatiotemporal impact of Xi'an's built environment on metro travel, which is of profound significance for the coordinated development between the city and metro construction.