## 1 Introduction  
In recent years, the control of multirobot systems has attracted a considerable amount of attention as these systems can overcome the main limitations associated with using a single robot. Many scholars have focused on the coordinated control of multi-agent systems [1], nonlinear dynamics with uncertainties [2; 3], nonholonomic mobile robots [4; 5], and general multiple mechanical systems [6]. An increasing number of studies have found that it is unacceptable to use only single- or double-integrator dynamics while neglecting the nonlinear dynamics to model some practical applications. Many researchers have begun to study Lagrange systems because of their generic representation of many mechanical systems, for example, the attitude dynamics of rigid bodies, robot manipulators, mobile robots, and walking robots [7; 8; 9; 10; 11; 12; 13]. However, most existing results can only be applied to ideal environments. They are not suitable for use in complex environments, for example, in the presence of obstacles. Therefore, research on the coordinated control of multiple Euler-Lagrange systems is essential and critical, especially when considering obstacles, model uncertainties, external disturbances, parameter uncertainties, and unknown nonlinear dynamics. An escort mission involves robots surrounding and maintaining a formation around a target. As the target moves, the formation also moves to ensure that the target is at the center. A specified distance is maintained between the robots and the target, and the robots are distributed around the target evenly [5]. An escort mission with multirobot systems has previously been studied [14; 15; 16]. However, most of the strategies proposed were only applied to a planar case, and they cannot be easily extended to Euler-Lagrange systems in three-dimensional cases. Thus, designing a suitable controller for escort missions in \(p-\) dimensional space (where \(p\geq 3\) is a positive integer) while avoiding obstacles and providing rigorous proof of convergence and stability is more meaningful. Among the many coordinated control frameworks for multirobot systems, behavior-based approaches have been extensively investigated [17; 18; 19; 20]. One of the behavioral methods is null-space-based behavioral (NSB) control. This strategy, proposed by [PERSON], is a task-priority inverse kinematic control approach [21]. The main feature of NSB control is that elementary tasks are arranged in priority and assembled to compose the final behaviors using null space projection matrices of a higher-priority task so that multiple tasks are simultaneously activated. Moreover, unlike classical behavior-based approaches, the NSB approach has an analytical structure that allows it to elaborate the stability properties of robotic missions. The escort mission considered in this study is discussed in the NSB control scheme, which has the advantages of flexibility and versatility. However, NSB control still has some unanswered questions, e.g., how to achieve more precise nonlinear dynamic control under this behavioral control architecture. Sliding mode control (SMC), which was introduced in the early 1960s, has been considered a powerful technique to aid nonlinear systems with system uncertainties, external disturbances, and so on [22; 23; 24]. However, the SMC control law consists of an equivalent control term and robust term. An equivalent control term requires certain knowledge of the system dynamics, which may be difficult to obtain in practice for complicated systems. The control signal of an SMC controller exhibits high-frequency oscillations, also called chattering, which leads to rapid oscillation about the sliding manifold. [PERSON] et al. [25] proposed a hybrid control law that could switch between proportional derivative (PD) control and SMC for the tracking control of robotic manipulators.