## 1 Introduction  
With the coming of the artificial intelligence era, multi-robot systems are becoming more attractive and more significant [1]. Multi-robot systems one of the emerging and popular solutions in various fields, such as industry, agriculture, aviation, etc. [2]. Concerning multi-robot systems, the control problem of formation maneuvers is an important topic [3, 4]. In many cases, the robots in a multi-robot system have to form some formation patterns in order to accomplish a given task in collaborative projects, military reconnaissance, and hazardous situations [5]. For the purpose of organizing and managing the robots, a coordinated control scheme needs to be pre-defined in the multi-robot system [6]. Some schemes have been developed, containing virtual structure methods, leader-follower approaches, behavior-based techniques, and so on [7]. In this paper, the leader-follower scheme was taken into consideration because the scheme can accomplish a given formation task with the guaranteed closed-loop stability. Although it suffers from the drawback of a'single point of failure', the leader-follower scheme is of merit for the formation maneuvers of small-and-medium-scale multi-robot systems [8; 9; 10]. This paper does not focus on how to design a coordinated control scheme, but it concentrates on the formation control design. Thus,the leader-follower scheme was directly adopted. In addition, the small-scale multi-robot systems were taken into account for the convenience of the control design. Inherently, the formation model of a multi-robot system contains nonlinearities and motion couples that create a significant challenge to the formation control design [11; 12]. In reality, a multi-robot system is inevitably subjected to some uncertainties and disturbances, including but not limited to modelling errors, inertia-and-mass variations, signal-transmission delays, unpredictable obstacles, etc. These uncertainties and disturbances significantly challenge the formation control [13; 14; 15; 16]. To deal with the control problem of formation maneuvers, many control methods have been reported, i.e., model predict control [17], adaptive control [18], interval type-2 fuzzy control [19], adaptive dynamic programming [20], etc. The methodology of the sliding mode control [21] is a synthetic tool. Some sliding-mode-based control approaches have been investigated for the control problem. Some studies have been reported, such as the first-order sliding mode control [22; 23], the integral sliding mode [4], the derivative and integral terminal sliding mode control [14], the terminal sliding mode control [24], and so on. As far as the methodology of sliding mode control is concerned, the invariance is its most attractive property, which means that a sliding-mode-based control system is completely and thoroughly robust against the uncertainties and disturbances entering the control system by the control channel. Dialectically, the methodology is criticized for its chattering phenomenon as well. Many sliding-mode-based control ideas focus on decreasing and even eliminating the chattering phenomenon, whereas the super-twisting sliding mode control is a kind of the second-order sliding mode control method [25]. The super-twisting sliding mode control has become popular because this control technique only needs the information of a sliding mode variable and gets rid of the dependence on the time derivative of this sliding mode variable [26]. The control technique can effectively force the sliding mode variable and its time derivative to the origin in finite time despite the existence of the bounded disturbances and uncertainties on the assumption that the boundary is known [27]. Unfortunately, this boundary can hardly be known with regard to the formation maneuvers of multi-robot systems. One can overestimate this boundary from the aspect of the closed-loop stability, but the overestimate definitely enlarges the necessary control gain of the super-twisting sliding mode control.