## 1 Introduction  
In recent years, the coordination control scheme of multiple robots has drawn considerable attention in various fields [1]. Multiple robots can be applied in many dangerous places to free the human being, including the earthquake rescue, the warehouse translations, and some tasks at nuclear power plants. A multi-robot system can be treated as a coupling network of some robots, where the robots communicate with each other to achieve some complex duties [2; 3]. Various investigations have been explored to achieve the coordination control of multiple robots. These investigations can be roughly classified into leader-follower formations [4; 5; 6; 7; 8], virtual structure mechanisms [9; 10; 11; 12], graph-based approaches [13; 14], and behavior-based methods [15; 16]. The leader-follower formations are attractive in the coordination control of multi-robot systems. Partly, such formations benefit multiple robots because the formations can have guaranteed formation stability via control design [17]. The basic control idea of the leader-follower mechanism is that multiple robots are divided into several leader-follower pairs. In the leader-follower mechanism, all follower robots share the same leader. In each pair, the leader robot moves along the predefined trajectory, while the follower robots track the leader with desired relative distance and angle. In the leader-follower system of multiple robots, only partial followers can obtain the state of the leader, and the interaction between follower robots and leader robot is local [18]. Many control methods have been applied in the leader-follower multi-robot systems, such as sliding mode control (SMC) based on nonlinear disturbance observer [18], SMC [19], second-order SMC [20], adaptive control [21; 22], predictive control [23], integral terminal SMC [24], and terminal SMC [25]. In actuality, it is unavoidable for any robots to be affected by uncertainties such as external disturbances, unmodeled dynamics, and parameter perturbations [26]. The dynamics of multi-robot systems becomes uncertain, due to these uncertainties [27]. These uncertainties can be categorized into unmatched uncertainties and matched uncertainties [28]. However, the SMC method, as a strong robust tool, has invariant nature to the matched uncertainties when an SMC system enters into the sliding mode. Unfortunately, the effects of unmatched uncertainties cannot be suppressed by the SMC methods [29]. The unmatched uncertainties can challenge the performance of the SMC system seriously. The characteristic of terminal SMC (T-SMC) has its nonlinear sliding surface. Compared with those traditional SMC approaches, the T-SMC method has faster convergence speed and higher accuracy. However, the T-SMC method has the singular problem due to its fractional function. Therefore, the derivative and integral T-SMC (DIT-SMC) method is proposed [30]. The DIT-SMC method is of merit. Due to the existence of the integral term, the sliding mode of the DIT-SMC method starts on the derivative and integral terminal sliding mode surface. Moreover, the DIT-SMC method can guarantee the exact estimation of finite error convergence time, and resolve the singular problem of the T-SMC. On the other hand, the derivative term of the DIT-SMC method can reduce the nonlinear effects to the stability of a DIT-SMC system. In the previous works [21; 22; 23; 24; 25; 26; 27; 28; 29; 30], the assumption that the uncertainties have a known boundary is assumed. Concerning the formation maneuvers of multi-robot systems, the assumption is not mild. In fact, the boundary of uncertainties in multiple robots is hard to be known exactly in advance. In case of the lack of the important information, several serious problems may be raised in reality, for example, the decrease of the formation robustness, the deterioration of the formation performance, as far as the deficiency of the formation stability. In order to resolve the problem of the uncertainties, the nonlinear disturbance observer is adopted.