In real transportation, it usually needed to carry large and heavy loads in many situations, both in indoor and outdoor environments. In such cases, it is crucial to maintain the rigid formation of the multi-robots system in order to keep the load not falling down during the transport. In addition, the obstacle avoidance should be solved for individual robots as well as the multiple robots as a whole. Accordingly, the MRS should perform tasks as depicted in Figure 1 and Figure 2. It consists of maintaining rigid formation to carry objects. Meanwhile, the perception system establishes an occupation grid map allowing planning safe and feasible paths. The perception system is responsible for gathering the image and information of the current environment. In the paper, a camera or a flying robot materializes the perception system. With the occupancy grid and given the final destination, an optimal path is determined thanks to the Q-learning algorithm.

In order to get environment model, we developed a computer vision based module to extract changes. Our sys-

tem compares successive images taken by a UAV (or a moveable camera). After background substraction, we obtain a binary matrix E(i, j).

In which 1 represents obstacles and 0 is free path. Here, in order to adapt to our experimental robot (Khepera III), we reshape the size of matrix E to fit to the real dimension of the working space (see in Figure 7). In this example, the environment is divided into 100 states where each state is a square of 30 cm × 30 cm. Rigid formation control part and Q-learning part can be found in [13]-[16].

An example illustrated in Figure 3, it introduced how the control strategy works. It is a model of the virtual environment used in the simulation. The heterogeneous multi-robots team must cross a wide unknown area from A to B. The “unknown” means that they cannot get the complete environmental information at the initial time step. Since the area is huge and unknown, the heterogeneous multi-robots team must pass the area steps by steps. Supposed that, in each time, they cross an area (3 × 3 m²) which we called a “room”. In this virtual environment, the multi-robots system is composed of three Khepera III (a kind of two-wheel non-holonomic robot), a humanoid robot Nao (http://www.aldebaran-robotics.com/), a camera (role as perception system) and a virtual robot supervisor (data processing). The environment model is decomposed into 21 rooms (see Figure 3, the room is indicated by a two-dimension array, respectively along the axis-x and axis-y). Each room is divided into 100 states, and each state is a square with side of 30 centimeters. For example, the initial A locates in room (2, 2) and the final B locates in room (1, 7) (see Figure 4). The total area of the environment is equal to 6 × 12 m².

The path planning of the unknown environment is displayed in Figure 5(b). The initial position (the green dot and circle) and final position (the blue dot and circle) respectively are [4; 2] and [1; 6]. In the experiment, multi- robots system maintained the vertical formation 2 from the beginning to the end. The initial position marked with green dot (the reference robot) and green circle. The final position marked with blue dot and blue circle.

Let us suppose that the multi-robots system entered the current room k (see in Figure 6(a)) from the previous room k − 1. They aim to go across the room k and enter into next room k + 1. The process includes two parts. In the first part, Nao led two Khepera III robots move ahead, because there is a free pass way in front of the multi-robots system on initial time step. In the second part, we put a barrier to block the pass way in front of the multi-robots system. Based on an event-based coordination strategy, HMRS can be self-adaptive to the sudden disturbance of the environment. The detailed process is as follows: (1) Nao explored the front area at each time step. As soon as it observed the obstacle, it enabled the top camera to send an image of current unknown environment. Then, through calculating the path planning by a supervisor, two Khepera III robots (multi-robots system) apply ANFIS rigid formation control to avoid obstacles. Nao executed the corresponding actions according to the results of path planning. Finally, multi-robots system crossed the current room k as well as they arrived at the initial position of room k + 1. The results and description of go forwards part and path planning part are as follows.

The pictures of the first part displayed in Figure 6. At the beginning of the experiment, HMRS went into room k from room k − 1. Nao led two Khepera III robots (MRS) keep going ahead as there is a pass way. The initial state of experiment showed in Figure 6(a) and the segment of the first part showed in Figure 6(b).

After the short go forwards part, we set an obstacle in order to stop HMRS and removed it after few seconds (see in Figure 7(a)). In this case, as Nao updated the current image and detected the obstacle, it demanded the external camera to give the image of the current room K to the supervisor. Using Q learning, the optimal path and actions obtained by supervisor (see in Figure 7(b)). Multi-robots System was interrupted and exchanged commands with the supervisor. The supervisor switched the go forwards control to rigid formation control.

The path planning demonstrated in Figure 7(b). Actions are 1 1 3 3 3 for the rest part of environment. In the part, two Khepera III robots (MRS) formed a vertical line rigid formation. By the ANFIS rigid formation control, MRS crossed the area without colliding with obstacles. After two continuous go forwards translational actions (see in Figure 7(b) and Figure 7(c)), multi-robots system turned left to finish the rest three left translational actions. Nao followed the MRS to turn left (see in the Figure 7(d) and Figure 7(e)) after the two continuous forwards translational actions. The rest three actions illustrated respectively in Figures 7(d)-(f). The final state of the experiment showed in Figure 7(f). They will continue to move in the room k + 1.