## 1 Introduction  
A wireless sensor network (WSN) comprises spatially circulated self-ruling sensors to agreeably screen and monitor physical or ecological conditions, out of which contain vibration, temperature, weight, sound, movement, or contaminations [1; 2; 3]. It presents a new generation of real-time embeddedsystems, which are characterized by having limited computation, energy, and memory resources. Several applications and scenarios, such as military and remote sensing applications, are reused by WSNs. Further, the improvement of WSNs, for example, in battlefield reconnaissance [4], is currently being utilized in numerous modern and regular citizen application territories, including mechanical or industrial procedure checking and control, machine wellbeing observation, condition and territory checking, medicinal service applications, home robotization, and traffic control [5; 6; 7]. It is worth mentioning that every sensor node in a certain network is commonly outfitted with a radio transceiver (or an equivalent wireless communications device); an energy source, usually known as a battery; as well as a micro-controller [8]. Another potential application where WSNs play a crucial role is in cooperative multi-robotic systems (CMRS) [9; 10; 11; 12; 13; 14], where several mobile robots cooperate on performing a specific mission within certain area of interest (AoI). For instance, the robots can utilize their mobility to provide sensing functionality for areas that are not covered or reachable by static sensors, thus enhancing the sensing and coverage capabilities of the legacy static sensor network. However, these robots usually communicate with each other, as well as with the base station, in order to have full coordination and optimal management while performing their missions and to send the sensed data to the monitoring center for further processing and decision-making. However, in order to have efficient, reliable, and scalable WSN, several parameters and configurations should be optimized, especially with the mobility challenges of the mobile robots, as well as the limited energy of the sensor nodes. Another type of sensor network is a hybrid network, where static, mobile, and flying nodes are utilized to collaboratively sense the AoI in a comprehensive and efficient manner [15; 16]. In order to utilize the limited energy source, in cooperative multi-robotic wireless sensor networks (CMR-WSNs, the sensor nodes are normally grouped into clusters, where all the nodes send their captured data to a central node called a cluster head (CH). This not only saves energy, but also mitigates interferences between the different nodes that are deployed within certain AoI. Typically, data is sent to a remote monitoring center for further analysis and decision-making. Therefore, CHs communicate with each other and send the captured data using multi-hop routing until the data reaches the remote and decision-making destination center. Both clustering and routing processes are vital in WSN operation and need to be optimized in order to increase the network lifetime. Generally, and as indicated by the WSN structure, routing conventions can be grouped mainly into flat-based and clustering-based protocols [3; 4; 5; 6]. Clustering-based routing conventions are the most widely recognized method that is utilized in WSNs. It is critical to refer to the fact that a massive measure of research on WSNs is coordinated towards expanding the network lifetime by making them energy proficient [3; 4; 5; 6; 7; 8]. The clustering method is considered as one of the key activities that are actively investigated for prolonging the network lifetime in WSNs [7; 8; 17; 18]. Furthermore, optimizing the nodes' power management in terms of sleep/wake times is very crucial to achieve an extended life network, especially in that the nodes are normally deployed in an area that is difficult to reach, and, as such, recharging their batteries may not be a viable option.