## 1 Introduction  
WSNs (Wireless Sensor Networks) are commonly regarded being among the most significant technologies in the 21 st century [1]. Small, inexpensive, and intelligent sensors placed in a physical space and connected via wireless networks and the Internet, recently developed microelectronic mechanical systems (MEMS) with wireless communication technologies, open up previously unimaginable possibilities for a range of civilian and military uses, such as monitoring the environment, keeping an eye on the battlefield, and controlling industrial processes [2]. WSNs differ as comparison to conventional wireless communication networks such as Cellular networks and ad hoc mobile networks (MANET) in that they possess particular qualities, such as a higher density of node deployment, higher sensor node significant energy, processing, and storage limits, as well as unreliability [3], all of which pose new difficulties in development and application of WSNs. WSNs have gotten a lot of interest from worldwide academic and industrial communitiesin the last decade. There has been a significant amount of research done to investigate and solve numerous designing and implementing difficulties, and significant progress has been achieved in the development and implementation of WSNs. WSNs are expected to be widely deployed in numerous military and civilian fields in the near future, revolutionizing the way people live, work, and engage in physical activities [4]. WSNs are comprised of significant number of cheap, low-power, and multi-purpose sensor nodes that are placed in a certain area. These sensor nodes are compact, yet they contain radio transceivers, embedded microprocessors, and sensors, allowing them to perform not only data processing but also sensing communication. They communicate across a short distance using a wireless medium and work together on a same goal, such as environmental monitoring, battlefield surveillance, or industrial process control. Mobile entities are typically used as sensor nodes in mobile sensor network systems to carry out network deployment and monitoring functions. Nevertheless, several mobile nodes are required for mobile sensor networks. The cost rises in direct proportion to the number of mobile sensor nodes. Therefore, combining a lot of inexpensive static sensor nodes with some mobile sensor nodes is a practical option. In order to complete their objectives, jumping nodes equipped with sensors and wireless communication can enter hostile and dangerous settings. Cooperatively deploying static sensor nodes and mobile nodes is efficient. The mobile nodes are able to expand network coverage and improve network connectivity. In WSN systems, jumping nodes are platforms carrying wireless communication modules. According to the application needs, the communication modules can be selected from short- to long-range communication modes. This research presents a comprehensive approach for determining predefined thresholds and demanding that jumping nodes be recharged by such robots. The contributions of the paper are listed below. When a sensor node's battery is ready to run out, the suggested algorithm provides a detailed plan for recharging it by jumping node. Because nodes closer to base stations are more likely to fail due to battery loss, a configuration with three zones around the base station is recommended. As a result, the closer nodes are put in zone 1, where they act as relays, transmitting data from the sensor nodes to the base station in zones 2 and 3. Zone 2 nodes relay to zone 3 nodes, whereas zone 3 nodes relay to zone 2 nodes. Zone 3 nodes use the least amount of energy because base station receive data from sensor nodes. Last but not least, simulations reveal that the suggested technique outperforms other standard techniques. Parameters like total distance travelled by nodes, number of messages sent and received among all nodes, average nodes moved, and the proportion of field coverage drop are utilized to improve service quality.