## 1 Introduction  
Networks of mobile wireless robots are increasingly considered in applications in hazardous environments where humans cannot perform some tasks because of safety issues and challenges in the environments [1; 2]. For instance, in underground scientific facilities [3], such as at CERN (the European Organization for Nuclear Research), mobile robot nodes could help in remote inspections and radiation surveys in different areas [4; 5; 6; 7; 8]. The use of wired communication in hostile environments has not proven reliable, with fiber-optic cables susceptible to tangling, breakage and being run over by the robots [2]. Wireless communication offers benefits over wired communication systems, such as low maintenance, higher robustness against failures stemming from physical damage, less manpower needed for managing the tethers and ease of mobility. Typical requirements for a wireless robot in hostile or underground environments are given below:  
1. the wireless robot should be able to travel distances longer than 200 m [6];
2. the robot should communicate with the base station, in the possible presence of electromagnetic fields and/or ionizing radiation, and should be able to avoid wireless communication failures, radio interference, multipath and deep fading effects [3; 9; 10];
3. the robot shall in no way interrupt the operation or damage any objects in the facilities where it is deployed. To meet these requirements and, more specifically, to improve wireless communication performance in non-line-of-sight (NLOS) conditions and underground tunnels, the concept of wireless tethering using intermediate relay nodes (forming a network of mobile robotic nodes) has been suggested by previous researchers [9; 10; 11; 12; 13]. A commonly-used model for networked wireless nodes is the server-relay-client (SRC) framework, as shown in Figure 1. In addition to the need for relay nodes, there is also a need for redundancy features to improve reliability, avoid communication failure and enable recovery in the event of failure in the wireless network. Figure 2 shows an example of using relay nodes for multi-hop wireless tethering from an operator command station to the client/task node in line-of-sight (LOS) or NLOS conditions. If the relay nodes are autonomous with decentralized operations, this allows the human operator to concentrate on controlling only the client node. An important intelligence feature necessary for the relay nodes is that they must be able to optimize their positions to maintain a stable, end-to-  
The wireless link quality and the network throughput have a strong correlation with the received radio signal strength (RSS) and the signal-to-noise ratio (SNR) [14, 15]. It has been demonstrated in [16, 17] that the network throughput can be improved by balancing the RSS (at the relay node) from the server and client nodes. As the RSS is proportional to the logarithmic distance between two wireless nodes in LOS conditions, the RSS at each side of the relay node can be balanced by optimizing its position. Moreover, continuously optimizing the relay node's position will enhance the wireless network performance as the dynamics in the environment (such as fading effects and movements of various objects) influence the RSS [18]. In our previous work [15], we exploited spatial diversity techniques to optimize the RSS at a mobile robot node. In this paper, we extend our previous work and propose an adaptive robust stochastic optimization (RSO) algorithm for autonomous wireless relay positioning using a spatially spread RSS sensing technique to dynamically optimize the RSS assuming an unknown, noisy radio environment. Redundancy in the network is shown to be improved by making use of the proposed method, so that the system can tolerate, to some extent, wireless device failures, for instance caused by single event effects (SEE) of ionizing radiation in the environment. The proposed algorithm is made robust to noise in the measurement and environment by using pre-processing filtering techniques.