# Research Trends in Collaborative Drones
## 5 Navigating under Uncertainty
### Approach and Methodology  
In the sequel, we outline a technique motivated from the work of [47] and first employed in [48; 49] in order to navigate such a terrain. Consider a terrain with available landmarks, e.g., road signs, monuments, or even other terrestrial indicators. The landmarks encountered may provide information whose interpretation by the drone may be prone to various types of errors. One can distinguish two types of errors, namely, recognition and advice. * Recognition errors may be due to misinterpretation of sensed data or confusion of objects. For example, a drone has found a green door which in fact is not a door but rather a window leading to an incorrectly recognized object. We assume that for some real number \(p\in[0,1]\), the value \(p\) is the probability that a drone performs recognition erroneously and \(1-p\) that it is correct. * Advice errors could be about landmarks because the information they provide is either not up to date or even outright wrong. For example, upon finding a landmark, a drone is advised to traverse a certain distance within the terrain in direction north where it will find the next landmark, say a restaurant, but this information is wrong because the restaurant is no longer there. Again, we may assume that for some real number \(q\in[0,1]\), the value \(q\) is the probability that the advice provided to a drone about a landmark is erroneously interpreted and \(1-q\) that it is correctly interpreted. The next step concerns mathematical assumptions of the model above. To facilitate calculations, one may assume that recognition errors are independent and identically distributed and advice errors are also independent and identically distributed. In other words, the drones are acting independently of each other. In addition, the outcome of the recognition process is random with a probability of success that depends on the parameter \(p\). A similar observation applies to the advice process. We can use this methodology to our advantage so as to improve the recognition and advice mechanisms for swarms of drones. There is an underlying graph determined by the terrain of landmarks. Landmarks are vertices of a graph \(G=(V,E)\) whose edges are discovered online by the recognition and/or advice process. In a typical setting, we start with a source node \(s\) and end with a target node \(t\). The drones are seeking a flight path connecting \(m+1\) vertices \(s:=v_{0},v_{1},\ldots,v_{i},v_{i+1},\ldots,v_{m}:=t\), see Figure 4.  
Figure 4: Flight path from source \(s\) to destination \(t\). Edge \((v_{i},v_{i+1})\) is an intermediate segment connecting landmarks \(v_{i}\) and \(v_{i+1}\). The vertical (thicker) arrows represent the landmarks encountered by the drones. A possible flight path, denoted as \(P\), consists of a number of vertices \(v_{0}:=s,v_{1},\ldots,v_{i}\), \(v_{i+1},\ldots,v_{m}:=t\) from \(s\) to \(t\). An edge \(\{v_{i},v_{i+1}\}\) corresponds to a segment of the flight path \(P\). It is said to be correctly traversed if and only if the advice provided about the landmark associated with vertex \(v_{i}\) is valid and correctly interpreted and the landmark associated with vertex \(v_{i+1}\) is correctly recognized. For \(i=0,\ldots,m-1\), the flight path \(P\) is correctly traversed if and only if each of its segments defined by edges \(\{v_{i},v_{i+1}\}\) are correctly traversed. At the start, a drone is given a flight plan. The flight plan defines the flight path \(P\). For each vertex \(v_{i}\), \(i=0,\ldots,m-1\), the flight plan comprises advice for searching for the next landmark, such as directional data. For each vertex \(v_{i+1}\), the flight plan contains recognition data, such as landmark characteristics. A flight plan is correctly performed solely if every single segment is correctly traversed. The next important step is for the swarm of drones to fuse information collected so to reach an optimal decision. The basic method is to employ error amplification.