## 4 Review of Existing Methods and Capabilities
### Path Planning
#### Moving Target  
Moving Target path planning deals with the algorithms utilized to find and follow moving targets. Less work has been performed in the area of moving target tracking as compared to fixed target tracking. However, several similar algorithms to fixed target tracking, including Partially Observable Markov Decision Processes (POMDPs) and Genetic Algorithms (GAs), have been used with some success for finding and tracking moving targets. [PERSON] _et al._[65; 66] developed a method of searching and tracking a moving target traveling with a known speed and direction on a road network while utilizing unattended ground sensors for target detection. This work was later developed and demonstrated with multiple-vehicles, multiple-targets, and a large series of ground sensors by [PERSON] and [PERSON] [67]. This approach relies upon unattended ground sensors to trigger when a moving target passes it's location. The sensor then informs the UAS of an intrusion and the associated information required to search and track the intruder. The system has shown some limitations due to sensor false alarms and delay in sending information due to limited line of sight data transmission capability. However, the functionality shows promise in supporting a network of ground sensors and vehicles to monitor roads or perimeters for intrusion. [PERSON] _et al._[68] proposed the use of probability density functions in coordination with a negotiation task assignment framework for UAS tasking. The algorithm uses information gathering-based task assignment with a two-layer framework. An information-gathering layer uses the probability density functions to generate minimized value future trajectories. The task assignment layer utilizes a negotiation-based task allocation to assign tasks to the UASs in the network. Results showed promising results to search an area with minimal overlapping while finding all targets being searched. [PERSON] _et al._[34] proposed a virtual force and receding horizon method that enabled multiple-UAS cooperative search in a fixed region for unknown moving targets. Virtual force algorithm alone can be limited by being trapped at local minima while the receding horizon has large computational requirements that limits the length it can look ahead. The algorithm presented combined the two methods in order to alleviate the limitations of each method. [PERSON] and [PERSON] [69] proposed a modified diffusion-based algorithm to manage target uncertainty while controlling multiple UASs with a hybrid receding horizon/potential method algorithm for a coordinated search for a moving target. The search area was divided into cells and the algorithm coordinated vehicle search tasks based upon weighting of cells of the search region. The cells not searched that were closer to a given UAS were given a higher weighting than ones closer to a different UAS. A hybrid method that combined potential and receding horizon methods was used to reduce the computational burden. [PERSON] _et al._[70] and [PERSON] _et al._[71; 72] proposed similar control algorithms for multiple UAS coordinated standoff tracking of moving targets by utilizing Lyapunov guidance vector fields. Both approaches utilized Lyapunov guidance vector fields to generate stable paths for the UASs to fly while tracking a moving target. Multiple-UASs could be used by phasing them around the vector field solution. Both approaches showed acceptable results for multiple vehicles orbiting and tracking a moving target. [PERSON] [73] proposed a method for urban searching of a moving target that considered complex geometry from buildings that can impact the ability of the sensor to see the target. The method utilizes search trees and particle filters to evaluate path options and provides efficient filtering along with a method of compressing the visibility function. [PERSON] and [PERSON] [74] propose a Markov chain-like model for target motion estimation approach similar to particle filtering in order to account for the uncertainties in the target location estimates.