Path Planning and Network Optimization for UAV Swarms for Multi-Target Tracking Shawon Dey, Hans D. Mittelmann, and Shankarachary Ragi, Senior Member, IEEE Abstract—This paper focuses on the development of decen- tralized collaborative sensing and sensor resource allocation algorithms where the sensors are located on-board autonomous unmanned aerial vehicles. We develop these algorithms in the context of single-target and multi-target tracking applications, where the objective is to maximize the tracking performance as measured by the mean-squared error between the target state estimate and the ground truth while minimizing the energy costs. The tracking performance depends on the quality of the target measurements made at the sensors, which depends on the relative location of the sensors with respect to the targets. Our goal is to control the motion of the swarm of vehicles with on-board sensors to maximize the target tracking performance. Each sensor generates local noisy measurements of the target location, and the sensors maintain and update target state estimates via Bayesian data fusion rules using local measurements and the information received from the neighboring sensors. The quality of the data fusion depends on the network graph over which the sensors exchange information and the relative distance between sensors, and these determine the overall target tracking performance. For the case of multi-target tracking scenario, we also introduce sensor assignment graph in order to allocate the sensors to appropriate targets and maximize the overall tracking performance. We also assume that each sensor is powered by a limited energy source; which we assume is drained by how frequently sensors exchange information. The goal of our study is to optimize the collective motion of the vehicles/sensors (also determines the network graph connectivity and sensor assignment graph connectivity for multi-target tracking) such that the mean-squared target tracking error and the network energy costs are jointly minimized. This problem belongs to a class of hard optimization problems called conflicting objective limited resource optimization (COLRO). We develop fast heuristic algorithms, using dynamic programming principles, to solve this COLRO problem in real-time using a numerical optimization solver called Knitro, and we evaluate its performance against a widely used particle swarm optimization approach. I. I NTRODUCTION There is a growing interest in decentralized and distributed autonomous sensing [1], [2], [3] and sensor allocation [4] methods, where the network connecting the sensors may be time-varying. With increasing number of sensor and surveil- lance systems in public places, there is a need for decentralized S. Dey and S. Ragi are with the Department of Electrical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA: shawon.dey@mines.sdsmt.edu, shankarachary.ragi@sdsmt.edu. H. D. Mittelmann is with the School of Mathematical and Sta- tistical Sciences, Arizona State University, Tempe, AZ 85287, USA: mittelmann@asu.edu. This work was supported in part by Air Force Office of Scientific Research under grant FA9550-19-1-0070. This paper was presented in part at the Proceedings of the 2019 IEEE National Aerospace Electronics Conference (NAECON) , Dayton, OH, July 15–19, 2019, pp. 88–91. methods [5], [6], to track moving targets (e.g. movement of an intruder, movement of enemy tanks in battle field, patrolling an area) with a network of sensors. However, the decentralized collaborative sensing [7], [8] in a wireless multi- sensor network is a challenging problem, especially when there are network energy costs involved. Since the battery-powered sensor nodes have limited energy and computing resources, there is a need for methods that can trade off between the target tracking performance and the energy costs of acquiring the measurements and sharing them (with peers) over a network. Furthermore, recent development in tracking systems make it possible to deploy a large number of sensors to track multiple targets and monitor large areas. However, the proper allocation of the sensors to targets and the collaboration [9] between them in order to obtain satisfactory tracking performance with the minimization of the energy costs is more challenging. In this study, we assume that the sensors are located on- board unmanned aerial vehicles (UAVs), where the goal is to optimize the motion controls of the vehicles for target tracking [10]. Such studies have been carried out in the past for various applications: format control [11], [12], industrial inspection [13] and remote sensing [14]. If a distributed set of autonomous vehicles are connected via a wireless network (vehicle is considered a wireless node), due to the movement of the vehicles, the links in the network graph may form and break as the relative distances between the nodes change over time, thus leading to a time-varying graph. Optimal control of UAVs over such time-varying network graphs is particularly challenging when the UAVs are performing various tasks over the network including information passing for data fusion and for cooperative optimization of motion controls. Further, if a swarm of UAVs is deployed over a large area to track multiple moving targets, the tracking performance of these UAVs may degrade with the increasing distances between the UAVs and the targets. In this type of scenario, it is highly effective to divide a swarm of UAVs into different smaller groups and control their motion by assigning them to appropriate targets. In this regard, we develop a sensor-target assignment method, which designs a graph to represent the assignment of the sensors to the targets for multi-target tracking, where the links in this graph may form and break depending on the relative motion of the UAVs with respect to that of the targets. In addition, as swarm-based systems [15] tend to have a large number of vehicles, optimizing each motion control variable in centralized manner may lead to computationally expensive optimization problems. To address this challenge, we develop multi-tier optimization strategies, where we first optimize the