John J. Enright

Micro UAV Path Planning for Reconnaissance in Wind

The problem addressed in this paper is the control of a micro unmanned aerial vehicle (MAV) for the purpose of obtaining video footage of a set of known ground targets with preferred azimuthal viewing angles, using fixed onboard cameras. Control is exercised only through the selection of waypoints, without modification of the MAVs pre-existing autopilot and waypoint following capability. Specifically, we investigate problems and potential solutions of performing this task in the presence of a known constant wind. Simulations are provided in the presence of randomly perturbed wind, based on the Air Force Research Laboratory equipment and the high fidelity simulator MultiUAV2.

On Multiple UAV Routing with Stochastic Targets: Performance Bounds and Algorithms

In this paper we consider the following problem. A number of Uninhabited Aerial Vehicles (UAVs), modeled as vehicles moving at constant speed along paths of bounded curvature, must visit stochastically-generated targets in a convex, compact region of the plane. Targets are generated according to a spatio-temporal Poisson process, uniformly in the region. It is desired to minimize the expected waiting time between the appearance of a target, and the time it is visited. We present partially centralized algorithms for UAV routing, assigning regions of responsibility to each vehicle, and compare their performance with respect to asymptotic performance bounds, in the light and heavy load limits. Simulation results are presented and discussed.

UAV ROUTING IN A STOCHASTIC, TIME-VARYING ENVIRONMENT

Abstract In this paper we consider the following problem. An Uninhabited Aerial Vehicle (UAV), modeled as a vehicle moving at unit speed along paths of bounded curvature, must visit stochastically-generated targets in a convex, compact region of the plane. Targets are generated according to a spatio-temporal Poisson process, uniformly in the region. It is desired to minimize the expected waiting time between the appearance of a target, and the time it is visited. We present algorithms for UAV routing, and compare their performance with respect to asymptotic performance bounds, in the light and heavy load limits. Simulation results are presented and discussed.

Stochastic and Dynamic Routing Problems for Multiple Uninhabited Aerial Vehicles

Consider a routing problem for a team of vehicles in the plane: target points appear randomly over time in a bounded environment and must be visited by one of the vehicles. It is desired to minimize the expected system time for the targets, that is, the expected time elapsed between the appearance of a target point and the instant it is visited. In this paper, such a routing problem is considered for a team of uninhabited aerial vehicles, modeled as vehicles moving with constant forward speed along paths of bounded curvature. Three algorithms are presented, each designed for a distinct set of operating conditions. Each is proven to provide a system time within a constant factor of the optimal when operating under the appropriate conditions. It is shown that the optimal routing policy depends on problem parameters such as the workload per vehicle and the vehicle density in the environment. Finally, there is discussion of a phase transition between two of the policies as the problem parameters are varied. In particular, for the case in which targets appear sporadically, a dimensionless parameter is identified which completely captures this phase transition and an estimate of the critical value of the parameter is provided.

Persistent patrol with limited-range on-board sensors

We propose and analyze the Persistent Patrol Problem (PPP). An unmanned aerial vehicle (UAV) moving with constant speed and unbounded acceleration patrols a bounded region of the plane where localized incidents occur according to a renewal process with known time intensity and spatial distribution. The UAV can detect incidents using on-board sensors with a limited visibility radius. We want to minimize the expected waiting time between the occurrence of an incident, and the time that it is detected. First, we provide a lower bound on the achievable expected detection time of any patrol policy in the limit as the visibility radius goes to zero. Second, we present the Biased Tile Sweep policy whose upper bound shows i) the lower bounds tightness, ii) the policys asymptotic optimality, and iii) that the desired spatial distribution of the searching vehicles position is proportional to the square root of the underlying spatial distribution of incidents it must find. Third, we present two online policies: i) a policy whose performance is provably within a constant factor of the optimal called TSP Sampling, ii) and the TSP Sampling with Receding Horizon heuristically yielding better performance than the former in practice. Fourth, we present a decision-theoretic approach to the PPP that attempts to solve for optimal policies offline. In addition, we use numerical experiments to compare performance of the four approaches and suggest suitable operational scenarios for each one.

UAV Routing and Coordination in Stochastic, Dynamic Environments

Recent years have witnessed great advancements in the science and technology for unmanned aerial vehicles (UAVs), e.g., in terms of autonomy, sensing, and networking capabilities. This chapter surveys algorithms on task assignment and scheduling for one or multiple UAVs in a dynamic environment, in which targets arrive at random locations at random times, and remain active until one of the UAVs flies to the target’s location and performs an on-site task. The objective is to minimize some measure of the targets’ activity, e.g., the average amount of time during which a target remains active. The chapter focuses on a technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. The main advantage of this approach is its ability to provide analytical estimates of the performance of the UAV system on a given problem, thus providing insight into how performance is affected by design and environmental parameters, such as the number of UAVs and the target distribution. In addition, the approach provides provable guarantees on the system’s performance with respect to an ideal optimum. To illustrate this approach, a variety of scenarios are considered, ranging from the simplest case where one UAV moves along continuous paths and has unlimited sensing capabilities, to the case where the motion of the UAV is subject to curvature constraints, and finally to the case where the UAV has a finite sensor footprint. Finally, the problem of cooperative routing algorithms for multiple UAVs is considered, within the same queueing-theoretical framework, and with a focus on control decentralization.

Coverage control for nonholonomic agents

Consider a coverage problem for a team of agents in the plane: target points appear sporadically over time in a bounded environment and must be visited by one of the agents. It is desired to minimize the expected elapsed time between the appearance of a target point, and the instant it is visited. For holonomic agents, this reduces to a continuous facility location problem, well studied in the geometric optimization literature. In this paper, we consider a team of nonholonomic vehicles constrained to move with constant forward speed along paths of bounded curvature. We show that, in this case, the optimal policy depends on the density of vehicles in the environment. In low density scenarios, the optimal policy resembles that of holonomic agents: the environment is partitioned into subregions of dominance, and each vehicle is responsible for targets appearing in its own subregion (territorial behavior). As the density increases, the optimal policy exhibits a transition to a gregarious behavior in which the team loiters in a coordinated pattern, and each vehicle visits targets that appear immediately in front of it.

Moon-Tracking Modes for Star Trackers

We examine the effectiveness and robustness of a moon-tracking backup mode for modern star trackers. This approach can be used to calculate a three-axis attitude solution from overexposed images of the moon. In examining this problem, we carefully consider the operational conditions under which this capability would be necessary and tailor our algorithmic approach appropriately. We describe a detailed simulation of the moon imaging process and outlinetherequiredimageprocessingstepsrequiredtoextractusefulinformationfromthemoonimages.Theimage processingextractsthemoonoutlineandestimatesthemoonpositionandorientationusinganonlinearleast-squares fit. Under most lighting conditions, our moon-vector estimates have an error of about 0.001 deg, and our sun-vector estimates have an error less than 0.25 deg. The capability of maintaining moderate accuracy attitude tracking in the presence of moon incursions is an important milestone toward a star-tracker-only attitude control system for microsatellites and nanosatellites. Nomenclature A, B, C, D = pixel vertex points a = radius of moon image, pixels b = semiminor axis of terminator curves, pixels CFG = rotation matrix (from G to F) E = overexposure factor e = eccentricity fi = error function fpix = focal length, pixels g = curve-fitting error hG = focus blur impulse response Ithresh = image intensity threshold

The Traveling Salesman Problem for the Reeds-Shepp Car and the Differential Drive Robot

In this paper we consider variations on the traveling salesman problem for the Reeds-Shepp car and differential drive robot. We consider the problem of finding the shortest path compatible with the dynamics of such models through a set of points. We present algorithms that asymptotically perform within a deterministic constant factor of the optimum, for any distribution of points. In addition, we consider a version of such problems in which the target points are dynamically generated by a stochastic process with uniform spatial density. In such a case, the objective will be to minimize the expected waiting time between the appearance of a target and the time it is visited by the vehicle. We present algorithms that (i) ensure stability of the system, for all target generation rates, and (ii) provably perform within a constant factor of the optimum

Optimal foraging of renewable resources

Consider a team of agents in the plane searching for and visiting target points that appear in a bounded environment, according to a stochastic renewal process with a known absolutely continuous spatial distribution. Agents must detect targets with limited-range onboard sensors. It is desired to minimize the expected waiting time between the appearance of a target point, and the instant it is visited. When the sensing radius is small, the system time is dominated by time spent searching, and it is shown that the optimal policy requires the agents to search a region at a relative frequency proportional to the square root of its renewal rate. On the other hand, when targets appear frequently, the system time is dominated by time spent servicing known targets, and it is shown that the optimal policy requires the agents to service a region at a relative frequency proportional to the cube root of its renewal rate. Furthermore, the presented algorithms in this case recover the optimal performance achieved by agents with full information of the environment. Simulation results verify the theoretical performance of the algorithms.