Meir Pachter

UAV Task Assignment with Timing Constraints

Abstract : This paper addresses the problem of task allocation for wide area search munitions. The munitions are required to search for, classify, attack, and verify the destruction of potential targets. We assume that target field information is communicated between all elements of the swarm. We generate a tour of optimal assignments for each vehicle using a Mixed Integer Linear Program, or MILP format. MILP can assign tasks that look infeasible, due to timing, by adding time to a UAVs path, and vehicle paths are then recalculated to match the required arrival times. The MILP formulation with variable arrival times provides an optimal solution to multiple-assignment problems for groups of UAVs with coupled tasks involving timing and task order constraints.

UAV Task Assignment with Timing Constraints via Mixed-Integer Linear Programming

Abstract : The optimal timing of air-to-ground tasks is undertaken. Specifically, a scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. The vehicles must perform multiple tasks on each target. The targets must be found, classified, attacked, and verified as destroyed. The optimal performance of these tasks requires cooperation amongst the vehicles such that critical timing constraints are satisfied. In this paper, an optimal task assignment and timing algorithm is developed, using a mixed integer linear program, or MILP, formulation. MILP can be used to assign all tasks to the vehicles in an optimal manner, including variable arrival times, for groups of air vehicles with coupled tasks involving timing and task order constraints. When the air vehicles have sufficient endurance, the existence of a solution is guaranteed.

Cooperative Aircraft Defense from an Attacking Missile using Proportional Navigation

A three-agent pursuit-evasion scenario where an Attacker missile using Proportional Navigation guidance pursues a Target aircraft is considered in this paper. The Target is aided by a Defender missile which is launched by a wingman and aims at intercepting the Attacker before it reaches the aircraft. An optimal control problem is posed which captures the goal of the Target-Defender team, namely, to maximize the separation between Target and Attacker at the instant of capture of the Attacker by the Defender. The optimal control law provides the heading angles for the Target and the Defender team.

Concepts for Generating Coherent Radar Phantom Tracks Using Cooperating Vehicles

Multiple cooperating Electronic Combat Air Vehicles (ECAVs) are used to generate phantom radar tracks in a multiple radar air defense network. The vehicles use a range delay deception transponder, which delays the radar pulses received by the ECAV and sends them back to the radar. This results in the radar calculating an erroneous target range. A radar network will correlate tracks to discern actual vehicle positions from phantom targets. The ECAV team, however, precisely positions and dynamically coordinates the motion of the vehicles so that all radars see the same phantom track. This paper presents twodimensional mathematical relationships between the motion of the vehicles and the motion of the phantom tracks. Closed form solutions are obtained for the ECAV trajectory given a specifled phantom track. Parametric analyses are performed with constraints on the overall vehicle dynamics, in which case ∞yable regions are established to ensure the integrity of the phantom target track. Results are presented for a single vehicle and a single radar engagement, and for up to four vehicles generating single and multiple phantom tracks for up to four radars correlating returns. This paper presents several concepts for generating phantom tracks using cooperating vehicles.

Autonomous Decision Making with Uncertainty for an Urban Intelligence, Surveillance and Reconnaissance (ISR) Scenario

In this paper, we consider an urban ISR scenario where a human operator is tasked to provide feedback regarding the nature of some objects of interest. The feedback is relayed to the stochastic controller of an unmanned aerial vehicle (UAV), which must determine an appropriate mission plan. A small (unmanned) aerial vehicle (SAV) loiters at a high altitude where it may survey a large territory. An operator decides which objects in the SAV’s field of view are of interest and which are not. Then a team of micro (unmanned) aerial vehicles (MAVs) is assigned individual tours to inspect the objects of interest at a low altitude. As a MAV flies over an object of interest, the operator must decide if the object has a feature that uniquely distinguishes it as a target. The key parameters are the operator’s response and the time taken for the operator to respond. The controller uses these parameters to compute the expected information gain of a revisit. In previous studies automatic target recognition (ATR) was used for making some decisions in the SAV and the MAVs. This paper investigates the use of human feedback alone for target recognition. Different methods for calculating expected information gain are examined and compared. In addition, results from a flight test of this controller are presented.

Optimal Perimeter Patrol Alert Servicing with Poisson Arrival Rate

This paper addresses a base perimeter patrol scenario where alerts are generated from a set of stations at random intervals. A Unmanned Aerial Vehicle patrols the perimeter and responds to alerts. After arriving at an alert site, the vehicle loiters for a time to enable the operator to determine if the alert is a nuisance trip or an actual threat. The false alarms are modeled as a Poisson process. A stochastic control optimization problem is developed to determine the optimal loiter time. The optimal length of time that a vehicle can dwell at an alert site while minimizing the expected service time is a function of the size of the alert queue and the alert rate. Results from where the algorithm was ∞ight tested as part of a base defense scenario is presented.

Optimal decision rules and human operator models for UAV operations

We present strategies for decision making under uncertainty and operator modeling for small UAV operations. Uncertainty comes from the stochastic nature of the environment and of the operator model. Time delays are accounted for using stochastic dynamic programming. Operator workload is addressed using scheduling theory. Operator confusion and its effect on the decision making process are considered as well.

Predicting Pop up Threats from an Adaptive Markov Model

We consider military scenarios in which an adversary has ground assets that are not observable most of the time, and on occasion, they pop up and become observable for short durations of time. It is desired to deploy Unmanned Air Vehicles and persistently deny the adversary time windows for launching weapons. We model the pop up phenomenon as an Adaptive Markov Chain, and use the model to predict future pop up threat locations. The UAVs are controlled to move towards the predicted threats to better perform Persistent Area Denial Mission. The objective is to reduce the time between the pop up and the time to reach the pop up. Preliminary simulation experiments are presented.

Average Reward Dynamic Programming Applied to a Persistent Visitation and Data Delivery Problem

We are interested in the persistent surveillance of an area of interest comprised of stations/ data nodes that need to be visited in a cyclic manner. The data collection task is undertaken by a UAV which autonomously executes the mission. In addition to geographically distributed stations, the scenario also includes a central depot, where data collected from the different nodes must be delivered. In this context, the performance criteria, in addition to a desired minimal cycle time, also entails minimizing the delay in delivering the data collected from each node to the depot. Each node has a priority/ weight associated with it that characterizes the relative importance between timely delivery of data from the nodes. We pose the problem as an average/ cycle reward maximization problem; where the UAV gains a reward that is a decreasing function of weighted delay in data delivery from the nodes. Since we aim to maximize the average reward, the solution also favors shorter overall cycle time. In a cycle, each station is visited exactly once; however, we allow the UAV to visit the depot more than once in a cycle. Evidently, this allows for quicker delivery of data from a higher priority node. We apply results from average reward maximization stochastic dynamic programming to our deterministic case and solve the problem using Linear Programming. We also discuss the special case of no penalty on delivery delay, whence the problem collapses to the well known metric Traveling Salesman Problem.Copyright

A Lower Bounding Linear Programming approach to the Perimeter Patrol Stochastic Control Problem.

One encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for large scale controlled Markov chains. In this article, we consider a perimeter patrol stochastic optimal control problem. To determine the optimal control policy, one has to solve a Markov decision problem, whose large size renders exact dynamic programming methods intractable. So, we propose a state aggregation based approximate linear programming method to construct provably good sub-optimal policies instead. The state-space is partitioned and the optimal cost-to-go or value function is restricted to be a constant over each partition. We show that the resulting restricted system of linear inequalities embeds a family of Markov chains of lower dimension, one of which can be used to construct a tight lower bound on the optimal value function. In general, the construction of the lower bound requires the solution to a combinatorial problem. But the perimeter patrol problem exhibits a special structure that enables tractable linear programming formulation for the lower bound. We demonstrate this and also provide numerical results that corroborate the efficacy of the proposed methodology.