Satyanarayana G. Manyam

Path planning for cooperative routing of air-ground vehicles

We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments on several randomly generated instances.

Precision airdrop transition altitude optimization via the one-in-a-set traveling salesman problem

Mission planning for ballistic precision airdrop (PAD) operations has traditionally focused on determining the optimal computed air release point (CARP) to release the payloads that minimizes the circle error average (CEA) of the payload impact pattern on the ground. More recent work has introduced the idea of varying the drogue-to-main parachute transition altitude of the ballistic payloads in order to improve airdrop accuracy and reduce bundle dispersion. By varying the transition altitude of the payload, its impact location can be controlled to lie anywhere on a finite 1D curve on the ground. The exact shape of this curve is defined by the system properties and the local wind field. Previous work has demonstrated the usage of these curves for determining the optimal transition altitudes that minimize the CEA. This paper discusses the limitations of optimizing the transition altitudes based on the ground impact CEA. An alternative cost function is proposed that explicitly represents the risk encountered when retrieving the payloads on the ground and returning them to a base location. This cost function is the solution to the traveling salesman problem (TSP). Additionally, an algorithm is introduced that models this PAD optimization problem as a one-in-a-set TSP. Established techniques from the TSP literature are then utilized to determine the transition altitudes. This cost function and algorithm is compared to CEA-based optimization for a scenario with complex terrain. The resulting TSP-based solution results in a 43% reduction in risk encountered when retrieving and returning the supplies to a base when compared to the CEA-based solution. Here, risk is modeled as the total distance traveled during the retrieval process; however, alternative models for risk can easily be considered within this solution framework.

GPS Denied UAV Routing with Communication Constraints

A novel GPS denied routing problem for UAVs is described, where the UAVs cooperatively navigate through a restricted zone deployed with noncommunicating Unattended Ground Sensors (UGS). The routing algorithm presenting in this paper ensures the UAVs maintain strict contact with at least one UGS, which allows the UGS act as beacons for relative navigation eliminating the need for dead reckoning. This problem is referred to as the Communication Constrained UAV Routing Problem (CCURP). Two architectures for cooperative navigation of two or three UAVs are considered. For the two UAV problem, a 92

On Tightly Bounding the Dubins Traveling Salesman's Optimum

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Dubins paths through a sequence of points: Lower and upper bounds

-approximation algorithm is developed. The three UAV problem is transformed into a one-in-a-set Traveling Salesman Problem (TSP), which is solved as a regular asymmetric TSP using existing methods after applying a second transformation. Computational results corroborating the performance bounds are presented.

Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points

The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal solution to the problem. In addition, relaxing the motion constraints and solving the resulting Euclidean TSP (ETSP) provides the only lower bound available for the problem. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This article addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal solution to the problem. In addition, relaxing the motion constraints and solving the resulting Euclidean TSP (ETSP) provides the only lower bound available for the problem. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This article addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.

Computation of lower bounds for a multiple depot, multiple vehicle routing problem with motion constraints

This article addresses an important path planning problem for robots and Unmanned Aerial Vehicles (UAVs) which aims to find a shortest path of bounded curvature passing through a given sequence of target points on a ground plane. Currently, there is no algorithm that can compute an optimal solution to this problem. Therefore, tight lower bounds are vital in determining the quality of any feasible solution to this problem. Novel tight lower bounding algorithms are presented in this article by relaxing some of the heading angle constraints at the target points. The proposed approach requires us to solve variants of an optimization problem called the Dubins interval problem between two points where the heading angles at the points are constrained to be within a specified interval. These variants can be solved using tools from optimal control theory. Specifically, two lower bounding algorithms are presented in this article using this approach and these bounds are then compared with the existing results in the literature. Computational results are also presented to corroborate the performance of the proposed algorithms.

Practical considerations for implementing an autonomous, persistent, intelligence, surveillance, and reconnaissance system

This article addresses an important path planning problem for robots and Unmanned Aerial Vehicles (UAVs), which is to find the shortest path of bounded curvature passing through a given sequence of target points on a ground plane. Currently, no algorithm exists that can compute an optimal solution to this problem. Therefore, tight lower bounds are vital in determining the quality of any feasible solution to this problem. Novel tight lower bounding algorithms are presented in this article by relaxing some of the heading angle constraints at the target points. The proposed approach requires us to solve variants of an optimization problem called the Dubins interval problem between two points where the heading angles at the points are constrained to be within a specified interval. These variants are solved using tools from optimal control theory. Using these approaches, two lower bounding algorithms are presented and these bounds are then compared with existing results in the literature. Computational results are presented to corroborate the performance of the proposed algorithms; the average reduction in the difference between upper bounds and lower bounds is 80 % to 85 % with respect to the trivial Euclidean lower bounds.

Optimizing multiple UAV cooperative ground attack missions

In this paper, the problem of planning paths for a collection of vehicles passing through a set of targets is considered. Each vehicle starts at a specified location (called a depot) and it is required that each target be on the path of at least one vehicle. Every vehicle has a motion constraint and the path of each vehicle must satisfy that constraint. In this article, we developed a method to compute lower bounds to this path planning problem by relaxing some of the constraints and posing it as a standard multiple traveling salesmen problem. For those problem instances where the distance between every pair of targets is at least 4 units, another method is developed to compute a lower bound using the convexity property of the length of such paths. The proposed bounds are numerically corroborated.

Path planning for multiple heterogeneous Unmanned Vehicles with uncertain service times

We are interested in the persistent surveillance of an area of interest comprised of heterogeneous tasks (or targets) that need to be completed (or visited) in a repeated manner subject to constraints on time between successive visits. The task is undertaken by a set of heterogeneous UAVs which autonomously execute the mission. In addition to geographically distributed tasks, the mission may also include a central node (control target), where data collected from the different targets need to be delivered. In this context, the performance of the system, in addition to the desired revisit rate of the tasks may also entail minimizing the delay in delivering the data collected from a target/task to the central node. We detail, in this paper, a completely autonomous Persistent, Intelligence, Surveillance and Reconnaissance (PISR) System, that addresses the mission requirements. In particular, we focus on practical considerations in terms of scalable optimization and heuristic methods that solve the underlying problem and also discuss the on-board implementation of the chosen optimization schema. We provide details on an in-house software framework that enables easy implementation of the optimization algorithms on commercial drones. To solve the problem, we consider three different optimization schemes based on branch and bound (tree search), MILP formulation and Dynamic Programming. We compare and contrast the three approaches with details on the respective benefits and pitfalls and also touch upon easily implementable heuristic methods motivated by the optimal solution.