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Linear And Nonlinear Programming

The use of unmanned aerial vehicles (UAVs) is growing rapidly across many civil application domains, including real-time monitoring, providing wireless coverage, remote sensing, search and rescue, delivery of goods, security and surveillance, precision agriculture, and civil infrastructure inspection. Smart UAVs are the next big revolution in the UAV technology promising to provide new opportunities in different applications, especially in civil infrastructure in terms of reduced risks and lower cost. Civil infrastructure is expected to dominate more than $45 Billion market value of UAV usage. In this paper, we present UAV civil applications and their challenges. We also discuss the current research trends and provide future insights for potential UAV uses. Furthermore, we present the key challenges for UAV civil applications, including charging challenges, collision avoidance and swarming challenges, and networking and security-related challenges. Based on our review of the recent literature, we discuss open research challenges and draw high-level insights on how these challenges might be approached.

Unmanned Aerial Vehicles: A Survey on Civil Applications and Key Research Challenges

Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or ‘instance’ parameter. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization and chance-constrained optimization. Robust optimization is a deterministic paradigm where one seeks a solution which simultaneously satisfies all possible constraint instances. In chance-constrained optimization a probability distribution is instead assumed on the uncertain parameters, and the constraints are enforced up to a pre-specified level of probability. Unfortunately however, both approaches lead to computationally intractable problem formulations. In this paper, we consider an alternative ‘randomized’ or ‘scenario’ approach for dealing with uncertainty in optimization, based on constraint sampling. In particular, we study the constrained optimization problem resulting by taking into account only a finite set of N constraints, chosen at random among the possible constraint instances of the uncertain problem. We show that the resulting randomized solution fails to satisfy only a small portion of the original constraints, provided that a sufficient number of samples is drawn. Our key result is to provide an efficient and explicit bound on the measure (probability or volume) of the original constraints that are possibly violated by the randomized solution. This volume rapidly decreases to zero as N is increased.

/pdf/uncertain-convex-programs-randomized-solutions-and-3vs4hcxix0.pdf

Uncertain convex programs: randomized solutions and confidence levels

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and "state-relevance weights" that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.

/pdf/the-linear-programming-approach-to-approximate-dynamic-4z83wfv7mc.pdf

The Linear Programming Approach to Approximate Dynamic Programming

Future Unmanned Aircraft Systems (UASs) are expected to be nearly autonomous and composed of heterogeneous Unmanned Aerial Vehicles (UAVs). While most of the current research focuses on UAV avionics and control algorithms, ground task automation has come to the attention of researchers during the past few years. Ground task automation not only relieves human operators, but may also expand the UAS operation area, improve system coverage and enable operation in risky environments without posing a threat to humans. We propose a model to evaluate the coverage of a given UAS. We also compare different solutions for various modules of an automated battery replacement system for UAVs. In addition, we propose a ground station capable of swapping a UAV's batteries, followed by a discussion of prototype components and tests of some of the prototype modules. The proposed platform is well-suited for high-coverage requirements and is capable of handling a heterogeneous UAV fleet.

Automatic Battery Replacement System for UAVs: Analysis and Design

The duration of missions that can be accomplished by a system of unmanned aerial vehicles (UAVs) is limited by the battery or fuel capacity of its constituent UAVs. However, a system of UAVs that is supported by automated refueling stations may support long term or even indefinite duration missions. We develop a mixed integer linear program (MILP) model to formalize the problem of scheduling a system of UAVs and multiple shared bases in disparate geographic locations. There are mission trajectories that must be followed by at least one UAV. A UAV may hand off the mission to another in order to return to base for fuel. To address the computational complexity of the MILP formulation, we develop a genetic algorithm to find feasible solutions when a state-of-the-art solver such as CPLEX cannot. In practice, the approach allows for a long-term mission to receive uninterrupted UAV service by successively handing off the task to replacement UAVs served by geographically distributed shared bases.

On the Scheduling of Systems of UAVs and Fuel Service Stations for Long-Term Mission Fulfillment

A key requirement for the complete autonomy of an unmanned aerial vehicle (UAV) is the replenishment of its energy source and other consumables. Such processes are typically overseen and conducted by a human operator, may be time consuming and effectively reduce the operating range of the system. To satisfy the requirements of UAV customers such as military surveillance networks, that seek faster, broader and more fully autonomous systems, and hobbyists, who seek to avoid the hassle associated with changing the fuel source, we develop automated energy recharging systems. Focusing on battery operated remote control helicopters, we employ the Axiomatic Design methodology to develop design concepts of platforms to act as automatic service stations. We propose three station designs for refilling platforms and one concept for battery exchange platforms. In addition, we analyze the economic feasibility of automatic consumable replenishment stations, consider two types of station (container refilling and container exchange) and discuss the application of these systems. Refilling platforms better suit low coverage unmanned aerial systems (UAS) while exchange stations allow high coverage with fewer UAVs.

UAV Consumable Replenishment: Design Concepts for Automated Service Stations

We obtain new linear programs for bounding the performance and proving the stability of queueing networks. They exploit the key facts that the transition probabilities of queueing networks are shift invariant on the relative interiors of faces and the cost functions of interest are linear in the state. A systematic procedure for choosing different quadratic functions on the relative interiors of faces to serve as surrogates of the differential costs in an inequality relaxation of the average cost function leads to linear program bounds. These bounds are probably better than earlier known bounds. It is also shown how to incorporate additional features, such as the presence of virtual multi-server stations to further improve the bounds. The approach also extends to provide functional bounds valid for all arrival rates.

New linear program performance bounds for queueing networks

Approximate closed form expressions for the mean cycle time in a G/G/m-queue often serve as practical and intuitive alternatives to more exact but less tractable analyses. However, the G/G/m-queue model may not fully address issues that arise in practical manufacturing systems. Such issues include tools with production parallelism, tools that are idle with work in process, travel to the queue, and the tendency of lots to defect from a failed server and return to the queue even after they have entered production. In this paper, we extend popular approximate mean cycle time formulae to address these practical manufacturing issues. Employing automated data extraction algorithms embedded in software, we test the approximations using parameters gleaned from production tool groups in IBM's 200 mm semiconductor wafer fabricator.

James R. Morrison

Papers

Automatic Battery Replacement System for UAVs: Analysis and Design

On the Scheduling of Systems of UAVs and Fuel Service Stations for Long-Term Mission Fulfillment

UAV Consumable Replenishment: Design Concepts for Automated Service Stations

New linear program performance bounds for queueing networks

Practical Extensions to Cycle Time Approximations for the $G/G/m$ -Queue With Applications