scholarly journals Learning-‘N-Flying: A Learning-Based, Decentralized Mission-Aware UAS Collision Avoidance Scheme

2021 ◽  
Vol 5 (4) ◽  
pp. 1-26
Author(s):  
Alëna Rodionova ◽  
Yash Vardhan Pant ◽  
Connor Kurtz ◽  
Kuk Jang ◽  
Houssam Abbas ◽  
...  
Keyword(s):  
Collision Avoidance ◽  
Computation Time ◽  
Unmanned Aircraft ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Online Computation ◽  
Multiple Case ◽  
Aircraft System ◽  
The City

Urban Air Mobility, the scenario where hundreds of manned and Unmanned Aircraft Systems (UASs) carry out a wide variety of missions (e.g., moving humans and goods within the city), is gaining acceptance as a transportation solution of the future. One of the key requirements for this to happen is safely managing the air traffic in these urban airspaces. Due to the expected density of the airspace, this requires fast autonomous solutions that can be deployed online. We propose Learning-‘N-Flying (LNF), a multi-UAS Collision Avoidance (CA) framework. It is decentralized, works on the fly, and allows autonomous Unmanned Aircraft System (UAS)s managed by different operators to safely carry out complex missions, represented using Signal Temporal Logic, in a shared airspace. We initially formulate the problem of predictive collision avoidance for two UASs as a mixed-integer linear program, and show that it is intractable to solve online. Instead, we first develop Learning-to-Fly (L2F) by combining (1) learning-based decision-making and (2) decentralized convex optimization-based control. LNF extends L2F to cases where there are more than two UASs on a collision path. Through extensive simulations, we show that our method can run online (computation time in the order of milliseconds) and under certain assumptions has failure rates of less than 1% in the worst case, improving to near 0% in more relaxed operations. We show the applicability of our scheme to a wide variety of settings through multiple case studies.

scholarly journals An unmanned aircraft system for maritime operations

2018 ◽  
Vol 15 (4) ◽  
pp. 172988141878633 ◽  
Author(s):  
Mario Monteiro Marques ◽  
Victor Lobo ◽  
R Batista ◽  
J Oliveira ◽  
A Pedro Aguiar ◽  
...  
Keyword(s):  
Collision Avoidance ◽  
Situational Awareness ◽  
Traffic Monitoring ◽  
Unmanned Aircraft ◽  
Automatic Identification ◽  
Identification System ◽  
Time Operation ◽  
Air System ◽  
Unmanned Air System ◽  
Aircraft System

Unmanned air systems are becoming ever more important in modern societies but raise a number of unresolved problems. There are legal issues with the operation of these vehicles in nonsegregated airspace, and a pressing requirement to solve these issues is the development and testing of reliable and safe mechanisms to avoid collision in flight. In this article, we describe a sense and avoid subsystem developed for a maritime patrol unmanned air system. The article starts with a description of the unmanned air system, that was developed specifically for maritime patrol operations, and proceeds with a discussion of possible ways to guarantee that the unmanned air system does not collide with other flying objects. In the system developed, the position of the unmanned air system is obtained by the global positioning system and that of other flying objects is reported via a data link with a ground control station. This assumes that the detection of those flying objects is done by a radar in the ground or by self-reporting via a traffic monitoring system (such as automatic identification system). The algorithm developed is based on game theory. The approach is to handle both the procedures, threat detection phase and collision avoidance maneuver, in a unified fashion, where the optimal command for each possible relative attitude of the obstacle is computed off-line, therefore requiring low processing power for real-time operation. This work was done under the research project named SEAGULL that aims to improve maritime situational awareness using fleets of unmanned air system, where collision avoidance becomes a major concern.

scholarly journals Sampling Based Approaches for Minimizing Regret in Uncertain Markov Decision Processes (MDPs)

2017 ◽  
Vol 59 ◽  
pp. 229-264 ◽  
Author(s):  
Asrar Ahmed ◽  
Pradeep Varakantham ◽  
Meghna Lowalekar ◽  
Yossiri Adulyasak ◽  
Patrick Jaillet
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Mixed Integer ◽  
Benchmark Problems ◽  
Minimax Regret ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Integer Linear Program Formulation ◽  
Markov Decision ◽  
Reward Functions

Markov Decision Processes (MDPs) are an effective model to represent decision processes in the presence of transitional uncertainty and reward tradeoffs. However, due to the difficulty in exactly specifying the transition and reward functions in MDPs, researchers have proposed uncertain MDP models and robustness objectives in solving those models. Most approaches for computing robust policies have focused on the computation of maximin policies which maximize the value in the worst case amongst all realisations of uncertainty. Given the overly conservative nature of maximin policies, recent work has proposed minimax regret as an ideal alternative to the maximin objective for robust optimization. However, existing algorithms for handling minimax regret are restricted to models with uncertainty over rewards only and they are also limited in their scalability. Therefore, we provide a general model of uncertain MDPs that considers uncertainty over both transition and reward functions. Furthermore, we also consider dependence of the uncertainty across different states and decision epochs. We also provide a mixed integer linear program formulation for minimizing regret given a set of samples of the transition and reward functions in the uncertain MDP. In addition, we provide two myopic variants of regret, namely Cumulative Expected Myopic Regret (CEMR) and One Step Regret (OSR) that can be optimized in a scalable manner. Specifically, we provide dynamic programming and policy iteration based algorithms to optimize CEMR and OSR respectively. Finally, to demonstrate the effectiveness of our approaches, we provide comparisons on two benchmark problems from literature. We observe that optimizing the myopic variants of regret, OSR and CEMR are better than directly optimizing the regret.

scholarly journals Train-Scheduling Optimization Model for Railway Networks with Multiplatform Stations

2019 ◽  
Vol 12 (1) ◽  
pp. 257
Author(s):  
Gianmarco Garrisi ◽  
Cristina Cervelló-Pastor
Keyword(s):  
Mathematical Formulation ◽  
Computation Time ◽  
Mixed Integer ◽  
Initial Population ◽  
Mixed Integer Linear Program ◽  
Transit System ◽  
Train Scheduling ◽  
Railway Networks ◽  
Np Hard Problem ◽  
Problem Instances

This paper focuses on optimizing the schedule of trains on railway networks composed of busy complex stations. A mathematical formulation of this problem is provided as a Mixed Integer Linear Program (MILP). However, the creation of an optimal new timetable is an NP-hard problem; therefore, the MILP can be solved for easy cases, computation time being impractical for more complex examples. In these cases, a heuristic approach is provided that makes use of genetic algorithms to find a good solution jointly with heuristic techniques to generate an initial population. The algorithm was applied to a number of problem instances producing feasible, though not optimal, solutions in several seconds on a laptop, and compared to other proposals. Some improvements are suggested to obtain better results and further improve computation time. Rail transport is recognized as a sustainable and energy-efficient means of transport. Moreover, each freight train can take a large number of trucks off the roads, making them safer. Studies in this field can help to make railways more attractive to travelers by reducing operative cost, and increasing the number of services and their punctuality. To improve the transit system and service, it is necessary to build optimal train scheduling. There is an interest from the industry in automating the scheduling process. Fast computerized train scheduling, moreover, can be used to explore the effects of alternative draft timetables, operating policies, station layouts, and random delays or failures.

How to Beat Flappy Bird: A Mixed-Integer Model Predictive Control Approach

2017 ◽  
Author(s):  
Matthew Piper ◽  
Pranav Bhounsule ◽  
Krystel K. Castillo-Villar
Keyword(s):  
Optimal Path ◽  
Computation Time ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Worst Case ◽  
Control Approach ◽  
Average Computation Time ◽  
Prediction And Control ◽  
Point Condition ◽  
Velocity Constraints

Flappy Bird is a mobile game that involves tapping the screen to navigate a bird through a gap between pairs of vertical pipes. When the bird passes through the gap, the score increments by one and the game ends when the bird hits the floor or a pipe. Surprisingly, Flappy Bird is a very difficult game and scores in single digits are not uncommon even after extensive practice. In this paper, we create three controllers to play the game autonomously. The controllers are: (1) a manually tuned controller that flaps the bird based on a vertical set point condition; (2) an optimization-based controller that plans and executes an optimal path between consecutive tubes; (3) a model-based predictive controller (MPC). Our results showed that on average, the optimization-based controller scored highest, followed closely by the MPC, while the manually tuned controller scored the least. A key insight was that choosing a planning horizon slightly beyond consecutive tubes was critical for achieving high scores. The average computation time per iteration for the MPC was half that of optimization-based controller but the worst case time (maximum time) per iteration for the MPC was thrice that of optimization-based controller. The success of the optimization-based controller was due to the intuitive tuning of the terminal position and velocity constraints while for the MPC the important parameters were the prediction and control horizon. The MPC was straightforward to tune compared to the other two controllers. Our conclusion is that MPC provides the best compromise between performance and computation speed without requiring elaborate tuning.

scholarly journals A solution framework for linear PDE-constrained mixed-integer problems

2021 ◽  
Author(s):  
Fabian Gnegel ◽  
Armin Fügenschuh ◽  
Michael Hagel ◽  
Sven Leyffer ◽  
Marcus Stiemer
Keyword(s):  
Computation Time ◽  
Mixed Integer ◽  
Continuous Control ◽  
State Variables ◽  
Mixed Integer Linear Program ◽  
Numerical Solution Method ◽  
Linear Pde ◽  
Finite Set ◽  
Continuous Constraints ◽  
Naive Approach

AbstractWe present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

scholarly journals Optimal Coordinated Bidding of a Profit Maximizing, Risk-Averse EV Aggregator in Three-Settlement Markets Under Uncertainty

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1755 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Real Time ◽  
Value At Risk ◽  
Risk Measure ◽  
Convex Combination ◽  
Computation Time ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Mixed Integer Linear Program ◽  
Market Prices

This paper develops a two-stage stochastic and dynamically updated multi-period mixed integer linear program (SD-MILP) for optimal coordinated bidding of an electric vehicle (EV) aggregator to maximize its profit from participating in competitive day-ahead, intra-day and real-time markets. The hourly conditional value at risk (T-CVaR) is applied to model the risk of trading in different markets. The objective of two-stage SD-MILP is modeled as a convex combination of the expected profit and the T-CVaR hourly risk measure. When day-ahead, intra-day and real-time market prices and fleet mobility are uncertain, the proposed two-stage SD-MILP model yields optimal EV charging/discharging plans for day-ahead, intra-day and real-time markets at per device level. The degradation costs of EV batteries are precisely modeled. To reflect the continuous clearing nature of the intra-day and real-time markets, rolling planning is applied, which allows re-forecasting and re-dispatching. The proposed two-stage SD-MILP is used to derive a bidding curve of an aggregator managing 1000 EVs. Furthermore, the model statistics and computation time are recorded while simulating the developed algorithm with 5000 EVs.

Distributionally Robust Hub Location

2020 ◽  
Vol 54 (5) ◽  
pp. 1189-1210 ◽  
Author(s):  
Shuming Wang ◽  
Zhi Chen ◽  
Tianqi Liu
Keyword(s):  
Convex Hull ◽  
Mixed Integer ◽  
Hub Location ◽  
Hub Location Problem ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Data Set ◽  
Second Stage ◽  
Robust Model ◽  
Distributionally Robust

We study the adaptive distributionally robust hub location problem with multiple commodities under demand and cost uncertainty in both uncapacitated and capacitated cases. The hub location decision anticipates the worst-case expected cost over an ambiguity set of possible distributions of the uncertain demand and cost, and the routing policy, being adaptive to the uncertainty realization, ships commodities through selected hubs. We investigate the adaptivity and tractability of the distributionally robust model under different distributional information about uncertainty. In the uncapacitated case in which demand and cost are independent and costs of different commodities are also mutually independent, the adaptive distributionally robust model is equivalent to a nonadaptive classical robust model and the second-stage routing decision follows an optimal static policy. We then relax the independence assumption and show that the second-stage routing decision follows an optimal scenario-wise policy if either the demand or the cost is supported on a convex hull of given scenarios. We extend our analysis to the capacitated case and show that the second-stage routing decision still follows an optimal scenario-wise policy if the demand is supported on the convex hull of given scenarios. In terms of tractability, for all mentioned cases, we reformulate the distributionally robust model as a moderate-sized mixed-integer linear program, and we recover the associated worst-case distribution by solving a collection of linear programs. Through numerical studies using the Civil Aeronautics Board data set, we demonstrate the advantages of the distributionally robust model by examining its superior out-of-sample performance against the classical robust model and the stochastic model.

scholarly journals Time Efficient Unmanned Aircraft Systems Deployment in Disaster Scenarios Using Clustering Methods and a Set Cover Approach

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 422
Author(s):  
Donald Mahoro Ntwari ◽  
Daniel Gutierrez-Reina ◽  
Sergio Luis Toral Marín ◽  
Hissam Tawfik
Keyword(s):  
Clustering Algorithms ◽  
Research Work ◽  
Computation Time ◽  
Search Space ◽  
Unmanned Aircraft ◽  
Set Cover ◽  
Connected Components ◽  
Clustering Methods ◽  
Minimum Number ◽  
Aircraft System

Unmanned aircraft, which are more commonly known as drones, are nowadays extensively used in an ever increasing set of applications. In a wider system, the aircraft are usually associated to additional elements such as ground-based controllers. Furthermore, when these components form a network of elements that can communicate, the system is said to form an Unmanned Aircraft System (UAS). This system is particularly effective when the aircraft within are organized into swarms with sets of objectives to accomplish. The extensive use of swarms into UASs is more and more exploited nowadays due to the decreasing cost of those aircraft. In the present work we are interested in a particular application of UASs, namely their deployment in disaster scenarios for communications services provision to targets on the ground. These ground targets, however, are not part of the UASs and should not be confused with ground-based controllers. The present work does not only focus on coverage for ground targets but also on a guaranteed minimum number of covers for each target, which is called the redundancy requirement. The research work also ensures that the deployed UAS forms a unique connected component so that a steady stream of communication is kept with the targets to cover. Research work similar to the present perform the initial deployment of their aircraft in a different manner, either randomly, based on a predetermined grid formation, or using other elaborated methods. This work proposes a new solution based on the use of clustering algorithms, combined to a design of the problem formulated as a set cover optimization model. The clustering phase is used to discretize the search space and ease the optimization phase by locating regions of interest, and then a further procedure is applied, only when needed, to reconnect scattered connected components and guarantee connectivity in the networks. This way of doing it has achieved a deployment of UASs with maximum coverage for all targets, a guaranteed minimum number of covers for each of them, and results in a competitive computation time. The latter also allowed for more scalability by extending the tests to very large input instances.

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