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40
A Review of Conflict Detection and Resolution Modeling Methods
 IEEE Transactions on Intelligent Transportation Systems
, 2000
"... A number of methods have been proposed to automate air traffic conflict detection and resolution (CD&R), but there has been little cohesive discussion or comparative evaluation of approaches. This paper presents a survey of 68 recent CD&R modeling methods, several of which are currently in u ..."
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Cited by 105 (2 self)
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A number of methods have been proposed to automate air traffic conflict detection and resolution (CD&R), but there has been little cohesive discussion or comparative evaluation of approaches. This paper presents a survey of 68 recent CD&R modeling methods, several of which are currently in use or under operational evaluation. A framework that articulates the basic functions of CD&R is used to categorize the models. The taxonomy includes: dimensions of state information (vertical, horizontal, or threedimensional); method of dynamic state propagation (nominal, worstcase, or probabilistic); conflict detection threshold; conflict resolution method (prescribed, optimized, force field, or manual); maneuvering dimensions (speed change, lateral, vertical, or combined maneuvers); and management of multiple aircraft conflicts (pairwise or global). An overview of important considerations for these and other CD&R functions is provided, and the current system design process is critiqued.
Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths
, 2005
"... This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize t ..."
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Cited by 70 (9 self)
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This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collisionfree segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic carlike robots is described, along with implementation results for 12 robots.
A Probabilistic Approach to Aircraft Conflict Detection
, 2000
"... Conflict detection and resolution schemes operating at the midrange and shortrange level of the air traffic management process are discussed. Probabilistic models for predicting the aircraft position in the nearterm and midterm future are developed. Based on the midterm prediction model, the ma ..."
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Cited by 51 (10 self)
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Conflict detection and resolution schemes operating at the midrange and shortrange level of the air traffic management process are discussed. Probabilistic models for predicting the aircraft position in the nearterm and midterm future are developed. Based on the midterm prediction model, the maximum instantaneous probability of conflict is proposed as a criticality measure for two aircraft encounters. Randomized algorithms are introduced to efficiently estimate this measure of criticality and provide quantitative bounds on the level of approximation introduced. For shortterm detection, approximate closedform analytical expressions for the probability of conflict are obtained, using the shortterm prediction model. Based on these expressions, an algorithm for decentralized conflict detection and resolution that generalizes potential fields methods for path planning to a probabilistic dynamic environment is proposed. The algorithms are validated using Monte Carlo simulations.
Protocolbased conflict resolution for air traffic control
 AIR TRAFFIC CONTROL QUARTERLY 15(1)
, 2002
"... This paper proposes a method for multipleaircraft conflict avoidance. We assume that aircraft cruise at constant altitude with varying velocities and that conflicts are resolved in the horizontal plane using heading change, velocity change, or a combination thereof. We assume that each aircraft’s ..."
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Cited by 22 (2 self)
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This paper proposes a method for multipleaircraft conflict avoidance. We assume that aircraft cruise at constant altitude with varying velocities and that conflicts are resolved in the horizontal plane using heading change, velocity change, or a combination thereof. We assume that each aircraft’s position, heading, and velocity are available to all aircraft involved in the conflict, we constrain the maneuver to be two straight paths of equal length, and we assume that all aircraft initiate conflict resolution maneuvers at the same time and that once an aircraft has initiated a maneuver, its velocity along the maneuver remains constant. Our multipleaircraft conflict resolution methodology is presented in two steps; first, we consider an unrealistic but geometrically simple exact conflict, in which the original trajectories of all aircraft collide at a point, in order to derive a closedform analytic solution for the required heading change, and then we consider a realistic inexact conflict, in which conflict points of multiple aircraft do not coincide. Heading change is a main control input for conflict resolution, yet velocity change is also used for an inexact conflict. We then construct a finite partition of the airspace around the conflict, and using our analytic solution, we derive a protocol for resolving the worstcase conflict within each partition. The result is a multipleaircraft conflict resolution protocol, or a simple rule which is easily understandable and
Optimal coordinated motions of multiple agents moving on a plane
 SIAM J. Control and Optimization
, 2003
"... Abstract. We address the problem of optimal coordinated motions of multiple agents moving in the same planar region. The agents ’ motions must satisfy a separation constraint throughout the encounter to be conflictfree. The objective is to determine the conflictfree maneuvers (motions) with the le ..."
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Cited by 17 (6 self)
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Abstract. We address the problem of optimal coordinated motions of multiple agents moving in the same planar region. The agents ’ motions must satisfy a separation constraint throughout the encounter to be conflictfree. The objective is to determine the conflictfree maneuvers (motions) with the least combined energy, while taking into account the fact that agents may have different priorities. A formal classification of conflictfree maneuvers into homotopy types is introduced by using their braid representation. Various local and global optimality conditions are derived through variational analysis in the presence of the separation constraint. In the case of two agents, these optimality conditions allow us to construct the optimal maneuvers geometrically. For the general multiagent case, a convex optimization algorithm is proposed to compute within each homotopy type a solution to the optimization problem restricted to the class of multilegged maneuvers. Since the number of types grows explosively with the number of agents, a stochastic algorithm is suggested as the “type chooser”, thus leading to a randomized optimization algorithm.
Optimal maneuver for multiple aircraft conflict resolution: A braid point of view
 in Proceedings of the IEEE Conference on Decision and Control
, 2000
"... In this paper, we study conflict resolution for multiple aircraft encounter situations on a plane. First, the homotopy types of resolution maneuvers for n aircraft encounters are classified according to their images in the joint spacetime coordinates, which are shown to bear a onetoone corresponde ..."
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Cited by 10 (8 self)
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In this paper, we study conflict resolution for multiple aircraft encounter situations on a plane. First, the homotopy types of resolution maneuvers for n aircraft encounters are classified according to their images in the joint spacetime coordinates, which are shown to bear a onetoone correspondence with the wellknown pure braid group PBn. Energy is then proposed as the cost function for choosing among all conflictfree maneuvers the optimal one. For two aircraft encounters, analytic expressions of the optimal resolution maneuvers are obtained, and for the multiple aircraft case, convex optimization technique is used to find the optimal twolegged resolution maneuver within each type. The introduced solution, however, becomes computationally intractable as the number of aircraft increases. The use of the probabilistic resolution algorithm in [1] as “random type chooser ” is then suggested as a randomized solution to the combinatorial optimization problem. Finally, simulation results are presented for some typical encounters.
Hybrid geodesics as optimal solutions to the collisionfree motion planning problem
 in Hybrid Systems: Computation and Control. 4th International Workshop
, 2001
"... Abstract. In this paper we address the problem of designing energy minimizing collisionfree maneuvers for multiple agents moving on a plane. We show that the problem is equivalent to that of finding the shortest geodesic in a certain manifold with nonsmooth boundary. This allows us to prove that th ..."
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Cited by 6 (5 self)
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Abstract. In this paper we address the problem of designing energy minimizing collisionfree maneuvers for multiple agents moving on a plane. We show that the problem is equivalent to that of finding the shortest geodesic in a certain manifold with nonsmooth boundary. This allows us to prove that the optimal maneuvers are C 1 by introducing the concept of uconvex manifolds. Moreover, due to the nature of the optimal maneuvers, the problem can be formulated as an optimal control problem for a certain hybrid system whose discrete states consist of different “contact graphs”. We determine the analytic expression for the optimal maneuvers in the two agents case. For the three agents case, we derive the dynamics of the optimal maneuvers within each discrete state. This together with the fact that an optimal maneuver is a C 1 concatenation of segments associated with different discrete states gives a characterization of the optimal solutions in the three agents case. 1 Introduction and
Optimal Resolution of En Route Conflicts
 In 4th USA/Europe Air Traffic Management R&D Seminar (ATM2001). Santa Fe
, 2001
"... Designing a Control Simulator involves many difficult problems: modeling conflict detection, trajectory uncertainties, solving conflict inside sectors, respecting military areas constraints, coordinating aircraft between sectors, etc. . . ..."
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Cited by 5 (1 self)
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Designing a Control Simulator involves many difficult problems: modeling conflict detection, trajectory uncertainties, solving conflict inside sectors, respecting military areas constraints, coordinating aircraft between sectors, etc. . .
Mehra / Deep Space Formation Flying Spacecraft Path Planning 429
 Proceedings of the Flight Mechanics Symposium, NASA Goddard Space Flight
, 1997
"... Efficient algorithms for collisionfree energy suboptimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of waypoints through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are en ..."
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Cited by 4 (0 self)
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Efficient algorithms for collisionfree energy suboptimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of waypoints through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are energyoptimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasiquadratic parameter optimization problem in terms of the waypoints parameters. The mathematical structure of the problem is further exploited to develop gradientbased algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20). KEY WORDS—path planning for multiple mobile robot systems, formation flying spacecraft, trajectory generation Notation al acceleration vector of spacecraft l alk component of acceleration vector of spacecraft l on axis k (k = x, y, z) Alk upper limit on the absolute value of alk c j, d j coefficients for the energy optimal trajectory of one spacecraft dlm distance between spacecraft l and m