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287
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 68 (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.
Computing differential invariants of hybrid systems as fixedpoints
, 2008
"... Abstract. We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations whose righthand sides are polynomials in the state variables. In order to verify nontrivial systems without solving their differential equations and without numerical errors, ..."
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Cited by 58 (21 self)
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Abstract. We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations whose righthand sides are polynomials in the state variables. In order to verify nontrivial systems without solving their differential equations and without numerical errors, we use a continuous generalization of induction, for which our algorithm computes the required differential invariants. As a means for combining local differential invariants into global system invariants in a sound way, our fixedpoint algorithm works with a compositional verification logic for hybrid systems. To improve the verification power, we further introduce a saturation procedure that refines the system dynamics successively with differential invariants until safety becomes provable. By complementing our symbolic verification algorithm with a robust version of numerical falsification, we obtain a fast and sound verification procedure. We verify roundabout maneuvers in air traffic management and collision avoidance in train control.
Reachability Analysis Using Polygonal Projections
 IN HYBRID SYSTEMS: COMPUTATION AND CONTROL
, 1999
"... Coho is a reachability analysis tool for systems modeled by nonlinear, ordinary differential equations. Coho represents highdimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geome ..."
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Cited by 57 (5 self)
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Coho is a reachability analysis tool for systems modeled by nonlinear, ordinary differential equations. Coho represents highdimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geometry to be exploited while also capturing dependencies in the behaviour of related variables. Reachability is performed by integration where methods from linear programming and linear systems theory are used to bound trajectories emanating from each face of the object. This paper has two contributions: first, we describe the implementation of Coho and, second, we present analysis results obtained by using Coho on several simple models.
KeYmaera: A hybrid theorem prover for hybrid systems
 IJCAR. VOLUME 5195 OF LNCS
, 2008
"... KeYmaera is a hybrid verification tool for hybrid systems that combines deductive, real algebraic, and computer algebraic prover technologies. It is an automated and interactive theorem prover for a natural specification and verification logic for hybrid systems. KeYmaera supports differential dyn ..."
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Cited by 56 (24 self)
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KeYmaera is a hybrid verification tool for hybrid systems that combines deductive, real algebraic, and computer algebraic prover technologies. It is an automated and interactive theorem prover for a natural specification and verification logic for hybrid systems. KeYmaera supports differential dynamic logic, which is a realvalued firstorder dynamic logic for hybrid programs, a program notation for hybrid automata. For automating the verification process, KeYmaera implements a generalized freevariable sequent calculus and automatic proof strategies that decompose the hybrid system specification symbolically. To overcome the complexity of real arithmetic, we integrate real quantifier elimination following an iterative background closure strategy. Our tool is particularly suitable for verifying parametric hybrid systems and has been used successfully for verifying collision avoidance in case studies from train control and air traffic management.
Towards a geometric theory of hybrid systems
 In HSCC’00, number 1790 in LNCS
, 2000
"... Abstract. We propose a framework for a geometric theory of hybrid systems. Given a deterministic, nonblocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non ..."
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Cited by 55 (18 self)
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Abstract. We propose a framework for a geometric theory of hybrid systems. Given a deterministic, nonblocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally nonsmooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.
A Probabilistic Approach to Aircraft Conflict Detection,”
 IEEE Transactions on Intelligent Transportation Systems,
, 2000
"... Abstract In this paper, we concentrate primarily on the detection component of conflict detection and resolution schemes operating at the midrange and short range level of the air traffic management process. Probabilistic models for midterm and short term prediction are introduced. Based on the m ..."
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Cited by 50 (11 self)
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Abstract In this paper, we concentrate primarily on the detection component of conflict detection and resolution schemes operating at the midrange and short range level of the air traffic management process. Probabilistic models for midterm and short term prediction are introduced. Based on the midterm prediction model, the maximum instantaneous probability of conflict is proposed as criticality measure of a two aircraft encounter situation. The computational issues involved in its estimate are solved by resorting to randomized methods which provide also quantitative bounds on the level of approximation introduced. As for short range detection, closedform analytical expressions though approximations for the probability of conflict are obtained by using the short term prediction model. Based on these expressions, an algorithm for decentralized conflict detection and resolution that generalizes potential fields ideas to path planning in a probabilistic dynamic environment is suggested. The proposed approaches are shown to be promising using Monte Carlo simulations.
A Feedback Stabilization and Collision Avoidance Scheme for Multiple Independent Nonholonomic Nonpoint Agents
, 2005
"... A navigation functions’ based methodology, established previously for decentralized navigation of multiple holonomic agents, is extended to address the problem of decentralized navigation of multiple nonholonomic agents. In contrast to our previous work, each agent does not require any knowledge ab ..."
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Cited by 49 (27 self)
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A navigation functions’ based methodology, established previously for decentralized navigation of multiple holonomic agents, is extended to address the problem of decentralized navigation of multiple nonholonomic agents. In contrast to our previous work, each agent does not require any knowledge about the velocities and the desired destinations of the other members of the team. Furthermore, the control inputs are the acceleration and rotational velocity of each vehicle, coping in this way with realistic dynamics of classes of mechanical systems. Asymptotic stability is guaranteed by LaSalle’s Invariance Principle for nonsmooth systems. The collision avoidance and global convergence properties are verified through simulations.
Hierarchical Hybrid Modeling of Embedded Systems
, 2001
"... This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy, and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, bu ..."
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Cited by 45 (5 self)
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This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy, and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools, and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in design of embedded control software using examples from automated highways concerning vehicle coordination.
Synthesizing Controllers for Nonlinear Hybrid Systems
, 1998
"... . Motivated by an example from aircraft conflict resolution we seek a methodology for synthesizing controllers for nonlinear hybrid automata. We first show how game theoretic methodologies developed for this purpose for finite automata and continuous systems can be cast in a unified framework. We th ..."
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Cited by 45 (11 self)
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. Motivated by an example from aircraft conflict resolution we seek a methodology for synthesizing controllers for nonlinear hybrid automata. We first show how game theoretic methodologies developed for this purpose for finite automata and continuous systems can be cast in a unified framework. We then present a conceptual algorithm for extending them to the hybrid setting. We conclude with a discussion of computational issues. 1 Introduction In the first part of this paper we show that verification of the safety of continuous nonlinear systems using the HamiltonJacobi equation may be considered as the continuous analog of infinite games on finite automata. In the second part we present a conceptual algorithm for calculating maximal controlled invariant sets for nonlinear hybrid systems and we present a motivating example: we describe an iteration process to calculate the maximal set of safe initial conditions for a twoaircraft maneuver. We conclude with a brief discussion of computa...
Distributed agentbased air traffic flow management
 IN: PROCEEDINGS OF THE SIXTH INTERNATIONAL JOINT CONFERENCE ON AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS
, 2007
"... Air traffic flow management is one of the fundamental challenges facing the Federal Aviation Administration (FAA) today. The FAA estimates that in 2005 alone, there were over 322,000 hours of delays at a cost to the industry in excess of three billion dollars. Finding reliable and adaptive solutions ..."
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Cited by 43 (18 self)
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Air traffic flow management is one of the fundamental challenges facing the Federal Aviation Administration (FAA) today. The FAA estimates that in 2005 alone, there were over 322,000 hours of delays at a cost to the industry in excess of three billion dollars. Finding reliable and adaptive solutions to the flow management problem is of paramount importance if the Next Generation Air Transportation Systems are to achieve the stated goal of accommodating three times the current traffic volume. This problem is particularly complex as it requires the integration and/or coordination of many factors including: new data (e.g., changing weather info), potentially conflicting priorities (e.g., different airlines), limited resources (e.g., air traffic controllers) and very heavy traffic volume (e.g., over 40,000 flights over the US airspace). In this paper we use FACET – an air traffic flow simulator developed at NASA and used extensively by the FAA and industry – to test a multiagent algorithm for traffic flow management. An agent is associated with a fix (a specific location in 2D space) and its action consists of setting the separation required among the airplanes going though that fix. Agents use reinforcement learning to set this separation and their actions speed up or slow down traffic to manage congestion. Our FACET based results show that agents receiving personalized rewards reduce congestion by up to 45% over agents receiving a global reward and by up to 67 % over a current industry approach (Monte Carlo estimation).