Inverse Norm Conflict Resolution

With the increase of people’s demand for agents, the activities of agents are no longer limited to simple environment and task format. Facing complex application scenarios, agents need to be able to make decisions and execute them autonomously. This paper studies the probabilistic action planning considering complex task constraints described by linear temporal logic. At the same time, the success rate and cost of task are both considered. The uncertain factors include agent behavior and environment attributes, and the task description is expressed by soft and hard constraints. The strategy of agent is generated here applying model checking in formal method. Single- and multi-agent model is established using Markov decision process, while task model is established using double-layer automata. Then, agent-task network model is designed to describe the constraints and the control strategy is solved through a coupled linear programming. The method above is verified through numerical simulation. The results show that the complex task constraints in the form of soft and hard constraints can be satisfied. The optimal strategy enable the agent to complete the task according to the constraint strength, and the control strategy can be adjusted by controlling the relaxation degree of control network model relevant to the penalty factor.

We present a method to find an optimal policy with respect to a reward function for a discounted Markov decision process under general linear temporal logic (LTL) specifications. Previous work has either focused on maximizing a cumulative reward objective under finite-duration tasks or maximizing an average reward for persistent (e.g., surveillance) tasks. This paper extends and generalizes these results by introducing a pair of occupancy measures to express the LTL satisfaction objective and the expected discounted reward objective, respectively. These occupancy measures are then connected to a single policy via a novel reduction resulting in a mixed integer linear program whose solution provides an optimal policy. Our formulation can also be extended to include additional constraints with respect to secondary reward functions. We illustrate the effectiveness of our approach in the context of robotic motion planning for complex missions under uncertainty and performance objectives.

In this paper, We consider an uncertain Markov decision process (MDP) with a control cost and a linear temporal logic (LTL) control specification. We propose a reinforcement learning (RL) based method for design of an optimal control policy by which the controlled MDP satisfies the control specification with probability 1 and minimizes an expected discounted sum of the control costs. First, we construct a deterministic Rabin automaton (DRA) that accepts all and only infinite words satisfying the LTL control specification. Second, we construct a product MDP of the MDP and the DRA to represent a dynamic control policy that satisfies the control specification. Third, we modify the product MDP in order to apply RL to the design of an optimal control policy. The control action of the modified product MDP is a pair of a pattern and an action, where the pattern is a set of actions. Moreover, we introduce a reward that represents both the satisfaction of the control specification and the minimally restrictiveness of the pattern. Finally, we proposed an algorithm for design of an optimal control policy that consists of a sequential decision making of two steps. At the first decision making, we select a pattern that maximizes a discounted sum of the reward. At the second one, we select an action from the pattern selected at the first one such that it minimizes the expected discounted sum of the costs. Moreover, we consider an illustrative example to show that the proposed algorithm can obtain an optimal control policy.

Conflict is inevitable to take place in collaborative design, and conflict resolution plays an important part in complex product collaborative design systems. Firstly, a mathematic description model in collaborative design considering resource conflict, process conflict and design conflict is given, and the mathematic model expresses the origin of conflict and shows that conflict resolution is a multiobjective planning problem. Next, a conflict resolution algorithm considering design objective optimization is presented, and fuzzy value and fuzzy grade are applied in the algorithm. Depending on both considering design variables having fundamental influences on its design objectives and the cost of conflict resolution, the algorithm can improve the quality and efficiency of conflict resolution. Finally, an example of single cylindrical gear reducer is used to show the validity of the algorithm.

This paper proposes an online human-aware behavior planning method to enable Unmanned Aerial Vehicles (UAVs) to dynamically satisfy high-level linear temporal logic (LTL) task descriptions from human collaborators. The proposed method has the potential to be applied to the industrial human–UAV collaboration. The specific process is as follows. Firstly, the global high-level task of the UAV is described using the formal language of LTL, which can usually be issued by human collaborators in natural language. Secondly, the task description is transformed into a deterministic Rabin automaton, and then the state values of the automaton are given by the distance from the accepted states. Thirdly, the Markov decision process is used to construct the probabilistic behavior model of the UAV offline. Based on this model, a finite state automaton in the finite horizon is dynamically constructed online, and the Cartesian product system within the horizon is constructed, in which the expected arrival states within the horizon are set by the minimum state values. Finally, aiming at maximizing the reachability probability of the expected states, the value iterative algorithm is introduced to solve the optimal behavior plan online within the finite horizon. After it, an infinite horizon planning and execution algorithm is formed. Experiments and analysis show that the results of the online behavior planning are consistent with the task logic at the semantic level, indicating the correctness of the proposed method. Moreover, the proposed method can effectively alleviate the state explosion caused by the global probabilistic model checking and improve the efficiency of plan generation.

Linear time temporal logic (LTL) has become a well established tool for specifying the dynamic behaviour of reactive systems with an interleaving semantics, and the automata-theoretic approach has proven to be a very useful mechanism for performing automatic verification in this setting. Especially alternating automata turned out to be a powerful tool in constructing efficient yet simple to understand decision procedures and directly yield further on-the-fly model checking procedures. In this paper we exhibit a decision procedure for LTL over Mazurkiewicz traces which generalises the classical automata-theoretic approach to a linear time temporal logic interpreted no longer over sequences but certain partial orders. Specifically, we construct a (linear) alternating Buchi automaton accepting the set of linearisations of traces satisfying the formula at hand. The salient point of our technique is to apply a notion of independence-rewriting to formulas of the logic. Furthermore, we show that the class of linear and trace-consistent alternating Buchi automata corresponds exactly to LTL formulas over Mazurkiewicz traces, lifting a similar result from Loding and Thomas formulated in the framework of LTL over words.

Several formal approaches have been proposed to analyse security protocols, e.g. (2,7,11,1,6,12). Recently, a great interest has been growing on the use of constraint solving approach. Initially proposed by Millen and Shmatikov (9), this approach allows analysis of a finite number of protocol sessions. Yet, the representation of protocol runs by symbolic traces (as opposed to concrete traces) captures the possibility of having unbounded message space, allowing analysis over an infinite state space. A constraint is defined as a pair consisting of a message M and a set of messages K that represents the intruder's knowledge. Millen and Shmatikov present a procedure to solve a set of constraints, i.e. that in each constraint, M can be built from K. When a set of constraints is solved, then a concrete trace representing an attack over the protocol can be extracted. Corin and Etalle (4) has improved the work of Millen and Shmatikov by presenting a more efficient procedure. However, none of these constraint-based systems provide enough flexibility and expresiveness in specifying security properties. For example, to check secrecy an artificial protocol role is added to simulate whether a secret can be learned by an intruder. Authentication cannot also be checked directly. Moreover, only a built-in notion of authentication is implemented by Millen and Shmatikov in his Prolog implementation (10). This problem motivates our current work. A logical formalism is considered to be an appropriate solution to improve the flexibility and expresiveness in specifying security properties. A preliminary attempt to use logic for specifying local security properties in a constraint-based setting has been carried out (3). Inspired by this work and the successful NPATRL (11,8), we currently explores a variant of linear temporal logic (LTL) over finite traces, PS-LTL , standing for pure-past security LTL (5). In contrast to standard LTL, this logic deals only with past events in a trace. In our current work, a protocol is modelled as in previous works (9,4,3), viz. by protocol roles. A protocol role is a sequence of send and receive events, together with status events to indicate, e.g. that a protocol role has completed her protocol run. A scenario is then used to deal with the number of sessions and protocol roles considered in the analysis. Integrating PS-LTL into our constraint solving approach presents a challenge, since we need to develop a sound and complete decision pro- cedure against symbolic traces, instead of concrete traces. Our idea to address this problem is by concretizing symbolic traces incrementally while deciding a formula. Basically, the decision procedure consists of two steps: transform and decide. The former step transforms a PS-LTL

A method for conflict detection and resolution based on the parameterization of the aircraft intents is presented. The method is also based on the use of predefined trajectory patterns, which are in fact flight intents; these patterns include standard airline procedures and air traffic control regulations. The conflict resolution problem is formulated as a parametric optimization problem subject to constraints; the optimality criterium is defined so that the deviation from the intended (preferred) trajectories in the lateral profile is minimized. The resolution trajectory patterns take into account changes of the nominal waypoints (vectoring) and changes of the aircraft speeds. The method is applied to the case of multiple conflicts among commercial transport aircraft in converging traffic in the terminal area; different scenarios are considered, which include locked aircraft, that is, aircraft whose trajectories are known and fixed. The conflict detection and resolution algorithm relies on a kinetic trajectory predictor (nonlinear point-mass model with variable mass), which is accurate, flexible, and transparent, and provides the high-fidelity prediction required in the analysis of the demanding terminal area traffic. The cost of the global conflict resolution process is assessed, in terms of extra distance traveled, extra flight time, and extra fuel consumed for each aircraft.

Given a Markov decision process (MDP) and a linear-time ($ømega$-regular or Linear Temporal Logic) specification which reasons about the infinite-trace behavior of a system, the controller synthesis problem aims to compute the optimal policy that satisfies said specification. Recently, problems that reason over the complementary infinite-frequency behavior of systems have been proposed through the lens of steady-state planning or steady-state policy synthesis. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior of the agent. We present an algorithm to find a deterministic policy satisfying $ømega$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.

NASA researchers, working under the Aviation System Capacity Program and in conjunction with the FAA Free Flight Program Office, have developed a set of decision support tools to assist terminal area air traffic controllers with control of arrival and departure traffic. Two of these tools, the Final Approach Spacing Tool (FAST) and the Expedite Departure Path (EDP) tool, provide air traffic controllers with heading, speed and altitude advisories to assist in spacing aircraft. This paper describes the conflict prediction and resolution algorithm shared by aFAST and EDP to produce conflict-free aircraft trajectories with realistic conflict resolution maneuvers. The process is accomplished in three stages: prediction, classification and resolution. A conflict prediction scheme is documented which incorporates all applicable FAA separation requirements, including automatic detection of separation during transition from staggered to simultaneous parallel approach operations. A method of classifying predicted conflicts with a limited set of criteria is detailed. Finally, a knowledge-based conflict resolution process is presented which allows for resolution of predicted conflicts in a manner consistent with controller practice: including prioritization of resolution tactics and mixture of multiple degrees of freedom to achieve separation. The scheme has been employed in both closed-loop simulations to determine solution stability and controller-in-the-loop simulations to begin development of the resolution tactics knowledge base.

We investigate logical consequence in temporal logics in terms of logical consecutions, i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be ‘correct’ in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logicLDTL, consisting of all formulas valid in the frame 〈L≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible inLDTLin a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible inLDTL. Also, we note that using the same technique it follows that the linear temporal logicL(N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logicsLDTLandL(N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (known fact), and the given deciding algorithms are explicit.

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL) that is able to express all $\omega$-regular specifications while still maintaining many of LTL's desirable properties like an intuitive syntax and a translation into non-deterministic B\"uchi automata of exponential size. But LDL lacks capabilities to express timing constraints. By adding parameterized operators to LDL, we obtain a logic that is able to express all $\omega$-regular properties and that subsumes parameterized extensions of LTL like Parametric LTL and PROMPT-LTL. Our main technical contribution is a translation of PLDL formulas into non-deterministic B\"uchi word automata of exponential size via alternating automata. This yields a PSPACE model checking algorithm and a realizability algorithm with doubly-exponential running time. Furthermore, we give tight upper and lower bounds on optimal parameter values for both problems. These results show that PLDL model checking and realizability are not harder than LTL model checking and realizability.

In this study, the author presents a new efficient algorithm for translating linear temporal logic (LTL) formulas to Buchi automata, which are used by LTL model checkers. The general idea of this algorithm is to generate Buchi automata from LTL formulas, using the principle of alternating automata and keeping only the positive transitions without generating the intermediate generalised automata. The LTL translation is the heart of any LTL model checker, which affects its performance. The translation performance is measured in addition to its speed and the size of the produced Buchi automaton (number of states and number of transitions), by correctness of produced Buchi automaton and its level of determinism. The author will show that this method is different from the others and it is very competitive with the most efficient translators to date.

Stochastic optimal control for aircraft conflict resolution under wind uncertainty

Based on the Kripke structure, linear temporal logic and generalized possibility measure, this article studies the model checking problems of generalized possibilistic fuzzy linear temporal logic (GPoFTL). The generalized possibilistic Kripke structure is introduced to describe the system model. The syntax of GPoFTL, which includes fuzzy temporal operators such as ``soon'', ``presently'', ``gradually'', ``within'', ``last'', ``nearly always'', ``almost alwayss'', ``in the long distant future'', ``in the middle of'', ``nearly until'' and ``almost until'', and its language semantics and path semantics under generalized possibility measure are given. Next, we explain the semantics of fuzzy temporal operators through some examples and prove that GPoFTL is an extension of generalized possibilistic linear temporal logic in fuzzy time temporal logic. Furthermore, the GPoFTL model checking algorithm is given by explicit calculation formulas one by one for any GPoFTL formula involving fuzzy temporal operators using fuzzy matrix operations. Last, the algorithm of necessary threshold model checking of GPoFTL is studied using automata theory and its time complexity is discussed.