Multi-Agent Task Planning under Temporal Logic Constraints: A Conflict-Resolution Approach

Temporal logic has been widely used to express complex task specifications for cyber-physical systems (CPSs). One way to synthesize a controller for CPS under temporal logic constraints is to first abstract the CPS as a discrete transition system, and then apply formal methods. This approach, however, is computationally demanding and its scalability suffers due to the curse of dimensionality. In this paper, we propose a control barrier function (CBF) approach to abstraction-free control synthesis under a linear temporal logic (LTL) constraint. We first construct the deterministic Rabin automaton of the specification and compute an accepting run. We then compute a sequence of LTL formulae, each of which must be satisfied during a particular time interval, and prove that satisfying the sequence of formulae is sufficient to satisfy the LTL specification. Finally, we compute a control policy for satisfying each formula by constructing an appropriate CBF. We present a quadratic program to compute the controllers, and show the controllers synthesized using the proposed approach guarantees the system to satisfy the LTL specification, provided the quadratic program is feasible at each time step. A numerical case study is presented to demonstrate the proposed approach.

Urban air mobility (UAM) refers to air transportation services in and over an urban area and has the potential to revolutionize mobility solutions. However, due to the projected scale of operations, current air traffic management (ATM) techniques are not viable . Increasingly autonomous systems are a pathway to accelerate the realization of UAM operations, but must be fielded safely and efficiently. The heavily regulated, safety critical nature of aviation may lead to multiple, competing safety constraints that can be traded off based on the operational context. In this paper, we design a framework which allows for the scalable planning of a UAM ATM system. We formalize safety oriented constraints derived from FAA regulations by encoding them as temporal logic formulae. We then propose a method for UAM ATM that is both scalable and minimally violates the temporal logic constraints. Numerical results show that the runtime for our proposed algorithm is suitable for very large problems and is backed by theoretical guarantees of correctness with respect to given temporal logic constraints.

In this paper, we consider detectability analysis for faults in systems governed by switched affine dynamics. By a fault, we mean a sudden and permanent change in the system dynamics. Given the model of the healthy system, such a fault can be detected via model invalidation, i.e., by collecting past observations over a finite horizon and checking whether these observations can be generated by the healthy system model. Whenever the faulty system model is also available, it is possible to find T, the minimum length of the horizon, with which the fault is guaranteed to be detected eventually (with a T-step delay at most). The procedure for finding such T is known as the fault detectability analysis, and can be accomplished by solving a mixed integer linear program (MILP) for switched affine systems. The main contribution of this work is to show the possibility of reducing the value of T, by augmenting the fault detectability analysis with additional linear temporal logic (LTL) constraints on the switching signals, if any. We express the LTL constraints (restricted in a finite horizon) with a nondeterministic finite state machine called a monitor, which is then transformed into a set of mixed integer linear constraints that can be easily integrated in the MILP used for the detectability analysis. The effectiveness of the proposed approach is illustrated with a drone altitude consensus protocol with switching communication topology.

Reinforcement Learning with Temporal Logic Constraints

An Approach to Agent Path Planning Under Temporal Logic Constraints

This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for obtaining correctness guarantees with respect to the linear temporal logic (LTL) specification. We show that the problem can be formulated as an optimal control problem in which both the semantic map and the logic formula evaluation are stochastic. Our first contribution is to reduce the stochastic control problem for a subclass of LTL to a deterministic shortest path problem by introducing a confidence parameter $delta$. A robot trajectory obtained from the deterministic problem is guaranteed to have minimum cost and to satisfy the logic specification in the true environment with probability $delta$. Our second contribution is to design an admissible heuristic function that guides the planning in the deterministic problem towards satisfying the temporal logic specification. This allows us to obtain an optimal and very efficient solution using the A* algorithm. The performance and correctness of our approach are demonstrated in a simulated semantic environment using a differential-drive robot.

We propose a new approach to modelling and reasoning about dynamic networks. Dynamic networks consist of nodes and edges whose operating status may change over time (for example, the edges may be unreliable and operate intermittently). Message-passing in such networks is inherently difficult and reasoning about the behaviour of message-passing algorithms is also difficult. We develop a series of abstract models which allow us to focus on the correctness of routing methods. We model the dynamic network as a ``demonic'' process which runs concurrently with routing updates and message-passing. This allows us to use temporal logic and fairness constraints to reason about dynamic networks. The models are implemented as multi-threaded programs and, to validate them, we use an experimental run-time verification tool called RuleR.

This paper addresses the optimal control problem of Boolean Control Networks under Linear Temporal Logic constraints. An algebraic framework based on the semi-tensor product approach is introduced to represent the product automata, enabling the formal verification and control of Boolean control networks with respect to LTL specifications. Two greedy algorithms are proposed: one for finite-horizon optimal control and another for infinite-horizon control, with the latter focusing on identifying optimal cycles. The efficiency of the proposed methods is demonstrated through two case studies, highlighting their potential for precise control in complex biological systems, such as gene regulatory networks.

Robust Model Predictive Control with Signal Temporal Logic constraints for Barcelona Wastewater System

Partially observable Markov decision processes (POMDPs) are models for sequential decision-making under uncertainty and incomplete information. Machine learning methods typically train recurrent neural networks (RNN) as effective representations of POMDP policies that can efficiently process sequential data. However, it is hard to verify whether the POMDP driven by such RNN-based policies satisfies safety constraints, for instance, given by temporal logic specifications. We propose a novel method that combines techniques from machine learning with the field of formal methods: training an RNN-based policy and then automatically extracting a so-called finite-state controller (FSC) from the RNN. Such FSCs offer a convenient way to verify temporal logic constraints. Implemented on a POMDP, they induce a Markov chain, and probabilistic verification methods can efficiently check whether this induced Markov chain satisfies a temporal logic specification. Using such methods, if the Markov chain does not satisfy the specification, a byproduct of verification is diagnostic information about the states in the POMDP that are critical for the specification. The method exploits this diagnostic information to either adjust the complexity of the extracted FSC or improve the policy by performing focused retraining of the RNN. The method synthesizes policies that satisfy temporal logic specifications for POMDPs with up to millions of states, which are three orders of magnitude larger than comparable approaches.

BIOCHAM-4 is a tool for modeling, analyzing and synthesizing biochemical reaction networks with respect to some formal, yet possibly imprecise, specification of their behavior. We focus here on one new capability of this tool to optimize the robustness of a parametric model with respect to a specification of its dynamics in quantitative temporal logic. More precisely, we present two complementary notions of robustness: the statistical notion of model robustness to parameter perturbations, defined as its mean functionality, and a metric notion of formula satisfaction robustness, defined as the penetration depth in the validity domain of the temporal logic constraints. We show how the formula robustness can be used in BIOCHAM-4 with no extra cost as an objective function in the parameter optimization procedure, to actually improve the model robustness. We illustrate these unique features with a classical example of the hybrid systems community and provide some performance figures on a model of MAPK signalling with 37 parameters.

Attributed to the increased automation, the day is not far wherein the robots will be seen doing a lot of sophisticated tasks, after which it is imperative that the offices and homes will have robots to replace the secretaries to be of common use for a large number of office-mates or house-mates. A mission comprises of a collection of high order tasks that a robot is asked to do with some logical and temporal constraints. The current approaches using model verification techniques have exponential complexity in terms of the number of variables, and are therefore not scalable to a very large level. The paper proposes a constrained mission specification language consisting of a sub-task as a logical relation between atomic tasks, a task as a collection of tasks to be performed one after the other, and a mission consisting of multiple tasks given by different users. An evolutionary approach is used to compute the solution to the mission that can scale to a very large number of variables. Problem specific heuristics are devised to compute a solution quickly. Particularly Dynamic Programming is used to align the solutions of multiple tasks to make a solution of a mission. Experimental results confirm that the proposed solution performs extremely well as compared to exhaustive search based approaches, model verification approaches and evolutionary approaches available in the literature. The results are demonstrated in simulations and on the Pioneer LX robot in the lab arena.

The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP) is a multi-agent task scheduling problem where the tasks are spatially distributed, with deadlines and workloads, and the number of agents is typically much smaller than the number of tasks. Thus, the agents have to form coalitions in order to maximise the number of completed tasks. The state-of-the-art CFSTP solver, the Coalition Formation with Look-Ahead (CFLA) algorithm, has two main limitations. First, its time complexity is exponential with the number of agents. Second, as we show, its look-ahead technique is not effective in real-world scenarios, such as open multi-agent systems, where new tasks can appear at any time. In this work, we study its design and define an extension, called Coalition Formation with Improved Look-Ahead (\(\text {CFLA}2\)), which achieves better performance. Since we cannot eliminate the limitations of CFLA in \(\text {CFLA}2\), we also develop a novel algorithm to solve the CFSTP, the first to be simultaneously anytime, efficient and with convergence guarantee, called Cluster-based Task Scheduling (CTS). In tests where the look-ahead technique is highly effective, CTS completes up to 30% (resp. 10%) more tasks than CFLA (resp. \(\text {CFLA}2\)) while being up to four orders of magnitude faster. Our results affirm CTS as the new state-of-the-art algorithm to solve the CFSTP.

In recent years, several constraintdbased temporal reasoning frameworks have been proposed. They consider temporal points or intervals as domain elements linked by temporal constraints. Temporal reasoning in these systems is based on constraint propagation. In this paper, we argue that a language based on constraint propagation can be a suitable tool for expressing and reasoning about temporal problems. We concentrate on Constraint Logic Programming (CLP) which is a powerful programming paradigm combining the advantages of Logic Programming and the efficiency of constraint solving. However, CLP presents some limitations in dealing with temporal reasoning. First, it uses an “arc consistency” propagation algorithm which is embedded in the inference engine, cannot be changed by the user, and is too weak in many temporal frameworks. Second, CLP is not able to deal with qualitative temporal constraints. We present a general meta CLP architecture which maintains the advantages of CLP, but overcomes these two main limitations. Each architectural level is a finite domain constraint solver (CLP(FD)) that reasons about constraints of the underlying level. Based on this conceptual architecture, we extend the CLP(FD) language and we specialize the extension proposed on Vilain and Kautz’s Point Algebra, on Allen’s Interval Algebra and on the STP framework by Dechter, Meiri and Pearl. In particular, we show that we can cope effectively with disjunctive constraints even in an intervaldbased framework.

The development of ALBATROSS: A Learning-Based, Transportation-Oriented Simulation System is summarized. This activity-based model of activity-travel behavior is derived from theories of choice heuristics that consumers apply when making decisions in complex environments. The model, one of the most comprehensive of its kind, predicts which activities are conducted when, where, for how long, and with whom, and the transport mode involved. In addition, various logical, temporal, spatial, spatial-temporal, and institutional constraints are incorporated in the model. The conceptual underpinnings of the model, its architecture, the functionality of its key agents, data collection, and model performance are discussed.