Probabilistic Temporal Logic for Motion Planning with Resource Threshold Constraints

Over the last two decades, there has been an extensive study of logical formalisms on specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for formal specification of real-time and complex systems, an up to date survey of these logics does not exist in the literature. In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time temporal logics and probabilistic temporal logics. We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.

Sampling-based Motion Planning with Temporal Logic Missions and Spatial Preferences

In this paper, the problem of motion planning for a mobile robot is addressed in which motion planning scenarios such as reachability, invariance, surveillance and sequencing missions are formulated with Linear Temporal Logic (LTL). First, by using the idea of invariant set theory, a novel algorithm is proposed for checking the satisfaction of temporal logic planning specification in the offline phase. Then, an optimal control strategy is designed in the presence of bounded additive disturbances to meet the given temporal logic specification and system constraints. Illustrative case studies for a robot with a double integrator model are presented to demonstrate the applicability of the proposed approach in motion planning tasks.

Sampling-based methods have advanced the state of the art in robotic motion planning and control across complex, high-dimensional domains. With few exceptions, such approaches only admit simple constraints and objectives, such as collision-avoidance and reaching a goal state. In this work we leverage the best of two worlds: the scalability of sampling-based motion planning and the precise formal guarantees of temporal logic. We present an incremental sampling-based algorithm that synthesizes a motion control policy satisfying a bounded Signal Temporal Logic formula over properties of a given environment. Our key insight is that we can bias the selection of samples using a quantitative measure of how well the best path in the current tree of samples satisfies the specification. This allows us both to converge to a path that satisfies the specification, and to improve upon an existing path, i.e. to satisfy the specification with maximum robustness. We illustrate the performance of our method in several case studies.

In this paper, we provide a novel scheme to solve the motion planning problem of multi-agent systems under high-level task specifications. First, linear temporal logic is applied to express the global task specification. Then an efficient and decentralization algorithm is proposed to decompose it into local tasks. Finally, we use control barrier function to synthesize the local controller for each agent under the LTL motion plan safety constraint. Simulation results prove the effectiveness and efficiency of our proposed method.

Cyber-physical systems often encompass complex concurrent behavior with timing constraints and probabilistic failures on demand. The analysis whether such systems with probabilistic timed behavior adhere to a given specification is essential. When the states of the system can be represented by graphs, the rule-based formalism of Probabilistic Timed Graph Transformation System (PTGTSs) can be used to suitably capture structure dynamics as well as probabilistic and timed behavior of the system. The model checking support for PTGTSs w.r.t. properties specified using Probabilistic Timed Computation Tree Logic (PTCTL) has been already presented. Moreover, for timed graph-based runtime monitoring, Metric Temporal Graph Logic (MTGL) has been developed for stating metric temporal properties on identified subgraphs and their structural changes over time.In this paper, we (a) extend MTGL to the Probabilistic Metric Temporal Graph Logic (PMTGL) by allowing for the specification of probabilistic properties, (b) adapt our MTGL satisfaction checking approach to PTGTSs, and (c) combine the approaches for PTCTL model checking and MTGL satisfaction checking to obtain a Bounded Model Checking (BMC) approach for PMTGL. In our evaluation, we apply an implementation of our BMC approach in AutoGraph to a running example.Keywordscyber-physical systemsprobabilistic timed systemsqualitative analysisquantitative analysisbounded model checking

Bounded model checking for interval probabilistic timed graph transformation systems against properties of probabilistic metric temporal graph logic

We present PCFTL (Probabilistic CounterFactual Temporal Logic), a new probabilistic temporal logic for the verification of Markov Decision Processes (MDP). PCFTL introduces operators for causal inference, allowing us to express interventional and counterfactual queries. Given a path formula φ, an interventional property is concerned with the satisfaction probability of φ if we apply a particular change I to the MDP (e.g., switching to a different policy); a counterfactual formula allows us to compute, given an observed MDP path τ, what the outcome of φ would have been had we applied I in the past and under the same random factors that led to observing τ. Our approach represents a departure from existing probabilistic temporal logics that do not support such counterfactual reasoning. From a syntactic viewpoint, we introduce a counterfactual operator that subsumes both interventional and counterfactual probabilities as well as the traditional probabilistic operator. This makes our logic strictly more expressive than PCTL⋆. The semantics of PCFTL rely on a structural causal model translation of the MDP, which provides a representation amenable to counterfactual inference. We evaluate PCFTL in the context of safe reinforcement learning using a benchmark of grid-world models.

In control theory, models of physical processes, such as systems of differential equations, are usually checked against specifications, such as stability and set invariance. In formal methods, rich specifications, such as languages and formulae of temporal logics, are checked against models of software programs and digital circuits, such as finite transition graphs. With the development and integration of cyber physical and safety critical systems, there is an increasing need for computational tools for verification and control of complex systems from rich, temporal logic specifications. The formal verification and synthesis problems have been shown to be undecidable even for very simple classes of infinitespace continuous and hybrid systems. However, provably correct but conservative approaches, in which the satisfaction of a property by a dynamical system is implied by the satisfaction of the property by a finite over-approximation (abstraction) of the system, have received a lot of attention in recent years. Some classes of systems allowing for computationally efficient verification and control from temporal logic specifications are reviewed. For continuous and discrete-time linear systems and continuous-time multi-linear systems, it is shown that finite abstractions can be constructed through polyhedral operations only. By using techniques from model checking and automata games, this allows for verification and control from specifications given as Linear Temporal Logic (LTL) formulae over linear predicates in the state variables. A connection between the existence of Lyapunov functions and finite bisimulations is established for discrete-time linear and switched linear systems. Finally, optimality and correctness requirements are combined in a model predictive approach to generate control strategies for discrete-time linear systems. The usefulness of these computational tools is illustrated with various examples such as verification and synthesis of biological circuits in synthetic biology and motion planning and control in robotics.

In this paper, a motion planning system based on predictive control and temporal logic specifications is established for the welding dual-arm robot with gantry. Firstly, based on the spatial structure of the dual-arm robot with gantry, a novel mathematical model is presented between the joint variables and the terminal attitude and the quaternion replaces the Euler Angle to describe the posture for avoiding gimbal lock. Then a constraint model predictive controller is constructed for the multi-variable, nonlinear and coupling model of the robot and the constraints of the environment. Meanwhile, the temporal logic formula is used for describing the complex welding tasks and reducing the workload of repeated programming. Next the expectation values and constraints are converted by the temporal logic formula will be sent to the predictive controller one by one. Finally, the simulation result shows that the system can effectively solve the problem of motion planning for the welding dual-arm robot with gantry.

With the advances of Artificial Intelligence (AI) and autonomous robotics, robots are increasingly involved closely with human society, such as in manufacturing system, autonomous driving and intelligent service robots. While robots are good at handling repeated routine work, human are more adaptive and flexible to changing factors that may bring uncertainties and cost non-trivial efforts for robots to overcome. Thus efficient collaboration between human and robots can bring huge economic profits, but also require high standard for robot controller during task completion because the safety of human must be guaranteed. In this paper, we build a formal design theory enabling an automated human-robot collaboration with performance guarantees. Markov Decision Processes (MDPs) are used to model robots with uncertainties and Partially Observable Markov Decision Processes (POMDPs) are used to model human with hidden intents. Within a supervisory control framework, we propose to use L* learning algorithm to learn a correct supervisor such that global collaboration task given as Probabilistic Computation Tree Logic (PCTL) can be satisfied. An example from manufacturing system is discussed to further illustrate the design method.

Motion planning for underwater vehicles must consider the effect of ocean\ncurrents. We present an efficient method to compute reachability and cost\nbetween sample points in sampling-based motion planning that supports\nlong-range planning over hundreds of kilometres in complicated flows. The idea\nis to search a reduced space of control inputs that consists of stream\nfunctions whose level sets, or streamlines, optimally connect two given points.\nSuch stream functions are generated by superimposing a control input onto the\nunderlying current flow. A streamline represents the resulting path that a\nvehicle would follow as it is carried along by the current given that control\ninput. We provide rigorous analysis that shows how our method avoids exhaustive\nsearch of the control space, and demonstrate simulated examples in complicated\nflows including a traversal along the east coast of Australia, using actual\ncurrent predictions, between Sydney and Brisbane.\n

In this paper, we propose algorithms for the on-line computation of control programs for dynamical systems that provably satisfy a class of temporal logic specifications. Such specifications have recently been proposed in the literature as a powerful tool to synthesize provably correct control programs, for example for embedded systems and robotic applications. The proposed algorithms, generalizing state-of-the-art algorithms for point-to-point motion planning, incrementally build finite transition systems representing a discrete subset of dynamically feasible trajectories. At each iteration, local mu-calculus model-checking methods are used to establish whether the current transition system satisfies the specifications. Efficient sampling strategies are presented, ensuring the probabilistic completeness of the algorithms. We demonstrate the effectiveness of the proposed approach on simulation examples.

Probabilistic Plan Synthesis for Coupled Multi-Agent Systems

In this work we present a methodology for intelligent motion planning in an uncertain environment using a non-local sensor, such as radar. This methodology is applied to an unmanned helicopter navigating a cluttered urban environment. We show that the problem of motion planning in a uncertain environment, under certain assumptions, can be posed as the adaptive optimal control of an uncertain Markov decision process, characterized by a known, control dependent system, and an unknown, control independent environment. The strategy for motion planning then reduces to computing the control policy based on the current estimate of the environment, also known as the "certainty equivalence principle" in the adaptive control literature. Our methodology allows the inclusion of a non-local sensor into the problem formulation, which significantly accelerates the convergence of the estimation and planning algorithms. Further we show that the motion planning and estimation problems, as formulated in this paper possess special structure which can be exploited to significantly reduce the computational burden of the associated algorithms. We apply this methodology to the problem of motion planning for an unmanned helicopter in a partially known model of the Texas A&M campus