Reasoning about LTL Synthesis over finite and infinite games

In the last few years, research formal methods for the analysis and the verification of properties of systems has increased greatly. A meaningful contribution in this area has been given by algorithmic methods developed in the context of synthesis. The basic idea is simple and appealing: instead of developing a system and verifying that it satisfies its specification, we look for an automated procedure that, given the specification returns a system that is correct by construction. Synthesis of reactive systems is one of the most popular variants of this problem, in which we want to synthesize a system characterized by an ongoing interaction with the environment. In this setting, large effort has been devoted to analyze specifications given as formulas of linear temporal logic, i.e., LTL synthesis. Traditional approaches to LTL synthesis rely on transforming the LTL specification into parity deterministic automata, and then to parity games, for which a so-called winning region is computed. Computing such an automaton is, in the worst-case, double-exponential in the size of the LTL formula, and this becomes a computational bottleneck in using the synthesis process in practice. The first part of this thesis is devoted to improve the solution of parity games as they are used in solving LTL synthesis, trying to give efficient techniques, in terms of running time and space consumption, for solving parity games. We start with the study and the implementation of an automata-theoretic technique to solve parity games. More precisely, we consider an algorithm introduced by Kupferman and Vardi that solves a parity game by solving the emptiness problem of a corresponding alternating parity automaton. Our empirical evaluation demonstrates that this algorithm outperforms other algorithms when the game has a small number of priorities relative to the size of the game. In many concrete applications, we do indeed end up with parity games where the number of priorities is relatively small. This makes the new algorithm quite useful in practice. We then provide a broad investigation of the symbolic approach for solving parity games. Specifically, we implement in a fresh tool, called SPGSolver, four symbolic algorithms to solve parity games and compare their performances to the corresponding explicit versions for different classes of games. By means of benchmarks, we show that for random games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms. The situation changes, however, for structured games, where symbolic algorithms seem to have the advantage. This suggests that when evaluating algorithms for parity-game solving, it would be useful to have real benchmarks and not only random benchmarks, as the common practice has been. LTL synthesis has been largely investigated also in artificial intelligence, and specifically in automated planning. Indeed, LTL synthesis corresponds to fully observable nondeterministic planning in which the domain is given compactly and the goal is an LTL formula, that in turn is related to two-player games with LTL goals. Finding a strategy for these games means to synthesize a plan for the planning problem. The last part of this thesis is then dedicated to investigate LTL synthesis under this different view. In particular, we study a generalized form of planning under partial observability, in which we have multiple, possibly infinitely many, planning domains with the same actions and observations, and goals expressed over observations, which are possibly temporally extended. By building on work on two-player games with imperfect information in the Formal Methods literature, we devise a general technique, generalizing the belief-state construction, to remove partial observability. This reduces the planning problem to a game of perfect information with a tight correspondence between plans and strategies. Then we instantiate the technique and solve some generalized planning problems

Human-robot co-navigation using anticipatory indicators of human walking motion

Mobile, interactive robots that operate in human-centric environments need the capability to safely and efficiently navigate around humans. This requires the ability to sense and predict human motion trajectories and to plan around them. In this paper, we present a study that supports the existence of statistically significant biomechanical turn indicators of human walking motions. Further, we demonstrate the effectiveness of these turn indicators as features in the prediction of human motion trajectories. Human motion capture data is collected with predefined goals to train and test a prediction algorithm. Use of anticipatory features results in improved performance of the prediction algorithm. Lastly, we demonstrate the closed-loop performance of the prediction algorithm using an existing algorithm for motion planning within dynamic environments. The anticipatory indicators of human walking motion can be used with different prediction and/or planning algorithms for robotics; the chosen planning and prediction algorithm demonstrates one such implementation for human-robot co-navigation

Formal Methods for Autonomous Systems

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications, which are analogous to behaviors and requirements in system design and give us the means to verify and synthesize system behaviors with formal guarantees. This monograph provides a survey of the current state of the art on applications of formal methods in the autonomous systems domain. We consider correct-by-construction synthesis under various formulations, including closed systems, reactive, and probabilistic settings. Beyond synthesizing systems in known environments, we address the concept of uncertainty and bound the behavior of systems that employ learning using formal methods. Further, we examine the synthesis of systems with monitoring, a mitigation technique for ensuring that once a system deviates from expected behavior, it knows a way of returning to normalcy. We also show how to overcome some limitations of formal methods themselves with learning. We conclude with future directions for formal methods in reinforcement learning, uncertainty, privacy, explainability of formal methods, and regulation and certification

Unified Multi-Rate Control: from Low Level Actuation to High Level Planning

In this paper we present a hierarchical multi-rate control architecture for nonlinear autonomous systems operating in partially observable environments. Control objectives are expressed using syntactically co-safe Linear Temporal Logic (LTL) specifications and the nonlinear system is subject to state and input constraints. At the highest level of abstraction, we model the system-environment interaction using a discrete Mixed Observable Markov Decision Problem (MOMDP), where the environment states are partially observed. The high level control policy is used to update the constraint sets and cost function of a Model Predictive Controller (MPC) which plans a reference trajectory. Afterwards, the MPC planned trajectory is fed to a low-level high-frequency tracking controller, which leverages Control Barrier Functions (CBFs) to guarantee bounded tracking errors. Our strategy is based on model abstractions of increasing complexity and layers running at different frequencies. We show that the proposed hierarchical multi-rate control architecture maximizes the probability of satisfying the high-level specifications while guaranteeing state and input constraint satisfaction. Finally, we tested the proposed strategy in simulations and experiments on examples inspired by the Mars exploration mission, where only partial environment observations are available

Hybrid conditional planning for service robotics

Planning is an indispensable ability for intelligent service robots operating in unstructured environments. Given service robots commonly have incomplete knowledge about and partial observability of handle such uncertainty. Moreover, the plans they compute should be feasible for real-world execution. Conditional planning is concerned with reaching goals from an initial state, in the presence of incomplete knowledge and partial observability; by utilizing sensing actions. Since all contingencies are considered in advance, a conditional plan is essentially a tree of actions where the root represents the initial state, leaves represent goal states, and each branch of the tree from the root to a leaf represents a possible execution of (deterministic) actuation actions and (non-deterministic) sensing actions to reach a goal state. Hybrid conditional planning extends conditional planning further by integrating lowlevel feasibility checks into executability conditions of actuation actions in conditional plans. We introduce a parallel offline algorithm called HCPlan, for computing hybrid conditional plans in robotics applications. HCPlan relies on modeling actuation actions and sensing actions in the causality-based action description language C+, and computation of the branches of a conditional plan in parallel using a SAT solver. In particular, thanks to external atoms, continuous feasibility checks (such as collision and reachability checks) are embedded into causal laws representing actuation actions and sensing actions; and thus each branch of a hybrid conditional plan describes a feasible execution of actions to reach their goals. Utilizing causal laws that describe iv non-deterministic effects of actions, sensing actions can be explicitly formalized; and thus each branch of a conditional plan can be computed without necessitating an ordering of sensing actions in advance. Furthermore, we introduce two different extensions of our hybrid conditional planner HCPlan: HCPlan-Anytime and HCPlan-Reactive. HCPlan-Anytime computes a partial hybrid conditional plan within a given time, by generating the branches with respect to their probability of execution. HCPlan-Reactive computes a hybrid conditional plan with a receding horizon. These extensions trade-off completeness of hybrid conditional plans for improved computation time, and provide useful important variations towards real-time use of the hybrid conditional planning. We develop comprehensive benchmarks for service robotics domain and evaluate our approach over these benchmarks with extensive experiments in terms of computational efficiency and plan quality. We compare HCPlan with other related conditional planners and approaches. We further demonstrate the usefulness of our approach in service robotics applications through dynamic simulations and physical implementations

Active Inference and Behavior Trees for Reactive Action Planning and Execution in Robotics

We propose a hybrid combination of active inference and behavior trees (BTs) for reactive action planning and execution in dynamic environments, showing how robotic tasks can be formulated as a free-energy minimization problem. The proposed approach allows to handle partially observable initial states and improves the robustness of classical BTs against unexpected contingencies while at the same time reducing the number of nodes in a tree. In this work, the general nominal behavior is specified offline through BTs, where a new type of leaf node, the prior node, is introduced to specify the desired state to be achieved rather than an action to be executed as typically done in BTs. The decision of which action to execute to reach the desired state is performed online through active inference. This results in the combination of continual online planning and hierarchical deliberation, that is an agent is able to follow a predefined offline plan while still being able to locally adapt and take autonomous decisions at runtime. The properties of our algorithm, such as convergence and robustness, are thoroughly analyzed, and the theoretical results are validated in two different mobile manipulators performing similar tasks, both in a simulated and real retail environment