arXiv subjects

Morteza Lahijanian

Publications and source records attributed to Morteza Lahijanian.

At least 55 records · Page 3Linked to original sources

arXiv2024

Admissibility Over Winning: A New Approach to Reactive Synthesis in Robotics

Reactive synthesis is a framework for modeling and automatically synthesizing strategies in robotics, typically through computing a \emph{winning} strategy in a 2-player game between the robot and the environment. Winning strategies, however, do not always exist, even in some simple cases. In such situations, it is still desirable for the robot to attempt its task rather than "giving up". In this work, we explore the notion of admissibility to define strategies beyond winning, tailored specifically for robotic systems. We introduce an ordering of admissible strategies and define \emph{admissibly rational strategies}, which aim to be winning and cooperative when possible, and non-violating and hopeful when necessary. We present an efficient synthesis algorithm and demonstrate that admissibly rational strategies produce desirable behaviors through case studies.

cs.RO↗

arXiv2024

Learning-Based Shielding for Safe Autonomy under Unknown Dynamics

Shielding is a common method used to guarantee the safety of a system under a black-box controller, such as a neural network controller from deep reinforcement learning (DRL), with simpler, verified controllers. Existing shielding methods rely on formal verification through Markov Decision Processes (MDPs), assuming either known or finite-state models, which limits their applicability to DRL settings with unknown, continuous-state systems. This paper addresses these limitations by proposing a data-driven shielding methodology that guarantees safety for unknown systems under black-box controllers. The approach leverages Deep Kernel Learning to model the systems' one-step evolution with uncertainty quantification and constructs a finite-state abstraction as an Interval MDP (IMDP). By focusing on safety properties expressed in safe linear temporal logic (safe LTL), we develop an algorithm that computes the maximally permissive set of safe policies on the IMDP, ensuring avoidance of unsafe states. The algorithms soundness and computational complexity are demonstrated through theoretical proofs and experiments on nonlinear systems, including a high-dimensional autonomous spacecraft scenario.

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arXiv2024

Uncertainty Propagation in Stochastic Systems via Mixture Models with Error Quantification

Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a novel approach to approximate the distribution of the system over a given finite time horizon with a mixture of distributions. The key novelty of our approach is that it not only provides tractable approximations for the distribution of a non-linear stochastic system, but also comes with formal guarantees of correctness. In particular, we consider the total variation (TV) distance to quantify the distance between two distributions and derive an upper bound on the TV between the distribution of the original system and the approximating mixture distribution derived with our framework. We show that in various cases of interest, including in the case of Gaussian noise, the resulting bound can be efficiently computed in closed form. This allows us to quantify the correctness of the approximation and to optimize the parameters of the resulting mixture distribution to minimize such distance. The effectiveness of our approach is illustrated on several benchmarks from the control community.

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arXiv2024

Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression

Leveraging autonomous systems in safety-critical scenarios requires verifying their behaviors in the presence of uncertainties and black-box components that influence the system dynamics. In this work, we develop a framework for verifying discrete-time dynamical systems with unmodelled dynamics and noisy measurements against temporal logic specifications from an input-output dataset. The verification framework employs Gaussian process (GP) regression to learn the unknown dynamics from the dataset and abstracts the continuous-space system as a finite-state, uncertain Markov decision process (MDP). This abstraction relies on space discretization and transition probability intervals that capture the uncertainty due to the error in GP regression by using reproducible kernel Hilbert space analysis as well as the uncertainty induced by discretization. The framework utilizes existing model checking tools for verification of the uncertain MDP abstraction against a given temporal logic specification. We establish the correctness of extending the verification results on the abstraction created from noisy measurements to the underlying system. We show that the computational complexity of the framework is polynomial in the size of the dataset and discrete abstraction. The complexity analysis illustrates a trade-off between the quality of the verification results and the computational burden to handle larger datasets and finer abstractions. Finally, we demonstrate the efficacy of our learning and verification framework on several case studies with linear, nonlinear, and switched dynamical systems.

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arXiv2024

Online Pareto-Optimal Decision-Making for Complex Tasks using Active Inference

When a robot autonomously performs a complex task, it frequently must balance competing objectives while maintaining safety. This becomes more difficult in uncertain environments with stochastic outcomes. Enhancing transparency in the robot's behavior and aligning with user preferences are also crucial. This paper introduces a novel framework for multi-objective reinforcement learning that ensures safe task execution, optimizes trade-offs between objectives, and adheres to user preferences. The framework has two main layers: a multi-objective task planner and a high-level selector. The planning layer generates a set of optimal trade-off plans that guarantee satisfaction of a temporal logic task. The selector uses active inference to decide which generated plan best complies with user preferences and aids learning. Operating iteratively, the framework updates a parameterized learning model based on collected data. Case studies and benchmarks on both manipulation and mobile robots show that our framework outperforms other methods and (i) learns multiple optimal trade-offs, (ii) adheres to a user preference, and (iii) allows the user to adjust the balance between (i) and (ii).

cs.RO↗

arXiv2024

Data-Driven Strategy Synthesis for Stochastic Systems with Unknown Nonlinear Disturbances

In this paper, we introduce a data-driven framework for synthesis of provably-correct controllers for general nonlinear switched systems under complex specifications. The focus is on systems with unknown disturbances whose effects on the dynamics of the system is nonlinear. The specifications are assumed to be given as linear temporal logic over finite traces (LTLf) formulas. Starting from observations of either the disturbance or the state of the system, we first learn an ambiguity set that contains the unknown distribution of the disturbances with a user-defined confidence. Next, we construct a robust Markov decision process (RMDP) as a finite abstraction of the system. By composing the RMDP with the automaton obtained from the LTLf formula and performing optimal robust value iteration on the composed RMDP, we synthesize a strategy that yields a high probability that the uncertain system satisfies the specifications. Our empirical evaluations on systems with a wide variety of disturbances show that the strategies synthesized with our approach lead to high satisfaction probabilities and validate the theoretical guarantees.

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arXiv2024

Recursively-Constrained Partially Observable Markov Decision Processes

Many sequential decision problems involve optimizing one objective function while imposing constraints on other objectives. Constrained Partially Observable Markov Decision Processes (C-POMDP) model this case with transition uncertainty and partial observability. In this work, we first show that C-POMDPs violate the optimal substructure property over successive decision steps and thus may exhibit behaviors that are undesirable for some (e.g., safety critical) applications. Additionally, online re-planning in C-POMDPs is often ineffective due to the inconsistency resulting from this violation. To address these drawbacks, we introduce the Recursively-Constrained POMDP (RC-POMDP), which imposes additional history-dependent cost constraints on the C-POMDP. We show that, unlike C-POMDPs, RC-POMDPs always have deterministic optimal policies and that optimal policies obey Bellman's principle of optimality. We also present a point-based dynamic programming algorithm for RC-POMDPs. Evaluations on benchmark problems demonstrate the efficacy of our algorithm and show that policies for RC-POMDPs produce more desirable behaviors than policies for C-POMDPs.

cs.AI↗

arXiv2024

Sound Heuristic Search Value Iteration for Undiscounted POMDPs with Reachability Objectives

Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the (indefinite-horizon) Maximal Reachability Probability Problem (MRPP), where the goal is to maximize the probability of reaching some target states. This is also a core problem in model checking with logical specifications and is naturally undiscounted (discount factor is one). Inspired by the success of point-based methods developed for discounted problems, we study their extensions to MRPP. Specifically, we focus on trial-based heuristic search value iteration techniques and present a novel algorithm that leverages the strengths of these techniques for efficient exploration of the belief space (informed search via value bounds) while addressing their drawbacks in handling loops for indefinite-horizon problems. The algorithm produces policies with two-sided bounds on optimal reachability probabilities. We prove convergence to an optimal policy from below under certain conditions. Experimental evaluations on a suite of benchmarks show that our algorithm outperforms existing methods in almost all cases in both probability guarantees and computation time.

cs.AI↗

arXiv2024

Efficient Strategy Synthesis for Switched Stochastic Systems with Distributional Uncertainty

We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of distributions that are $\varepsilon-$close, in the Wasserstein distance sense, to a nominal one. We propose algorithms for the efficient synthesis of distributionally robust control strategies that maximize the satisfaction probability of reach-avoid specifications with either a given or an arbitrary (not specified) time horizon, i.e., unbounded-time reachability. The framework consists of two main steps: finite abstraction and control synthesis. First, we construct a finite abstraction of the switched stochastic system as a \emph{robust Markov decision process} (robust MDP) that encompasses both the stochasticity of the system and the uncertainty in the noise distribution. Then, we synthesize a strategy that is robust to the distributional uncertainty on the resulting robust MDP. We employ techniques from optimal transport and stochastic programming to reduce the strategy synthesis problem to a set of linear programs, and propose a tailored and efficient algorithm to solve them. The resulting strategies are correctly refined into switching strategies for the original stochastic system. We illustrate the efficacy of our framework on various case studies comprising both linear and non-linear switched stochastic systems.

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arXiv2024

Data-Driven Permissible Safe Control with Barrier Certificates

This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process (GP) regression and obtaining probabilistic errors for this estimate. Then, we develop an algorithm for constructing piecewise stochastic barrier functions to find a maximal permissible strategy set using the learned GP model, which is based on sequentially pruning the worst controls until a maximal set is identified. The permissible strategies are guaranteed to maintain probabilistic safety for the true system. This is especially important for learning-enabled systems, because a rich strategy space enables additional data collection and complex behaviors while remaining safe. Case studies on linear and nonlinear systems demonstrate that increasing the size of the dataset for learning the system grows the permissible strategy set.

cs.LG↗

arXiv2024

IntervalMDP.jl: Accelerated Value Iteration for Interval Markov Decision Processes

In this paper, we present IntervalMDP.jl, a Julia package for probabilistic analysis of interval Markov Decision Processes (IMDPs). IntervalMDP.jl facilitates the synthesis of optimal strategies and verification of IMDPs against reachability specifications and discounted reward properties. The library supports sparse matrices and is compatible with data formats from common tools for the analysis of probabilistic models, such as PRISM. A key feature of IntervalMDP.jl is that it presents both a multi-threaded CPU and a GPU-accelerated implementation of value iteration algorithms for IMDPs. In particular, IntervalMDP.jl takes advantage of the Julia type system and the inherently parallelizable nature of value iteration to improve the efficiency of performing analysis of IMDPs. On a set of examples, we show that IntervalMDP.jl substantially outperforms existing tools for verification and strategy synthesis for IMDPs in both computation time and memory consumption.

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arXiv2024

Introducing Delays in Multi-Agent Path Finding

We consider a Multi-Agent Path Finding (MAPF) setting where agents have been assigned a plan, but during its execution some agents are delayed. Instead of replanning from scratch when such a delay occurs, we propose delay introduction, whereby we delay some additional agents so that the remainder of the plan can be executed safely. We show that finding the minimum number of additional delays is APX-Hard, i.e., it is NP-Hard to find a $(1+\varepsilon)$-approximation for some $\varepsilon>0$. However, in practice we can find optimal delay-introductions using Conflict-Based Search for very large numbers of agents, and both planning time and the resulting length of the plan are comparable, and sometimes outperform the state-of-the-art heuristics for replanning.

cs.RO↗

arXiv2024

Shielded Deep Reinforcement Learning for Complex Spacecraft Tasking

Autonomous spacecraft control via Shielded Deep Reinforcement Learning (SDRL) has become a rapidly growing research area. However, the construction of shields and the definition of tasking remains informal, resulting in policies with no guarantees on safety and ambiguous goals for the RL agent. In this paper, we first explore the use of formal languages, namely Linear Temporal Logic (LTL), to formalize spacecraft tasks and safety requirements. We then define a manner in which to construct a reward function from a co-safe LTL specification automatically for effective training in SDRL framework. We also investigate methods for constructing a shield from a safe LTL specification for spacecraft applications and propose three designs that provide probabilistic guarantees. We show how these shields interact with different policies and the flexibility of the reward structure through several experiments.

cs.LG↗

arXiv2024

Promises of Deep Kernel Learning for Control Synthesis

Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes. Hence, it is potentially a promising tool to learn and control complex dynamical systems. In this work, we develop a scalable abstraction-based framework that enables the use of DKL for control synthesis of stochastic dynamical systems against complex specifications. Specifically, we consider temporal logic specifications and create an end-to-end framework that uses DKL to learn an unknown system from data and formally abstracts the DKL model into an Interval Markov Decision Process (IMDP) to perform control synthesis with correctness guarantees. Furthermore, we identify a deep architecture that enables accurate learning and efficient abstraction computation. The effectiveness of our approach is illustrated on various benchmarks, including a 5-D nonlinear stochastic system, showing how control synthesis with DKL can substantially outperform state-of-the-art competitive methods.

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arXiv2024

Optimal Planning for Timed Partial Order Specifications

This paper addresses the challenge of planning a sequence of tasks to be performed by multiple robots while minimizing the overall completion time subject to timing and precedence constraints. Our approach uses the Timed Partial Orders (TPO) model to specify these constraints. We translate this problem into a Traveling Salesman Problem (TSP) variant with timing and precedent constraints, and we solve it as a Mixed Integer Linear Programming (MILP) problem. Our contributions include a general planning framework for TPO specifications, a MILP formulation accommodating time windows and precedent constraints, its extension to multi-robot scenarios, and a method to quantify plan robustness. We demonstrate our framework on several case studies, including an aircraft turnaround task involving three Jackal robots, highlighting the approach's potential applicability to important real-world problems. Our benchmark results show that our MILP method outperforms state-of-the-art open-source TSP solvers OR-Tools.

cs.RO↗

arXiv2024

Stochastic Games for Interactive Manipulation Domains

As robots become more prevalent, the complexity of robot-robot, robot-human, and robot-environment interactions increases. In these interactions, a robot needs to consider not only the effects of its own actions, but also the effects of other agents' actions and the possible interactions between agents. Previous works have considered reactive synthesis, where the human/environment is modeled as a deterministic, adversarial agent; as well as probabilistic synthesis, where the human/environment is modeled via a Markov chain. While they provide strong theoretical frameworks, there are still many aspects of human-robot interaction that cannot be fully expressed and many assumptions that must be made in each model. In this work, we propose stochastic games as a general model for human-robot interaction, which subsumes the expressivity of all previous representations. In addition, it allows us to make fewer modeling assumptions and leads to more natural and powerful models of interaction. We introduce the semantics of this abstraction and show how existing tools can be utilized to synthesize strategies to achieve complex tasks with guarantees. Further, we discuss the current computational limitations and improve the scalability by two orders of magnitude by a new way of constructing models for PRISM-games.

cs.RO↗

arXiv2023

Sampling-based Reactive Synthesis for Nondeterministic Hybrid Systems

This paper introduces a sampling-based strategy synthesis algorithm for nondeterministic hybrid systems with complex continuous dynamics under temporal and reachability constraints. We model the evolution of the hybrid system as a two-player game, where the nondeterminism is an adversarial player whose objective is to prevent achieving temporal and reachability goals. The aim is to synthesize a winning strategy -- a reactive (robust) strategy that guarantees the satisfaction of the goals under all possible moves of the adversarial player. Our proposed approach involves growing a (search) game-tree in the hybrid space by combining sampling-based motion planning with a novel bandit-based technique to select and improve on partial strategies. We show that the algorithm is probabilistically complete, i.e., the algorithm will asymptotically almost surely find a winning strategy, if one exists. The case studies and benchmark results show that our algorithm is general and effective, and consistently outperforms state of the art algorithms.

eess.SY↗

arXiv2023

Formal Abstraction of General Stochastic Systems via Noise Partitioning

Verifying the performance of safety-critical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with non-standard (e.g., non-affine, non-symmetric, non-unimodal) noise distributions for verification purposes. The method uses a finite partitioning of the noise domain to construct an interval Markov chain (IMC) abstraction of the system via transition probability intervals. Noise partitioning allows for a general class of distributions and structures, including multiplicative and mixture models, and admits both known and data-driven systems. The partitions required for optimal transition bounds are specified for systems that are monotonic with respect to the noise, and explicit partitions are provided for affine and multiplicative structures. By the soundness of the abstraction procedure, verification on the IMC provides guarantees on the stochastic system against a temporal logic specification. In addition, we present a novel refinement-free algorithm that improves the verification results. Case studies on linear and nonlinear systems with non-Gaussian noise, including a data-driven example, demonstrate the generality and effectiveness of the method without introducing excessive conservatism.

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