arXiv subjects

Richard M. Murray

Publications and source records attributed to Richard M. Murray.

At least 19 recordsLinked to original sources

arXiv2025

A Compositional Approach to Diagnosing Faults in Cyber-Physical Systems

Identifying the cause of a system-level failure in a cyber-physical system (CPS) can be like tracing a needle in a haystack. This paper approaches the problem by assuming that the CPS has been designed compositionally and that each component in the system is associated with an assume-guarantee contract. We exploit recent advances in contract-based design that show how to compute the contract for the entire system using the component-level contracts. When presented with a system-level failure, our approach is able to efficiently identify the components that are responsible for the system-level failure together with the specific predicates in those components' specifications that are involved in the fault. We implemented this approach using Pacti and demonstrate it through illustrative examples inspired by an autonomous vehicle in the DARPA urban challenge.

eess.SY↗

arXiv2025

Quadrotor Morpho-Transition: Learning vs Model-Based Control Strategies

Quadrotor Morpho-Transition, or the act of transitioning from air to ground through mid-air transformation, involves complex aerodynamic interactions and a need to operate near actuator saturation, complicating controller design. In recent work, morpho-transition has been studied from a model-based control perspective, but these approaches remain limited due to unmodeled dynamics and the requirement for planning through contacts. Here, we train an end-to-end Reinforcement Learning (RL) controller to learn a morpho-transition policy and demonstrate successful transfer to hardware. We find that the RL control policy achieves agile landing, but only transfers to hardware if motor dynamics and observation delays are taken into account. On the other hand, a baseline MPC controller transfers out-of-the-box without knowledge of the actuator dynamics and delays, at the cost of reduced recovery from disturbances in the event of unknown actuator failures. Our work opens the way for more robust control of agile in-flight quadrotor maneuvers that require mid-air transformation.

cs.RO↗

arXiv2025

ATMO: An Aerially Transforming Morphobot for Dynamic Ground-Aerial Transition

Designing ground-aerial robots is challenging due to the increased actuation requirements which can lead to added weight and reduced locomotion efficiency. Morphobots mitigate this by combining actuators into multi-functional groups and leveraging ground transformation to achieve different locomotion modes. However, transforming on the ground requires dealing with the complexity of ground-vehicle interactions during morphing, limiting applicability on rough terrain. Mid-air transformation offers a solution to this issue but demands operating near or beyond actuator limits while managing complex aerodynamic forces. We address this problem by introducing the Aerially Transforming Morphobot (ATMO), a robot which transforms near the ground achieving smooth transition between aerial and ground modes. To achieve this, we leverage the near ground aerodynamics, uncovered by experimental load cell testing, and stabilize the system using a model-predictive controller that adapts to ground proximity and body shape. The system is validated through numerous experimental demonstrations. We find that ATMO can land smoothly at body postures past its actuator saturation limits by virtue of the uncovered ground-effect.

cs.RO↗

arXiv2024

Flow-Based Synthesis of Reactive Tests for Discrete Decision-Making Systems with Temporal Logic Specifications

Designing tests to evaluate if a given autonomous system satisfies complex specifications is challenging due to the complexity of these systems. This work proposes a flow-based approach for reactive test synthesis from temporal logic specifications, enabling the synthesis of test environments consisting of static and reactive obstacles and dynamic test agents. The temporal logic specifications describe desired test behavior, including system requirements as well as a test objective that is not revealed to the system. The synthesized test strategy places restrictions on system actions in reaction to the system state. The tests are minimally restrictive and accomplish the test objective while ensuring realizability of the system's objective without aiding it (semi-cooperative setting). Automata theory and flow networks are leveraged to formulate a mixed-integer linear program (MILP) to synthesize the test strategy. For a dynamic test agent, the agent strategy is synthesized for a GR(1) specification constructed from the solution of the MILP. If the specification is unrealizable by the dynamics of the test agent, a counterexample-guided approach is used to resolve the MILP until a strategy is found. This flow-based, reactive test synthesis is conducted offline and is agnostic to the system controller. Finally, the resulting test strategy is demonstrated in simulation and experimentally on a pair of quadrupedal robots for a variety of specifications.

cs.FL↗

arXiv2024

Specifying and Analyzing Networked and Layered Control Systems Operating on Multiple Clocks

We consider the problem of reasoning about networked and layered control systems using assume-guarantee specifications. As these systems are formed by the interconnection of components that operate under various clocks, we introduce a new logic, Multiclock Logic (MCL), to be able to express the requirements of components form the point of view of their local clocks. Specifying components locally promotes independent design and component reuse. We carry out a contract-based analysis of a control system implemented via two control algorithms (model predictive control and feedback linearization) running on their own processors and clocks. Then we implement each of the contracts to build a system. The system performs as desired when the requirements derived from our system-level analysis are respected. Violating the constraints required by the contract-based analysis of the system leads to error.

eess.SY↗

arXiv2023

Lipschitz Continuity of Signal Temporal Logic Robustness Measures: Synthesizing Control Barrier Functions from One Expert Demonstration

Control Barrier Functions (CBFs) allow for efficient synthesis of controllers to maintain desired invariant properties of safety-critical systems. However, the problem of identifying a CBF remains an open question. As such, this paper provides a constructive method for control barrier function synthesis around one expert demonstration that realizes a desired system specification formalized in Signal Temporal Logic (STL). First, we prove that all STL specifications have Lipschitz-continuous robustness measures. Second, we leverage this Lipschitz continuity to synthesize a time-varying control barrier function. By filtering control inputs to maintain the positivity of this function, we ensure that the system trajectory satisfies the desired STL specification. Finally, we demonstrate the effectiveness of our approach on the Robotarium.

eess.SY↗

arXiv2023

Pacti: Scaling Assume-Guarantee Reasoning for System Analysis and Design

Contract-based design is a method to facilitate modular system design. While there has been substantial progress on the theory of contracts, there has been less progress on scalable algorithms for the algebraic operations in this theory. In this paper, we present: 1) principles to implement a contract-based design tool at scale and 2) Pacti, a tool that can efficiently compute these operations. We then illustrate the use of Pacti in a variety of case studies.

cs.LO↗

arXiv2023

Barrier-Based Test Synthesis for Safety-Critical Systems Subject to Timed Reach-Avoid Specifications

We propose an adversarial, time-varying test-synthesis procedure for safety-critical systems without requiring specific knowledge of the underlying controller steering the system. From a broader test and evaluation context, determination of difficult tests of system behavior is important as these tests would elucidate problematic system phenomena before these mistakes can engender problematic outcomes, e.g. loss of human life in autonomous cars, costly failures for airplane systems, etc. Our approach builds on existing, simulation-based work in the test and evaluation literature by offering a controller-agnostic test-synthesis procedure that provides a series of benchmark tests with which to determine controller reliability. To achieve this, our approach codifies the system objective as a timed reach-avoid specification. Then, by coupling control barrier functions with this class of specifications, we construct an instantaneous difficulty metric whose minimizer corresponds to the most difficult test at that system state. We use this instantaneous difficulty metric in a game-theoretic fashion, to produce an adversarial, time-varying test-synthesis procedure that does not require specific knowledge of the system's controller, but can still provably identify realizable and maximally difficult tests of system behavior. Finally, we develop this test-synthesis procedure for both continuous and discrete-time systems and showcase our test-synthesis procedure on simulated and hardware examples.

eess.SY↗

arXiv2022

Evaluation Metrics for Object Detection for Autonomous Systems

This paper studies the evaluation of learning-based object detection models in conjunction with model-checking of formal specifications defined on an abstract model of an autonomous system and its environment. In particular, we define two metrics -- \emph{proposition-labeled} and \emph{class-labeled} confusion matrices -- for evaluating object detection, and we incorporate these metrics to compute the satisfaction probability of system-level safety requirements. While confusion matrices have been effective for comparative evaluation of classification and object detection models, our framework fills two key gaps. First, we relate the performance of object detection to formal requirements defined over downstream high-level planning tasks. In particular, we provide empirical results that show that the choice of a good object detection algorithm, with respect to formal requirements on the overall system, significantly depends on the downstream planning and control design. Secondly, unlike the traditional confusion matrix, our metrics account for variations in performance with respect to the distance between the ego and the object being detected. We demonstrate this framework on a car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL).

cs.RO↗

arXiv2022

Synthesizing Reactive Test Environments for Autonomous Systems: Testing Reach-Avoid Specifications with Multi-Commodity Flows

We study automated test generation for verifying discrete decision-making modules in autonomous systems. We utilize linear temporal logic to encode the requirements on the system under test in the system specification and the behavior that we want to observe during the test is given as the test specification which is unknown to the system. First, we use the specifications and their corresponding non-deterministic Büchi automata to generate the specification product automaton. Second, a virtual product graph representing the high-level interaction between the system and the test environment is constructed modeling the product automaton encoding the system, the test environment, and specifications. The main result of this paper is an optimization problem, framed as a multi-commodity network flow problem, that solves for constraints on the virtual product graph which can then be projected to the test environment. Therefore, the result of the optimization problem is reactive test synthesis that ensures that the system meets the test specifications along with satisfying the system specifications. This framework is illustrated in simulation on grid world examples, and demonstrated on hardware with the Unitree A1 quadruped, wherein dynamic locomotion behaviors are verified in the context of reactive test environments.

cs.RO↗

arXiv2022

OUTformation: Distributed Data-Gathering with Feedback under Unknown Environment and Communication Delay Constraints

Towards the informed design of large-scale distributed data-gathering architectures under real-world assumptions such as nonzero communication delays and unknown environment dynamics, this paper considers the effects of allowing feedback communication from the central processor to external sensors. Using simple but representative state-estimation examples, we investigate fundamental tradeoffs between the mean-squared error (MSE) of the central processor's estimate of the environment state, and the total power expenditure per sensor under more conventional architectures without feedback (INformation) versus those with broadcast feedback (OUTformation). The primary advantage of enabling feedback is that each sensor's understanding of the central processor's estimate improves, which enables each sensor to determine when and what parts of its current observations to transmit. We use theory to demonstrate conditions in which OUTformation maintains the same MSE as INformation with less power expended on average, and conditions in which OUTformation obtains less MSE than INformation at additional power cost. These performance tradeoffs are also considered under settings where environments undergo less variation, and sensors implement random backoff times to prevent transmission collisions. Our results are supported via numerical studies, which show that the properties derived in theory still hold even when some of the simplifying assumptions are removed.

eess.SY↗

arXiv2022

Robust Safe Control Synthesis with Disturbance Observer-Based Control Barrier Functions

In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller synthesis framework with control Lyapunov functions (CLFs) and control barrier functions (CBFs) in the presence of disturbance. A high-gain input observer method is adapted to estimate the time-varying unmodelled dynamics of the CBF with an error bound using the first-order time derivative of the CBF. This approach leads to an easily tunable low order disturbance estimator structure with a design parameter as it utilizes only the CBF constraint. The estimated unknown input and associated error bound are used to ensure robust safety and exponential stability by formulating a CLF-CBF quadratic program. The proposed method is applicable to both relative degree one and higher relative degree CBF constraints. The efficacy of the proposed approach is demonstrated using a numerical simulations of an adaptive cruise control system and a Segway platform with an external disturbance.

eess.SY↗

arXiv2022

Towards Better Test Coverage: Merging Unit Tests for Autonomous Systems

We present a framework for merging unit tests for autonomous systems. Typically, it is intractable to test an autonomous system for every scenario in its operating environment. The question of whether it is possible to design a single test for multiple requirements of the system motivates this work. First, we formally define three attributes of a test: a test specification that characterizes behaviors observed in a test execution, a test environment, and a test policy. Using the merge operator from contract-based design theory, we provide a formalism to construct a merged test specification from two unit test specifications. Temporal constraints on the merged test specification guarantee that non-trivial satisfaction of both unit test specifications is necessary for a successful merged test execution. We assume that the test environment remains the same across the unit tests and the merged test. Given a test specification and a test environment, we synthesize a test policy filter using a receding horizon approach, and use the test policy filter to guide a search procedure (e.g. Monte-Carlo Tree Search) to find a test policy that is guaranteed to satisfy the test specification. This search procedure finds a test policy that maximizes a pre-defined robustness metric for the test while the filter guarantees a test policy for satisfying the test specification. We prove that our algorithm is sound. Furthermore, the receding horizon approach to synthesizing the filter ensures that our algorithm is scalable. Finally, we show that merging unit tests is impactful for designing efficient test campaigns to achieve similar levels of coverage in fewer test executions. We illustrate our framework on two self-driving examples in a discrete-state setting.

eess.SY↗

arXiv2021

Risk-Averse Decision Making Under Uncertainty

A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others. Traditionally, policy synthesis techniques are proposed such that a total expected cost or reward is minimized or maximized. However, optimality in the total expected cost sense is only reasonable if system behavior in the large number of runs is of interest, which has limited the use of such policies in practical mission-critical scenarios, wherein large deviations from the expected behavior may lead to mission failure. In this paper, we consider the problem of designing policies for MDPs and POMDPs with objectives and constraints in terms of dynamic coherent risk measures, which we refer to as the constrained risk-averse problem. For MDPs, we reformulate the problem into a infsup problem via the Lagrangian framework and propose an optimization-based method to synthesize Markovian policies. For MDPs, we demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. For POMDPs, we show that, if the coherent risk measures can be defined as a Markov risk transition mapping, an infinite-dimensional optimization can be used to design Markovian belief-based policies. For stochastic finite-state controllers (FSCs), we show that the latter optimization simplifies to a (finite-dimensional) DCP and can be solved by the DCCP framework. We incorporate these DCPs in a policy iteration algorithm to design risk-averse FSCs for POMDPs.

cs.AI↗

arXiv2021

Synthesis of Static Test Environments for Observing Sequence-like Behaviors in Autonomous Systems

In this paper, we investigate formal test-case generation for high-level mission objectives, specifically reachability, of autonomous systems. We use Kripke structures to represent the high-level decision-making of the agent under test and the abstraction of the test environment. First, we define the notion of a test specification, focusing on a fragment of linear temporal logic represented by sequence temporal logic formulas. Second, we formulate the problem of test graph synthesis to find a test configuration for which the agent must satisfy the test specification to satisfy its mission objectives. We an algorithm, based on network flows, for synthesizing a test graph by restricting transitions, represented by edge deletions, on the original graph induced by the Kripke structures. The algorithm synthesizes the test graph iteratively using an integer linear program. We prove completeness for our algorithm, and we show that the edge deletions in each iteration maintain feasibility of the integer linear program in the subsequent iteration. We formalize the notion of a minimally constrained test graph in terms of maximum flow, and prove the synthesized test graph to be minimally constrained. We demonstrate our algorithm on a simple graph and on gridworlds.

eess.SY↗

arXiv2021

Leveraging Classification Metrics for Quantitative System-Level Analysis with Temporal Logic Specifications

In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models.

eess.SY↗

arXiv2021

Constrained Risk-Averse Markov Decision Processes

We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.

cs.AI↗

arXiv2021

Limits of Probabilistic Safety Guarantees when Considering Human Uncertainty

When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents' trajectories (i.e. confidence tubes that contain trajectories with probability $δ$), which can then be used to guarantee safety with probability $1-δ$. However, almost all existing works consider $δ\geq 0.001$. The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with $δ< 10^{-8}$, and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low $δ$. Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for $δ\leq 10^{-8}$. These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.

cs.RO↗