Showing papers by "Richard M. Murray published in 2012"

Receding Horizon Temporal Logic Planning

Abstract: We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate the associated computational complexity of LTL synthesis, we propose a receding horizon framework that effectively reduces the synthesis problem into a set of smaller problems. The proposed control structure consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator reduces the trajectory generation problem into a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system with respect to its specification regardless of the environment in which the system operates. In addition, we present a response mechanism to handle failures that may occur due to a mismatch between the actual system and its model. The effectiveness of the proposed technique is demonstrated through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but is also capable of properly handling violation of the environment assumption that is explicitly stated as part of the system specification.

Robust control of uncertain Markov Decision Processes with temporal logic specifications

Abstract: We present a method for designing a robust control policy for an uncertain system subject to temporal logic specifications. The system is modeled as a finite Markov Decision Process (MDP) whose transition probabilities are not exactly known but are known to belong to a given uncertainty set. A robust control policy is generated for the MDP that maximizes the worst-case probability of satisfying the specification over all transition probabilities in this uncertainty set. To this end, we use a procedure from probabilistic model checking to combine the system model with an automaton representing the specification. This new MDP is then transformed into an equivalent form that satisfies assumptions for stochastic shortest path dynamic programming. A robust version of dynamic programming solves for a e-suboptimal robust control policy with time complexity O(log1/e) times that for the non-robust case.

Quantized Consensus by Means of Gossip Algorithm

Abstract: This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint It is assumed that at each time update, only a pair of agents can update their own states in terms of the quantized data being exchanged The agents are also required to communicate with one another in a stochastic fashion It is shown that a quantized consensus is reached for an arbitrary quantizer by means of the stochastic gossip algorithm proposed in a recent paper The expected value of the time at which a quantized consensus is reached is lower and upper bounded in terms of the topology of the graph for a uniform quantizer In particular, it is shown that these bounds are related to the principal submatrices of the weighted Laplacian matrix A convex optimization is also proposed to determine a set of probabilities used to pick a pair of agents that leads to a fast convergence of the gossip algorithm

Synergistic dual positive feedback loops established by molecular sequestration generate robust bimodal response

Abstract: Feedback loops are ubiquitous features of biological networks and can produce significant phenotypic heterogeneity, including a bimodal distribution of gene expression across an isogenic cell population. In this work, a combination of experiments and computational modeling was used to explore the roles of multiple feedback loops in the bimodal, switch-like response of the Saccharomyces cerevisiae galactose regulatory network. Here, we show that bistability underlies the observed bimodality, as opposed to stochastic effects, and that two unique positive feedback loops established by Gal1p and Gal3p, which both regulate network activity by molecular sequestration of Gal80p, induce this bimodality. Indeed, systematically scanning through different single and multiple feedback loop knockouts, we demonstrate that there is always a concentration regime that preserves the system’s bimodality, except for the double deletion of GAL1 and the GAL3 feedback loop, which exhibits a graded response for all conditions tested. The constitutive production rates of Gal1p and Gal3p operate as bifurcation parameters because variations in these rates can also abolish the system’s bimodal response. Our model indicates that this second loss of bistability ensues from the inactivation of the remaining feedback loop by the overexpressed regulatory component. More broadly, we show that the sequestration binding affinity is a critical parameter that can tune the range of conditions for bistability in a circuit with positive feedback established by molecular sequestration. In this system, two positive feedback loops can significantly enhance the region of bistability and the dynamic response time.

Backtracking temporal logic synthesis for uncertain environments

Abstract: This paper considers the problem of synthesizing correct-by-construction robotic controllers in environments with uncertain but fixed structure. “Environment” has two notions in this work: a map or “world” in which some controlled agent must operate and navigate (i.e., evolve in a configuration space with obstacles); and an adversarial player that selects continuous and discrete variables to try to make the agent fail (as in a game). Both the robot and the environment are subjected to behavioral specifications expressed as an assume-guarantee linear temporal logic (LTL) formula. We then consider how to efficiently modify the synthesized controller when the robot encounters unexpected changes in its environment. The crucial insight is that a portion of this problem takes place in a metric space, which provides a notion of nearness. Thus if a nominal plan fails, we need not resynthesize it entirely, but instead can “patch” it locally. We present an algorithm for doing this, prove soundness (correctness of output), and demonstrate it on an example gridworld.

On synthesizing robust discrete controllers under modeling uncertainty

Abstract: We investigate the robustness of reactive control protocols synthesized to guarantee system's correctness with respect to given temporal logic specifications. We consider uncertainties in open finite transition systems due to unmodeled transitions. The resulting robust synthesis problem is formulated as a temporal logic game. In particular, if the specification is in the so-called generalized reactivity [1] fragment of linear temporal logic, so is the augmented specification in the resulting robust synthesis problem. Hence, the robust synthesis problem belongs to the same complexity class with the nominal synthesis problem, and is amenable to polynomial time solvers. Additionally, we discuss reasoning about the effects of different levels of uncertainties on robust synthesizability and demonstrate the results on a simple robot motion planning scenario.

Optimal Control with Weighted Average Costs and Temporal Logic Specifications

Abstract: We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.

Towards formal synthesis of reactive controllers for dexterous robotic manipulation

Abstract: In robotic finger gaiting, fingers continuously manipulate an object until joint limitations or mechanical limitations periodically force a switch of grasp. Current approaches to gait planning and control are slow, lack formal guarantees on correctness, and are generally not reactive to changes in object geometry. To address these issues, we apply advances in formal methods to model a gait subject to external perturbations as a two-player game between a finger controller and its adversarial environment. High-level specifications are expressed in linear temporal logic (LTL) and low-level control primitives are designed for continuous kinematics. Simulations of planar manipulation with our synthesized correct-by-construction gait controller demonstrate the benefits of this approach.

A case study on reactive protocols for aircraft electric power distribution

Abstract: We consider the problem of designing a control protocol for the aircraft electric power system that meets system requirements and reacts dynamically to changes in internal system states. We formalize these requirements by translating them into a temporal logic specification language describing the correct behaviors of the system, and apply formal methods to automatically synthesize a controller protocol that satisfies system properties and requirements. Through an example, we perform a design exploration to show the benefits and tradeoffs between centralized and distributed control architectures.

Verification of Periodically Controlled Hybrid Systems: Application to an Autonomous Vehicle

Abstract: This article introduces Periodically Controlled Hybrid Automata (PCHA) for modular specification of embedded control systems. In a PCHA, control actions that change the control input to the plant occur roughly periodically, while other actions that update the state of the controller may occur in the interim. Such actions could model, for example, sensor updates and information received from higher-level planning modules that change the set point of the controller. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariant properties of PCHAs is presented. For PCHAs with polynomial continuous vector fields, it is possible to check these conditions automatically using, for example, quantifier elimination or sum of squares decomposition. We examine the feasibility of this automatic approach on a small example. The proposed technique is also used to manually verify safety and progress properties of a fairly complex planner-controller subsystem of an autonomous ground vehicle. Geometric properties of planner-generated paths are derived which guarantee that such paths can be safely followed by the controller.

Decentralised minimal-time dynamic consensus

Abstract: This paper considers a group of agents that aim to reach an agreement on individually received time-varying signals by local communication. In contrast to static network averaging problem, the consensus considered in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises a minimal number of local observations of a randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically as suggested by Olshevsky and Tsitsiklis.

Reactive controllers for differentially flat systems with temporal logic constraints

Abstract: We propose a procedure for the synthesis of control protocols for systems governed by nonlinear differential equations and constrained by temporal logic specifications. This procedure relies on a particular finite-state abstraction of the underlying continuous dynamics and a discrete representation of the external environmental signals. A two-player game formulation provides computationally efficient means to construct a discrete strategy based on the finite-state model. We focus on systems with differentially flat outputs, which, in a straightforward manner, allows the construction of continuous control signals from the discrete transitions dictated by the discrete strategy. The resulting continuous-time output trajectories are provably guaranteed to robustly satisfy the original specifications.

Quantifying crosstalk in biochemical systems

Abstract: Recent work has introduced biocircuit architectures that exhibit robust oscillatory behavior in organisms ranging from cyanobacteria to mammals. Complementary research in synthetic biology has introduced oscillators in vivo and in vitro suggesting that robust oscillation can be recapitulated using a small number of biochemical components. In this work, we introduce signaling crosstalk in biocircuits as a consequence of enzyme-mediated biochemical reactions. As a motivating example, we consider an in vitro oscillator with two types of crosstalk: crosstalk in production and degradation of RNA signals. We then propose a framework for quantifying crosstalk and use it to derive several dynamical constraints and suggest design techniques for ameliorating crosstalk in vitro biochemical systems. We demonstrate that the effects of crosstalk can be attenuated through the effective tuning of two key parameters in order to recover desired system dynamics. As an example, we show that by changing the balance between production and degradation crosstalk, we can tune a system to be stable or exhibit oscillatory behavior.

Learning diffeomorphism models of robotic sensorimotor cascades

Abstract: The problem of bootstrapping consists in designing agents that can learn from scratch the model of their sensorimotor cascade (the series of robot actuators, the external world, and the robot sensors) and use it to achieve useful tasks. In principle, we would want to design agents that can work for any robot dynamics and any robot sensor(s). One of the difficulties of this problem is the fact that the observations are very high dimensional, the dynamics is nonlinear, and there is a wide range of “representation nuisances” to which we would want the agent to be robust. In this paper, we model the dynamics of sensorimotor cascades using diffeomorphisms of the sensel space. We show that this model captures the dynamics of camera and range-finder data, that it can be used for long-term predictions, and that it can capture nonlinear phenomena such as a limited field of view. Moreover, by analyzing the learned diffeomorphisms it is possible to recover the “linear structure” of the dynamics independently of the commands representation.

Temporal logic control of switched affine systems with an application in fuel balancing

Abstract: We consider the problem of synthesizing hierarchical controllers for discrete-time switched affine systems subject to exogenous disturbances that guarantee that the trajectories of the system satisfy a high-level specification expressed as a linear temporal logic formula. Our method builds upon recent results on temporal logic planning and embedded controller synthesis. First, the control problem is lifted to a discrete level by constructing a finite transition system that abstracts the behavior of the underlying switched system. At the discrete level, we recast the problem as a two player temporal logic game by treating the environment driven switches as adversaries. The solution strategy for the game (i.e. the discrete plan) is then implemented at the continuous level by solving finite-horizon optimal control problems that establish reachability between discrete states and that compensate the effects of continuous disturbances. We also extend the earlier work by making efficient use of propositions in the temporal logic formula to drive the abstraction procedure and to facilitate the computation of continuous input at implementation time. An aircraft fuel system example is formulated; and solved using the proposed method. This sample problem demonstrates the applicability of the abstraction procedure and correct-by-construction controllers to regulate the fuel levels in multiple tanks during interesting operations like aerial refueling.

Switching protocol synthesis for temporal logic specifications

Abstract: We consider the problem of synthesizing a robust switching controller for nonlinear hybrid systems to guarantee that the trajectories of the system satisfy a high level specification expressed in linear temporal logic. Two different types of finite transition systems, namely under-approximations and over-approximations, that abstract the behavior of the underlying continuous dynamical system are defined. Using these finite abstractions, it is possible to leverage tools from logic and automata theory to synthesize discrete mode sequences or strategies. In particular, we show that the discrete synthesis problem for an under-approximation can be reformulated as a model checking problem and that for an over-approximation can be transformed into a two-player game, which can then be solved by using off-the-shelf tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the trajectories for the nonlinear hybrid system. Moreover, in the case of over-approximations, it is shown that one can easily accommodate specifications that require reacting to possibly adversarial external events within the same framework.

Fault detection and isolation from uninterpreted data in robotic sensorimotor cascades

Abstract: One of the challenges in designing the next generation of robots operating in non-engineered environments is that there seems to be an infinite amount of causes that make the sensor data unreliable or actuators ineffective. In this paper, we discuss what faults are possible to detect using zero modeling effort: we start from uninterpreted streams of observations and commands, and without a prior knowledge of a model of the world. We show that in sensorimotor cascades it is possible to define static faults independently of a nominal model. We define an information-theoretic usefulness of a sensor reading and we show that it captures several kind of sensorimotor faults frequently encountered in practice. We particularize these ideas to models proposed in previous work as suitable candidates for describing generic sensorimotor cascades. We show several examples with camera and range-finder data, and we discuss a possible way to integrate these techniques in an existing robot software architecture.

Performance metrics for a biomolecular step response

Abstract: Establishing performance metrics is a key part of a systematic design process. In particular, specifying metrics useful for quantifying performance in the ongoing efforts towards biomolecular circuit design is an important problem. Here we address this issue for the design of a fast biomolecular step response that is uniform across different cells and widely different environmental conditions using a combination of simple mathematical models and experimental measurements using single-cell time-lapse microscopy. We evaluate two metrics, the difference of the step response from an ideal step and the relative difference between multiple realizations of the step response, that can provide a single number to measure performance. We use a model of protein productiondegradation to show that these performance metrics correlate with response features of speed and noise. Finally, we work through an experimental methodology to estimate these metrics for step responses that have been acquired for inducible protein expression circuits in E. coli. These metrics will be useful to evaluate biomolecular step responses, as well as for setting similar performance measures for other design goals.

Turbulence measurements with fast two-color interferometry on Alcator C-Mod

Abstract: CONCLUSIONS AND FUTURE WORK The two-color interferometer diagnostic on Alcator C-Mod has been successfully upgraded to measure line-integrated electron density fluctuations. Upgraded electronics enable fast digitization and phase demodulation in software. TCI has been quantitatively verified against phase-contrast imaging for the quasi-coherent mode and broadband L-mode turbulence. The system has measured core turbulence features in ICRF-heated mode conversion flow drive experiments in I-mode plasmas. The features correlate with the peaking of the electron temperature profile during the sawtooth cycle. Associated electron density and temperature gradient scale-lengths increase during sawtooth cycle; the trapped-electron mode (TEM) may be unstable. Gyrokinetic simulations verifying trapped electron mode instability are underway. The TCI fluctuation diagnostic could be improved with several changes: Increasing the CO2 laser power to improve signal-to-noise. Increasing the kR range by adjusting the beam collimation. Increasing the kR resolution by adding detectors. TWO-COLOR INTERFEROMETRY (TCI)

Synthesis of Reactive Protocols for Vehicle-to-Vehicle Communication

Abstract: We present a synthesis method for communication protocols for active safety applications that satisfy certain formal specifications on quality of service requirements. The protocols are developed to provide reliable communication services for automobile active safety applications. The synthesis method transforms a specification into a distributed implementation of senders and receivers that together satisfy the quality of service requirements by transmitting messages over an unreliable medium. We develop a specification language and an execution model for the implementations, and demonstrate the viability of our method by developing a protocol for a traffic scenario in which a car runs a red light at a busy intersection.