Showing papers by "Richard M. Murray published in 2010"

Autonomous driving in urban environments: approaches, lessons and challenges

Abstract: The development of autonomous vehicles for urban driving has seen rapid progress in the past 30 years. This paper provides a summary of the current state of the art in autonomous driving in urban environments, based primarily on the experiences of the authors in the 2007 DARPA Urban Challenge (DUC). The paper briefly summarizes the approaches that different teams used in the DUC, with the goal of describing some of the challenges that the teams faced in driving in urban environments. The paper also highlights the long-term research challenges that must be overcome in order to enable autonomous driving and points to opportunities for new technologies to be applied in improving vehicle safety, exploiting intelligent road infrastructure and enabling robotic vehicles operating in human environments.

Receding horizon control for temporal logic specifications

Abstract: In this paper, we describe a receding horizon framework that satisfies a class of linear temporal logic specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. The resulting embedded control software consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator essentially reduces the trajectory generation problem to 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. To handle failures that may occur due to a mismatch between the actual system and its model, we propose a response mechanism and illustrate, through an example, how the system is capable of responding to certain failures and continues to exhibit a correct behavior.

Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective

Abstract: We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[Pk], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[Pk ? M], i.e., the probability that Pk is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[Pk ? M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[Pk ? M]. We also recover the results in the literature when using Pr[Pk ? M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper.

Controlling biological networks by time-delayed signals

Abstract: This paper describes the use of time-delayed feedback to regulate the behaviour of biological networks. The general ideas on specific transcriptional regulatory and neural networks are demonstrated. It is shown that robust yet tunable controllers can be constructed that provide the biological systems with model-engineered inputs. The results indicate that time delay modulation may serve as an efficient biocompatible control tool.

A Case Study in Approximate Linearization: The Acrobot Example

Abstract: The acrobot is a simple mechanical system patterned after a gymnast performing on a single parallel bar. By swinging her legs, a gymnast is able to bring herself into an inverted position with her center of mass above the part and is able to perform manuevers about this configuration. This report studies the use of nonlinear control techniques for designing a controller to operate in a neighborhood of the manifold of inverted equilibrium points. The techniques described here are of particular interest because the dynamic model of the acrobot violates many of the necessary conditions required to apply current methods in linear and nonlinear control theory. The approach used in this report is to approximate the system in such a way that the behavior of the system about the manifold of equilibrium points is correctly captured. In particular, we construct an approximating system which agrees with the linearization of the original system on the equilibrium manifold and is full state linearizable. For this class of approximations, controllers can be constructed using recent techniques from differential geometric control theory. We show that application of control laws derived in this manner results in approximate trajectory tracking for the system under certain restrictions on the class of desired trajectories. Simulation results based on a simplified model of the acrobot are included. Research supported in part by an IBM Manufacturing fellowship and the National Science Foundation, under grant IRI-90-14490. Fred O’Green Assistant Professor of Engineering

Networks with the Smallest Average Distance and the Largest Average Clustering

Abstract: We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal.

Automatic Synthesis of Robust Embedded Control Software

Abstract: We propose a methodology for automatic synthesis of embedded control software that accounts for exogenous disturbances. The resulting system is guaranteed, by construction, to satisfy a given specification expressed in linear temporal logic. The embedded control software consists of three components: a goal generator, a trajectory planner, and a continuous controller. We demonstrate the effectiveness of the proposed technique 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 also capable of handling violation of the environment assumptions.

A bio-plausible design for visual pose stabilization

Abstract: We consider the problem of purely visual pose stabilization (also known as servoing) of a second-order rigid-body system with six degrees of freedom: how to choose forces and torques, based on the current view and a memorized goal image, to steer the pose towards a desired one. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. This particular computational structure has several numerically favorable characteristics (sparse, local, and parallel), and thus permits an efficient engineering implementation. We show results of the control law tested on an indoor helicopter platform.

Resource optimisation in a wireless sensor network with guaranteed estimator performance

Abstract: New control paradigms are needed for large networks of wireless sensors and actuators in order to efficiently utilise system resources. In this study, the authors consider the problem of discrete-time state estimation over a wireless sensor network. Given a tree that represents the sensor communications with the fusion centre, the authors derive the optimal estimation algorithm at the fusion centre, and provide a closed-form expression for the steady-state error covariance matrix. They then present a tree reconfiguration algorithm that produces a sensor tree that has low overall energy consumption and guarantees a desired level of estimation quality at the fusion centre. The authors further propose a sensor tree construction and scheduling algorithm that leads to a longer network lifetime than the tree reconfiguration algorithm. Examples are provided throughout the paper to demonstrate the algorithms and theory developed.

Limits on the network sensitivity function for homogeneous multi-agent systems on a graph

Abstract: This paper explores some tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of Mason's direct rule. An analysis of the role of cycles shows that these structures influence and considerably limit the behavior of the system. We also derive a networked version of Bode's integral formula, showing that it still holds for multi-agent systems.

Experimental demonstration of the dynamics and stability of a low Reynolds number swimmer near a plane wall

Abstract: The motion of microorganisms as well as of tiny robotic swimmers for biomedical applications is governed by low Reynolds number (Re) hydrodynamics, where viscous effects dominate and inertial effects are negligible. This paper presents experimental results that verify theoretical predictions of our recent work which analyzed the dynamics and stability of a low-Re swimmer near a plane wall. The experimental setup uses macro-scale swimmer prototypes which are propelled by rotating cylinders in highly viscous silicone oil. The motion is recorded by a video camera and position measurements are taken by an optical tracking system. The results show good qualitative agreement with our recent theoretical predictions.

Simple delay-based implementation of continuous-time controllers

Abstract: The objective of this work is to study the benefits that delay can provide in simplifying the control process of large-scale systems, motivated by the availability of different types of delays in man-made and biological systems. We show that a continuous-time linear time-invariant (LTI) controller can be approximated by a simple controller that mainly uses delay blocks instead of integrators. More specifically, three methods are proposed to approximate a pre-designed stabilizing LTI controller arbitrarily precisely by a simple delay-based controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the developed approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then addressed.

Reply to “Comments on “Consensus and Cooperation in Networked Multi-Agent Systems””

Abstract: There are essentially four points that Dr. Chebotarev's raises in [1]. Point 1. Chebotarev claims that Lemma 2 is not correct as stated and gives a counter example consisting of a simple directed tree. This counterexample points out two issues with the lemma as stated. The second portion of Lemma 2, referring to the case in which there are c components, only applies to graphs in which there are disjoint components of the graph (no edges between the components). This is clear from the proof of this fact (which simply consists of separating the nodes so that the Laplacian is block diagonal, implying a disjoint set of nodes), but is ambiguous in the statement of the lemma.

Conguration controllability of simple mechanical control systems

Abstract: In this paper we present a denition of \conguration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is derived. This condition involves an object which we call the symmetric product. Of particular interest is a denition of \equilibrium controllability" for which we are able to derive computable sucient conditions. Examples illustrate the theory.

Delay-Based Controller Design for Continuous-Time and Hybrid Applications

Abstract: Motivated by the availability of different types of delays in embedded systems and biological circuits, the objective of this work is to study the benefits that delay can provide in simplifying the implementation of controllers for continuous-time systems. Given a continuous-time linear time-invariant (LTI) controller, we propose three methods to approximate this controller arbitrarily precisely by a simple controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then investigated. We also study the design of an LTI continuous-time controller satisfying given control objectives whose delay-based implementation needs the least number of delay blocks. A direct application of this work is in the sampled-data control of a real-time embedded system, where the sampling frequency is relatively high and/or the output of the system is sampled irregularly. Based on our results on delay-based controller design, we propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. Unlike a typical sampled-data controller, the hybrid controller introduced here -— consisting of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback -— is robust to sampling jitter and can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation.

Quantification and Minimization of Crosstalk Sensitivity in Networks

Abstract: Crosstalk is defined as the set of unwanted interactions among the different entities of a network. Crosstalk is present in various degrees in every system where information is transmitted through a means that is accessible by all the individual units of the network. Using concepts from graph theory, we introduce a quantifiable measure for sensitivity to crosstalk, and analytically derive the structure of the networks in which it is minimized. It is shown that networks with an inhomogeneous degree distribution are more robust to crosstalk than corresponding homogeneous networks. We provide a method to construct the graph with the minimum possible sensitivity to crosstalk, given its order and size. Finally, for networks with a fixed degree sequence, we present an algorithm to find the optimal interconnection structure among their vertices.

Simple condition for stability of systems interconnected over networks

Abstract: In this paper, analysis of dynamical systems interconnected over networks is considered. A framework for the analysis of the stability of interconnection is given. Previous results that studies the single-input/single-output case for a constant interconnection matrix are generalised to the multi-input/multi-output case where arbitrary dynamic interconnection is allowed. The analysis shows existence of a separation principle that is very useful in the sense of the simplicity for stability analysis. Stability can be checked graphically using a Nyquist-like criterion. The problem with time-delays and interconnection variation and robustness appear to be natural special cases.

Tuning a synthetic in vitro oscillator using control-theoretic tools

Abstract: This paper demonstrates the effectiveness of simple control-theoretic tools in generating simulation-guided experiments on a synthetic in vitro oscillator. A theoretical analysis of the behavior of such system is motivated by high cost, time consuming experiments, together with the excessive number of tuning parameters. A simplified model of the synthetic oscillator is chosen to capture only its essential features. The model is analyzed using the small gain theorem and the theory of describing functions. Such analysis reveals what are the parameters that primarily determine when the system can admit stable oscillations. Experimental verification of the theoretical and numerical findings is carried out and confirms the predicted results regarding the role of production and degradation rates.

Synthesis of embedded control systems with high sampling frequencies

Abstract: Motivated by current technological advances in the design of real-time embedded systems, this work deals with the digital control of a continuous-time linear time-invariant (LTI) system whose output can be sampled at a high frequency. Since a typical sampled-data controller operating at a high sampling frequency needs heavy (high-precision) computation to alleviate its sensitivity to measurement and computational errors, the objective is to design a robust hybrid controller for high-frequency applications with limited computational power. To this end, we exploit our recent results on delay-based controller design and propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. This robust hybrid controller, which consists of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback, can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation. We also discuss how to find a continuous-time LTI controller satisfying prescribed design specifications so that its corresponding digital controller requires the least processing time.

Simple Delay-Based Controller Design

Abstract: The objective of this work is to study the benefits that delay can provide in simplifying the control process of large- scale systems, motivated by the availability of different types of delays in man-made and biological systems. We show that a continuous-time linear time-invariant (LTI) controller can be approximated by a simple controller that mainly uses delay blocks instead of integrators. More specifically, three methods are proposed to approximate a pre-designed stabilizing LTI controller arbitrarily precisely by a simple delay-based controller composed of delay blocks, at most two integrators and possibly a unity feedback. Different problems associated with the developed approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then addressed.

Specification, Design and Verification of Distributed Embedded Systems

Abstract: We are investigating the specification, design and verification of distributed systems that combine communications, computation and control in dynamic, uncertain and adversarial environments. Our goal is to develop methods and tools for designing control policies, specifying the properties of the resulting distributed embedded system and the physical environment, and proving that the specifications are met. Accomplishments in this project over the last year include the development of new methods for synthesizing control protocols from linear temporal logic specifications, development of a framework to reason about information flow in terms of partially ordered sets (posets) and the development of a compositional framework for programming stochastically interacting robots.