Search by property

This page provides a simple browsing interface for finding entities described by a property and a named value. Other available search interfaces include the page property search, and the ask query builder.

List of results

• Grasping with flexible fingers presents an … Grasping with flexible fingers presents an attractive approach for</br>certain robotic tasks. Its implementation requires simultaneous</br>position and force control of flexible manipulators, an area about</br>which there is little information in the literature. This paper</br>presents an initial effort at designing controllers for flexible link</br>robots to control both position and force. The analysis is done on a</br>two degree-of-freedom two-link manipulator with the last link</br>flexible. A control strategy is proposed and asymptotic stability is</br>proved. Results from using this control law in simulations and on an</br>experimental setup are presented.nd on an experimental setup are presented.  +
• How does one evaluate the performance of a … How does one evaluate the performance of a stochastic system in the absence of a perfect model (i.e. probability distribution)? We address this question under the framework of optimal uncertainty quantification (OUQ), which is an information-based approach for worst-case analysis of stochastic systems. We are able to generalize previous results and show that the OUQ problem can be solved using convex optimization when the function under evaluation can be expressed in a polytopic canonical form (PCF). We also propose iterative methods for scaling the convex formulation to larger systems. As an application, we study the problem of storage placement in power grids with renewable generation. Numerical simulation results for simple artificial examples as well as an example using the IEEE 14-bus test case with real wind generation data are presented to demonstrate the usage of OUQ analysis. to demonstrate the usage of OUQ analysis.  +
• Ideal cell-free expression systems can the … Ideal cell-free expression systems can theoretically emulate an in vivo cellular environment in a controlled in vitro platform. This is useful for expressing proteins and genetic circuits in a controlled manner as well as for providing a prototyping environment for synthetic biology. To achieve the latter goal, cell-free expression systems that preserve endogenous Escherichia coli transcription-translation mechanisms are able to more accurately reflect in vivo cellular dynamics than those based on T7 RNA polymerase transcription. We describe the preparation and execution of an efficient endogenous E. coli based transcription-translation (TX-TL) cell-free expression system that can produce equivalent amounts of protein as T7-based systems at a 98% cost reduction to similar commercial systems. The preparation of buffers and crude cell extract are described, as well as the execution of a three tube TX-TL reaction. The entire protocol takes five days to prepare and yields enough material for up to 3000 single reactions in one preparation. Once prepared, each reaction takes under 8 hr from setup to data collection and analysis. Mechanisms of regulation and transcription exogenous to E. coli, such as lac/tet repressors and T7 RNA polymerase, can be supplemented.6 Endogenous properties, such as mRNA and DNA degradation rates, can also be adjusted.7 The TX-TL cell-free expression system has been demonstrated for large-scale circuit assembly, exploring biological phenomena, and expression of proteins under both T7- and endogenous promoters. Accompanying mathematical models are available. The resulting system has unique applications in synthetic biology as a prototyping environment, or "TX-TL biomolecular breadboard."nment, or "TX-TL biomolecular breadboard."  +
• In a complex real-time operating environme … 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.way platform with an external disturbance.  +
• In an aircraft electric power system, one … In an aircraft electric power system, one or more supervisory control units actuate a set of electromechanical switches to dynamically distribute power from generators to loads, while satisfying safety, reliability, and real-time performance requirements. To reduce expensive redesign steps, this control problem is generally addressed by minor incremental changes on top of consolidated solutions. A more systematic approach is hindered by a lack of rigorous design methodologies that allow estimating the impact of earlier design decisions on the final implementation. To achieve an optimal implementation that satisfies a set of requirements, we propose a platform-based methodology for electric power system design, which enables independent implementation of system topology (i.e., interconnection among elements) and control protocol by using a compositional approach. In our flow, design space exploration is carried out as a sequence of refinement steps from the initial specification toward a final implementation by mapping higher level behavioral and performance models into a set of either existing or virtual library components at the lower level of abstraction. Specifications are first expressed using the formalisms of linear temporal logic, signal temporal logic, and arithmetic constraints on Boolean variables. To reason about different requirements, we use specialized analysis and synthesis frameworks and formulate assume guarantee contracts at the articulation points in the design flow. We show the effectiveness of our approach on a proof-of-concept electric power system design.f-of-concept electric power system design.  +
• In many autonomy applications, performance … 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.lysis that incorporates perception models.  +
• In mobile sensor networks, sensor measurem … In mobile sensor networks, sensor measurements</br>as well as control commands are transmitted over</br>wireless time-varying links. It then becomes considerably</br>important to address the impact of imperfect communication</br>on the overall performance. In this paper, we</br>study the effect of time-varying communication links on</br>the control performance of a mobile sensor node. In</br>particular, we investigate the impact of fading. We derive</br>key performance measure parameters to evaluate the</br>overall feedback control performance over narrowband</br>channels. We show that fading can result in considerable</br>delay and/or poor performance of the mobile sensor</br>depending on the system requirements. To improve the</br>performance, we then show how the application layer can</br>use the channel status information of the physical layer</br>to adapt control commands accordingly. We show that</br>sharing information across layers can improve the overall</br>performance considerably. We verify our analytical</br>results by simulating a wireless speed control problem.mulating a wireless speed control problem.  +
• In multicellular organisms, cells actively … In multicellular organisms, cells actively sense, respond to, and control their own population density. Synthetic mammalian quorum sensing circuits could provide insight into principles of population control and improve cell therapies. However, a key challenge is avoiding their inherent sensitivity to “cheater” mutations that evade control. Here, we repurposed the plant hormone auxin to enable orthogonal mammalian cell-cell communication and quorum sensing. Further, we show that a “paradoxical” circuit design, in which auxin stimulates and inhibits net cell growth at different concentrations, achieves population control that is robust to cheater mutations, controlling growth for 43 days of continuous culture. By contrast, a non-paradoxical control circuit limited growth but was susceptible to mutations. These results establish a foundation for future cell therapies that can respond to and control their own population sizes.to and control their own population sizes.  +
• In recent years, numerous distributed algo … In recent years, numerous distributed algorithms </br>have been proposed which, when executed by a team of </br>dynamic agents, result in the completion of a joint task. </br>However, for any such algorithm to be practical, one should be </br>able to guarantee that the task is still satisfactorily executed </br>even when agents fail to communicate with others or to </br>perform their designated actions correctly. In this paper, </br>we present a concept of robustness which is well-suited for </br>general distributed algorithms for teams of dynamic agents. </br>Our definition extends a similar notion introduced in the </br>distributed computation literature for consensus problems. We </br>illustrate the definition by considering a variety of algorithms.on by considering a variety of algorithms.  +
• In robotic finger gaiting, fingers continu … 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.demonstrate the benefits of this approach.  +
• In systems and synthetic biology, it is co … In systems and synthetic biology, it is common to build chemical reaction network (CRN) models of biochemical circuits and networks. Although automation and other high-throughput techniques have led to an abundance of data enabling data-driven quantitative modeling and parameter estimation, the intense amount of simulation needed for these methods still frequently results in a computational bottleneck. Here we present bioscrape (Bio-circuit Stochastic Single-cell Reaction Analysis and Parameter Estimation) - a Python package for fast and flexible modeling and simulation of highly customizable chemical reaction networks. Specifically, bioscrape supports deterministic and stochastic simulations, which can incorporate delay, cell growth, and cell division. All functionalities - reaction models, simulation algorithms, cell growth models, partitioning models, and Bayesian inference - are implemented as interfaces in an easily extensible and modular object-oriented framework. Models can be constructed via Systems Biology Markup Language (SBML) or specified programmatically via a Python API. Simulation run times obtained with the package are comparable to those obtained using C code - this is particularly advantageous for computationally expensive applications such as Bayesian inference or simulation of cell lineages. We show the package’s simulation capabilities on a variety of example simulations of stochastic gene expression. We also demonstrate the package by using it to do parameter inference on a model of integrase enzyme-mediated DNA recombination dynamics with experimental data. The bioscrape package is publicly available online (Pandey, Poole, et al., 2023) along with more detailed documentation and examples. more detailed documentation and examples.  +
• In the geometric theory of nonlinear contr … In the geometric theory of nonlinear control systems, the notion of a distribution and</br>the dual notion of codistribution play a central role. Many results in nonlinear control</br>theory require certain distributions to be integrable. Distributions (and codistributions)</br>are not generically integrable and, moreover, the integrability property is not likely to</br>persist under small perturbations of the system. Therefore, it is natural to consider the</br>problem of approximating a given codistribution by an integrable codistribution, and to</br>determine to what extent such an approximation may be used for obtaining approximate</br>solutions to various problems in control theory. In this note, we concentrate on the</br>purely mathematical problem of approximating a given codistribution by an integrable</br>codistribution. We present an algorithm for approximating an m-dimensional nonintegrable</br>codistribution by an integrable one using a homotopy approach. The method yields an</br>approximating codistribution that agrees with the original codistribution on an</br>m-dimensional submanifold E_0 of R^n.n an m-dimensional submanifold E_0 of R^n.  +
• In the problem of bootstrapping, an agent … In the problem of bootstrapping, an agent must learn to use an unknown body, in an unknown world, starting from zero information about the world, its sensors, and its actuators. So far, this fascinating problem has not been given a proper formalization. In this paepr, we provide a possible rigorous definition of one of the key aspects of bootstrapping, namely the fact that an agent must be able to use âuninterpretedâ observations and commands. We show that this can be formalized by positing the existence of representation nuisances that act on the data, and which must be tolerated by an agent. The classes of nuisances tolerated indirectly encode the assumptions needed about the world, and therefore the agent's ability to solve smaller or larger classes of bootstrapping instances. Moreover, we argue that the behavior of an agent that claims optimality must actually be invariant to the representation nuisances, and we discuss several design principles to obtain such invariance.sign principles to obtain such invariance.  +
• In this article is presented a dynamical s … In this article is presented a dynamical systems framework for analysing multi-agent rendezvous problems and characterize the dynamical behaviour of the collective system. Recently, the problem of rendezvous has been addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of the problem. The proposed approach is based on the set invariance theory and focusses on how to generate feedback between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions of the agents and the dynamics is modelled as linear first-order systems. These algorithms have also been applied to non-linear first-order systems.</br></br>The rendezvous problem in the framework of cooperative and competitive dynamical systems is analysed that has had some remarkable applications to biological sciences. Cooperative and competitive dynamical systems are shown to generate monotone flows by the classical Muller--Kamke theorem, which is analysed using the set invariance theory. In this article, equivalence between the rendezvous problem and invariance of an appropriately defined cone is established. The problem of rendezvous is cast as a stabilization problem, with a the set of constraints on the trajectories of the agents defined on the phase plane. The n-agent rendezvous problem is formulated as an ellipsoidal cone invariance problem in the n-dimensional phase space. Theoretical results based on set invariance theory and monotone dynamical systems are developed. The necessary and sufficient conditions for rendezvous of linear systems are presented in the form of linear matrix inequalities. These conditions are also interpreted in the Lyapunov framework using multiple Lyapunov functions. Numerical examples that demonstrate application are also presented.emonstrate application are also presented.  +
• In this chapter, we present a framework fo … In this chapter, we present a framework for online control customization that</br>makes use of finite-horizon, optimal control combined with real-time</br>trajectory generation and optimization. The results are based on a novel</br>formulation of receding-horizon optimal control that replaces the traditional</br>terminal constraints with a control Lyapunov function-based terminal cost.</br>This formulation leads to reduced computational requirements and allows proof</br>of stability under a variety of realistic assumptions on computation. By</br>combining these theoretical advances with advances in computational power for</br>real-time, embedded systems, we demonstrate the efficacy of online control</br>customization via optimization-based control. The results are demonstrated</br>using a nonlinear, flight control experiment at Caltech.ear, flight control experiment at Caltech.  +
• In this letter we present a decomposition … In this letter we present a decomposition for control systems whose drift vector field</br>is the geodesic spray associated with an affine connection. With the geometric insight</br>gained with this decomposition, we are able to easily prove some special results for this</br>class of control systems. Examples illustrate the theory.l systems. Examples illustrate the theory.  +
• In this note we consider the following pro … In this note we consider the following problem. Suppose a set of sensors is jointly trying to estimate a process. One sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors. What is the sensor schedule that results in the mininmum error covariance? We describe a stoachastic sensor selection strategy that is easy to implement and is computationally tractable. The problem described above comes up in many domains out of which we discuss two. In the sensor selection problem, there are multiple sensors that cannot operate simultaneously (eg, sonars in the same frequency band). Thus measurements need to be scheduled. In the sensor coverage problem, a geographical area needs to be covered by mobile sensors each with limited range. Thus from every position, the sensors obtain a different viewpoint of the area and the sensors need to optimize their positions. The algorithm is applied to these problems and illustrated through simple examples.s and illustrated through simple examples.  +
• In this paper analysis of interconnected d … In this paper analysis of interconnected dynamical systems</br>is considered. A framework for the analysis of the stability</br>of interconnection is given. The results from Fax and</br>Murray that studies the SISO-case for a constant interconnection</br>matrix are genralized to the MIMO-case where</br>arbitrary interconnection is allowed. The analysis show existness</br>of a separation principle that is very useful in the</br>sense of the simplicity for stability analysis. Stability could</br>be checked graphically using a Nyquist-like criterion. The</br>problem with time-delays and interconnection variation and</br>robustness appear to be natural special cases of the general</br>framework, and hence, simple stability criteria are derived</br>easly.mple stability criteria are derived easly.  +
• In this paper various design techniques ar … In this paper various design techniques are applied to the trajectory tracking problem for a mobile</br>robot with trailers. Using simulations and experiments, we evaluate linear and nonlinear designs</br>on the basis of implementation issues, stability and performance. After a careful design of their</br>gains, the various feedback controllers have very close performance measures. In both the</br>simulations and the experiments, all the controllers show a strong dependence on the knowledge</br>of the reference trajectory. The flatness of the system is exploited in precomputing this quantity.s exploited in precomputing this quantity.  +
• In this paper we analyze the effects of fl … In this paper we analyze the effects of fluid noise, actuator bandwidth,</br>magnitude saturation and rate limits on rotating stall control by</br>studying a two dimensional system which is the approximation</br>of the dynamics on the attracting saddle-sink connections of the three</br>state low $B$ parameter Moore Greitzer model together with the</br>dynamics of the bleed valve controller. We show that the region of</br>attraction to the stabilized rotating stall </br>equilibria is seriously restrained by the fluid noise level, the</br>actuator bandwidth, magnitude saturation and rate limits. The</br>bandwidth and rate requirement for a fixed extension of stable region</br>is estimated by calculating the stable manifold of the saddle fixed</br>point of the two dimensional system.fixed point of the two dimensional system.  +
• In this paper we apply some recently devel … In this paper we apply some recently developed control laws for</br>stabilization of mechanical systems with nonholonomic constraints to</br>an experimental system consisting of a mobile robot towing a trailer.</br>We verify the applicability of various control laws which have</br>appeared in the recent literature, and compare the performance of</br>these controllers in an experimental setting. In particular, we show</br>that time-periodic, non-smooth controllers can be used to achieve</br>exponential stability of a desired equilibrium configuration, and that</br>these controllers outperform smooth, time-varying control laws. We</br>also point out several practical considerations which must be taken</br>into account when implementing these controllers.count when implementing these controllers.  +
• In this paper we are concerned with the ch … In this paper we are concerned with the challenge of flight control of computationally-constrained micro-aerial vehicles that must rely primarily on vision to navigate confined spaces. We turn to insects for inspiration. We demonstrate that it is possible to control a robot with inertial, flight-like dynamics in the plane using insect-inspired visual autocorrelators or âelementary motion detectorsâ (EMDs) to detect patterns of visual optic flow. The controller, which requires minimal computation, receives visual information from a small omnidirectional array of visual sensors and computes thrust outputs for a fan pair to stabilize motion along the centerline of a corridor. To design the controller, we provide a frequency- domain analysis of the response of an array of correlators to a flat moving wall. The model incorporates the effects of motion parallax and perspective and provides a means for computing appropriate inter-sensor angular spacing and visual blurring. The controller estimates the state of robot motion by decomposing the correlator response into harmonics, an analogous operation to that performed by tangential cells in the fly. This work constitutes the first-known demonstration of control of non-kinematic inertial dynamics using purely correlators.nertial dynamics using purely correlators.  +
• In this paper we characterize the impact o … In this paper we characterize the impact of imperfect communication</br>on the performance of a decentralized mobile sensor network.</br>We first examine and demonstrate the trade-offs between communication</br>and sensing objectives, by determining the optimal sensor configurations</br>when introducing imperfect communication. We further illustrate the</br>performance degradation caused by non-ideal communication links in</br>a decentralized mobile sensor network. To address this, we propose a</br>decentralized motion-planning algorithm that considers communication</br>effects. The algorithm is a cross-layer design based on the proper interface</br>of physical and application layers. Simulation results will show the</br>performance improvement attained by utilizing this algorithm.ment attained by utilizing this algorithm.  +
• In this paper we consider a state estimati … In this paper we consider a state estimation problem over a wireless sensor network. A fusion center dynamically forms a local multi-hop tree of sensors and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. Using estimation quality as a metric, two communication schemes are studied and compared. In scheme one, sensor nodes communicate measurement data to their parent nodes, while in scheme two, sensor nodes communicate their local state estimates to their parent nodes. We show that under perfect communication links, the two schemes produce the same estimate at the fusion center with unlimited computation at each sensor node; scheme one is always better than scheme two with limited computation. When data packet drops occur on the communication links, we show that scheme two always outperforms scheme one with unlimited computation; with limited computation, we show that there exists a critical packet arrival rate, above which, scheme one outperforms scheme two. Simulations are provided to demonstrate the two schemes under various circumstances.e two schemes under various circumstances.  +
• In this paper we consider nonlinear system … In this paper we consider nonlinear systems with steady-state or Hopf bifurcations for</br>which the bifurcated modes are linearly uncontrollable. The goal is to find state</br>feedbacks such that the bifurcation for the closed loop system is supercritical, and at</br>the same time, the linearly controllable subsystem is asymptotically stable. Necessary and</br>sufficient conditions for the non-existence of sufficiently smooth state feedbacks have</br>been obtained under certain nondegeneracy conditions. For the cases when those conditions</br>are not satisfied, we give explicit constructions of the feedbacks. The construction has</br>the following separation property: for any linear state feedback such that the</br>controllable subsystem is asymptotically stable, we could construct gains in the nonlinear</br>state feedbacks such that the closed loop system is asymptotically stable at the</br>bifurcation point.totically stable at the bifurcation point.  +
• In this paper we consider state estimation … In this paper we consider state estimation carried over a sensor network. A fusion center forms a local multi-hop tree of sensors and gateways and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. The number of hops that the sensors use to communicate data with the fusion center is optimized such that either the overall transmission energy is minimized or the network lifetime is maximized. In both cases the fusion center provides a specified level of estimation accuracy. Some heuristic algorithms are proposed which lead to suboptimal solutions in the energy minimization problem, while an algorithm that leads to the global optimal solution is proposed in the lifetime maximization problem. In both cases, the algorithms are shown to have low computational complexity. Examples are provided to demonstrateand algorithms.are provided to demonstrateand algorithms.  +
• In this paper we consider task scheduling … In this paper we consider task scheduling when</br>sensing and controlling over a network with packet dropping</br>links. We find optimum ways of allocating limited computing</br>resources for estimation and control of a number</br>of linear dynamical systems with different characteristics</br>over communication links with different qualities. We find</br>theoretical expressions relating the optimum sampling rates to</br>the characteristics of the communication links and dynamics of</br>the plants.When considering resource allocation for estimation</br>of the plants, we derive optimum ways of task scheduling for</br>two performance metrics: decay rate and the asymptotic value</br>of the estimation error variance. When scheduling the control</br>tasks, we consider rate of convergence of the state and the</br>overall control cost as performance measures. The work lays</br>the theoretical foundations for considering the impact of both</br>limited computing and communication resources on estimation</br>and control.ation resources on estimation and control.  +
• In this paper we consider the impact of co … In this paper we consider the impact of communication noise on distributed sensing and estimation in mobile networks. We characterize when a node should rely on getting information from others and when it should rely on self exploration. In doing so, we explore the trade-offs between sensing and communication by finding the optimum network configuration under communication constraints. We also show how to achieve the optimum configuration in a distributed manner. While our main results are presented in one dimension (1D), we provide insight into the two dimension (2D) setup and extend a number of key results to 2D. and extend a number of key results to 2D.  +
• In this paper we consider the problem of e … In this paper we consider the problem of estimating discrete</br>variables in a class of hybrid systems where we assume that the continuous</br>variables are available for measurement. Using lattice and order</br>theory we develop a framework for constructing an observer on an enlarged</br>space of variables with lattice structure, which updates only two</br>variables at each step. We apply our ideas to a multi-robot system example,</br>the RoboFlag Drill.-robot system example, the RoboFlag Drill.  +
• In this paper we consider the problem of g … In this paper we consider the problem of generating feasible motions</br>for a towed cable, flight control system that has been proposed for</br>use in remote sensor applications. Using the fact that the system is</br>differentially flat, we illustrate how to construct feasible</br>trajectories for the system and demonstrate the strengths and</br>limitations of this approach. Simulations of the full dynamics are</br>included to illustrate the proposed techniques. A significant</br>limitation of the current approach is the numerical instability of the</br>algorithm, resulting in the need for careful tuning of parameters to</br>achieve convergence.ning of parameters to achieve convergence.  +
• In this paper we consider the problem of n … In this paper we consider the problem of network reconstruction, with applications to biochemical reaction networks. In particular, we consider the problem of global network reconstruction when there are a limited number of sensors that can be used to simultaneously measure state information. We introduce dynamical structure functions as a way to formulate the network reconstruction problem and motivate their usage with an example physical system from synthetic biology. In particular, we argue that in synthetic biology research, network verification is paramount to robust circuit operation and thus, network reconstruction is an invaluable tool. Nonetheless, we argue that existing approaches for reconstruction are hampered by limited numbers of biological sensors with high temporal resolution. In this way, we motivate the global network reconstruction problem using partial network information and prove that by performing a series of reconstruction experiments, where each experiment reconstructs a subnetwork dynamical structure function, the global dynamical structure function can be recovered in most cases. We illustrate these reconstruction techniques on a recently developed four gene biocircuit, an event detector, and show that it is capable of differentiating the temporal order of input events.iating the temporal order of input events.  +
• In this paper we consider the problem of r … In this paper we consider the problem of repre- senting a biological system and its environment using a stochas- tic modeling framework. We first introduce a decomposition of the global chemical reaction system into two systems: a system of interest and its environment. We then present and derive a decomposition of the chemical master equation to achieve a representation describing the dynamics of the system of inter- est, perturbed by an environmental disturbance. We use this decomposition to model examples of two types of environmental disturbances: the disturbance a system experiences through loading effects from limited resources and the disturbance a system experiences when perturbed by an antibiotic that modifies transcription or translation rates.difies transcription or translation rates.  +
• In this paper we describe the response of … In this paper we describe the response of a Kinetic Monte Carlo model to </br>time-varying growth conditions. We vary temperature and partial pressure </br>sinusoidally and identify behavior typical of low-dimensional nonlinear </br>systems. In particular, the frequency content of the roughness response is </br>sensitive to the presence of steps in the surface.e to the presence of steps in the surface.  +
• In this paper we discuss a resilient, risk … In this paper we discuss a resilient, risk-aware software architecture for onboard, real-time autonomous operations that is intended to robustly handle uncertainty in space- craft behavior within hazardous and unconstrained environ- ments, without unnecessarily increasing complexity. This architecture, the Resilient Spacecraft Executive (RSE), serves three main functions: (1) adapting to component failures to allow graceful degradation, (2) accommodating environments, science observations, and spacecraft capabilities that are not fully known in advance, and (3) making risk-aware decisions without waiting for slow ground-based reactions. This RSE is made up of four main parts: deliberative, habitual, and reflexive layers, and a state estimator that interfaces with all three. We use a risk-aware goal-directed executive within the deliberative layer to perform risk-informed planning, to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Other state-of-the-art algorithms to be integrated into the RSE include correct-by-construction control synthesis and model-based estimation and diagnosis. We demonstrate the feasibility of the architecture in a simple implementation of the RSE for a simulated Mars rover scenario.e RSE for a simulated Mars rover scenario.  +
• In this paper we discuss the application o … In this paper we discuss the application of correct-by-construction techniques to a resilient, risk-aware software architecture for onboard, real-time autonomous operations. We mean to combat complexity and the accidental introduction of bugs through the use of verifiable auto-coding software and correct-by-construction techniques, and discuss the use of a toolbox for correct-by-construction Temporal Logic Planning (TuLiP) for such a purpose. We describe some of TuLiPâs current functionality, specifically its ability to model symbolic discrete systems and synthesize software controllers and control policies that are correct-by-construction. We then move on to discuss the use of these techniques to define a deliberative goal-directed executive capability that performs risk-informed action-planning â to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Finally, we discuss an application of the TuLiP process to a simple rover resilience scenario.ess to a simple rover resilience scenario.  +
• In this paper we evaluate the actuator rat … In this paper we evaluate the actuator rate requirements for control of rotating stall</br>using a bleed valve and provide tools for predicting these requirements. Modification of</br>both the stable and unstable parts of the compressor characteristic via addition of</br>continuous air injection serves to reduce the requirement of a bleed valve used for the</br>purpose of rotating stall stabilization. Analytical tools based on low order models (2-3</br>states) and simulation tools based on a reduced order model (37 states) are described. A</br>bleed actuator rate limit study is presented to compare the actuator requirements</br>predicted by theory, simulation, and experiment. The comparisons show that the predictions</br>obtained from theory and simulations share the same trend as the experiments, with</br>increasing accuracy as the complexity of the underlying model increases. Some insights on</br>the design of a bleed-compressor pair are given.sign of a bleed-compressor pair are given.  +
• In this paper we explore the use of time-d … In this paper we explore the use of time-delayed differential equation as a means of obtaining a simplified description of very high order dynamics.This paper finds results for a particular type of system, a single-input single-output (SISO) linear system with a nonlinear feedback. We begin with a high dimensional system in state space and reduce the dimension by finding a delay based approximation which could be a smaller set of integro-differential equations or DDEs. We argue that approximations of high order linear subsystems whose distribution functions have relatively smaller variance such as delta functions, give a conservative approximation of a system's stable parameter space. Through examples inspired by biology, we show how these approximations can be used to verify stability. We analyze the system's stability and robustness dependence on statistical properties, mainly relative variance and expectation for a symmetric distribution function.ion for a symmetric distribution function.  +
• In this paper we give a formulation of dif … In this paper we give a formulation of differential flatness---a concept originally</br>introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence</br>between exterior differential systems. Systems which are differentially flat have several</br>useful properties which can be exploited to generate effective control strategies for</br>nonlinear systems. The original definition of flatness was given in the context of</br>differentiable algebra, and required that all mappings be meromorphic functions. Our</br>formulation of flatness does not require any algebraic structure and allows one to use</br>tools from exterior differential systems to help characterize differentially flat systems.</br>In particular, we shown that in the case of single input control systems (i.e.,</br>codimension 2 Pfaffian systems), a system is differentially flat if and only if it is</br>feedback linearizable via static state feedback. However, in higher codimensions feedback</br>linearizability and flatness are *not* equivalent: one must be careful with the role of</br>time as well the use of prolongations which may not be realizable as dynamic feedbacks in</br>a control setting. Applications of differential flatness to nonlinear control systems and</br>open questions will be discussed.tems and open questions will be discussed.  +
• In this paper we introduce the Caltech Mul … In this paper we introduce the Caltech</br>Multi-Vehicle Wireless Testbed (MVWT), a platform for testing</br>decentralized control methodologies for multiple vehicle</br>coordination and formation stabilization. The testbed consists of</br>eight mobile vehicles, an overhead vision system providing</br>GPS-like position information and wireless Ethernet for</br>communications. Each vehicle rests on omni-direction casters and</br>is powered by two high-performance ducted fans. Thus, a unique</br>feature of our testbed is that the vehicles have second order</br>dynamics, requiring real-time feedback algorithms to stabilize the</br>system while performing cooperative tasks. The testbed will be</br>used by various research groups at Caltech and elsewhere as a</br>means to validate theoretical advances in multiple-vehicle</br>coordination and control, networked control systems, real time</br>networking and high confidence distributed computation.d high confidence distributed computation.  +
• In this paper we investigate methods for s … In this paper we investigate methods for steering systems with nonholonomic</br>constraints between arbitrary configurations. Early work by Brockett derives the optimal</br>controls for a set of canonical systems in which the tangent space to the configuration</br>manifold is spanned by the input vector fields and their first order Lie brackets. Using</br>Brockett's result as motivation, we derive suboptimal trajectories for systems which are</br>not in canonical form and consider systems in which it takes more than one level of</br>bracketing to achieve controllability. These trajectories use sinusoids at integrally</br>related frequencies to achieve motion at a given bracketing level. We define a class of</br>systems which can be steered using sinusoids (chained systems) and give conditions under</br>which a class of two-input systems can be converted into this form.t systems can be converted into this form.  +
• In this paper we investigate the optimal c … In this paper we investigate the optimal control of affine connection</br>control systems. The formalism of the affine connection can be used to</br>describe geometrically the dynamics of me chanical systems, including those</br>with nonholonomic constraints. In the standard variational approach to such</br>problems, one converts an n dimensional second order system into a 2n</br>dimensional first order system, and uses these equations as constraints on</br>the optimization. An alternative approach, which we develop in this paper,</br>is to include the system dynamics as second order constraints of the</br>optimization, and optimize relative to variations in the configuration</br>space. Using the affine connection, its associated tensors, and the notion</br>of covariant differentiation, we show how variations in the configuration</br>space induce variations in the tangent space. In this setting, we derive</br>second order equations have a geometric formulation parallel to that of the</br>system dynamics. They also specialize to results found in the literature.ialize to results found in the literature.  +
• In this paper we look at the problem of mu … In this paper we look at the problem of multi-sensor data fusion when data is being communicated over </br>channels that drop packets randomly. We are motivated by </br>the use of wireless links for communication among nodes in </br>upcoming sensor networks. We wish to identify the information that should be communicated by each node to others given </br>that some of the information it had transmitted earlier might </br>have been lost. We solve the problem exactly for the case </br>of two sensors and study the performance of the algorithm </br>when more sensors are present. For the two-sensor case, the </br>performance of our algorithm is optimal in the sense that if </br>a packet is received from the other sensor, it is equivalent to </br>receiving all previous measurements, irrespective of the packet </br>drop pattern. irrespective of the packet drop pattern.  +
• In this paper we present a control law for … In this paper we present a control law for globally asymptotically stabilizing a class</br>of controllable nonlinear systems without drift. The control law converts into closed loop</br>feedback earlier strategies for open loop steering of nonholonomic systems using sinusoids</br>at integrally related frequencies. The global result is obtained by introducing saturation</br>functions. Simulation results for stabilizing a simple kinematic model of an automobile</br>are included.matic model of an automobile are included.  +
• In this paper we present a definition of " … In this paper we present a definition of "configuration controllability" for</br>mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric</br>minus potential energy. A computable test for this new version of controllability is also</br>derived. This condition involves a new object which we call the symmetric product. Of</br>particular interest is a definition of "equilibrium controllability" for which</br>we are able to derive computable sufficient conditions. Examples illustrate the theory.onditions. Examples illustrate the theory.  +
• In this paper we present a dynamical syste … In this paper we present a dynamical systems framework for analyzing multi-agent rendezvous problems</br>and characterize the dynamical behavior of the collective system. Recently, the problem of rendezvous has been</br>addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of</br>the problem. The proposed approach is based on set invariance theory and focusses on how to generate feedback</br>between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions</br>of the agents and the dynamics is modeled as linear first order systems. The proposed framework however is not</br>fundamentally limited to linear first order dynamics and can be extended to analyze rendezvous of higher order agents.analyze rendezvous of higher order agents.  +
• In this paper we present a dynamical syste … In this paper we present a dynamical systems representation for multi-agent rendezvous on</br>the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories</br>of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's</br>formula, make sure that the two-agent system attains rendezvous. The main result of this paper</br>is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied</br>are su±cient to guarantee rendezvous.fied are su±cient to guarantee rendezvous.  +
• In this paper we present two methods, the … In this paper we present two methods, the nonholonomic method and the vakonomic</br>method, for deriving equations of motion for a mechanical system with constraints. The</br>resulting equations are compared. Results are also presented from an experiment for a</br>model system: a ball rolling without sliding on a rotating table. Both sets of equations</br>of motion for the model system are compared with the experimental results. The effects of</br>various forms of friction are considered in the nonholonomic equations. With appropriate</br>friction terms, the nonholonomic equations of motion for the model system give reasonable</br>agreement with the experimental observations.eement with the experimental observations.  +
• In this paper we provide new design princi … In this paper we provide new design principles</br>for estimation over wireless fading channels in mobile sensor</br>networks. We show how to optimize receiver and transmitter</br>designs to improve estimation performance in the application</br>layer. On the receiver side, we show that the optimum packet</br>drop mechanism is the one that provides a balance between</br>information loss and communication noise. On the transmitter</br>side, we show how to optimize and adapt the transmission</br>rate for performance improvement in the application layer.</br>We further provide stability conditions for different design</br>strategies. The work confirms that delay-sensitive mobile</br>sensor applications require new design paradigms and applying</br>the same design principles of data networks can lead</br>to performance degradation. The work also highlights the</br>importance of cross-layer feedback and provides alternative</br>designs if such feedbacks are not available.signs if such feedbacks are not available.  +
• In this paper we study the problem of synt … In this paper we study the problem of synthesizing correct-by-construction Behavior Trees (BTs) controlling agents in adversarial environments. The proposed approach combines the modularity and reactivity of BTs with the formal guarantees of Linear Temporal Logic (LTL) methods. Given a set of admissible environment specifications, an agent model in form of a Finite Transition System and the desired task in form of an LTL formula, we synthesize a BT in polynomial time, that is guaranteed to correctly execute the desired task. To illustrate the approach, we present three examples of increasing complexity.t three examples of increasing complexity.  +
• In this paper we study the stabilization p … In this paper we study the stabilization problem for control systems</br>defined on SE(3), the Euclidean group of rigid--body motions.</br>Assuming one actuator is available for each degree of freedom, we</br>exploit geometric properties of Lie groups (and corresponding Lie</br>algebras) to generalize the classical PD control in a coordinate--free</br>way. For the SO(3) case, the compactness of the group gives rise to a</br>natural metric structure and to a natural choice of preferred control</br>direction: an optimal (in the sense of geodesic) solution is given to</br>the attitude control problem. In the SE(3) case, no natural metric is</br>uniquely defined, so that more freedom is left in the control design.</br>Different formulations of PD feedback can be adopted by extending the</br>SO(3) approach to the whole of SE(3) or by breaking the problem into a</br>control problem on SO(3) x R^3. For the simple SE(2) case,</br>simulations are reported to illustrate the behavior of the different</br>choices. Finally, we discuss the trajectory tracking problem and show</br>how to reduce it to a stabilization problem, mimicking the usual</br>approach in R^n.blem, mimicking the usual approach in R^n.  +