Property:Abstract
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G
Grasping with flexible fingers presents an attractive approach for
certain robotic tasks. Its implementation requires simultaneous
position and force control of flexible manipulators, an area about
which there is little information in the literature. This paper
presents an initial effort at designing controllers for flexible link
robots to control both position and force. The analysis is done on a
two degree-of-freedom two-link manipulator with the last link
flexible. A control strategy is proposed and asymptotic stability is
proved. Results from using this control law in simulations and on an
experimental setup are presented. +
C
Convex optimal uncertainty quantification: Algorithms and a case study in energy storage placement for power grids +
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. +
P
Protocols for Implementing an Escherichia coli Based TX-TL Cell-Free Expression System for Synthetic Biology +
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." +
R
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. +
A
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. +
L
Leveraging Classification Metrics for Quantitative System-Level Analysis with Temporal Logic Specifications +
In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models. +
E
In mobile sensor networks, sensor measurements
as well as control commands are transmitted over
wireless time-varying links. It then becomes considerably
important to address the impact of imperfect communication
on the overall performance. In this paper, we
study the effect of time-varying communication links on
the control performance of a mobile sensor node. In
particular, we investigate the impact of fading. We derive
key performance measure parameters to evaluate the
overall feedback control performance over narrowband
channels. We show that fading can result in considerable
delay and/or poor performance of the mobile sensor
depending on the system requirements. To improve the
performance, we then show how the application layer can
use the channel status information of the physical layer
to adapt control commands accordingly. We show that
sharing information across layers can improve the overall
performance considerably. We verify our analytical
results by simulating a wireless speed control problem. +
S
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. +
W
In recent years, numerous distributed algorithms
have been proposed which, when executed by a team of
dynamic agents, result in the completion of a joint task.
However, for any such algorithm to be practical, one should be
able to guarantee that the task is still satisfactorily executed
even when agents fail to communicate with others or to
perform their designated actions correctly. In this paper,
we present a concept of robustness which is well-suited for
general distributed algorithms for teams of dynamic agents.
Our definition extends a similar notion introduced in the
distributed computation literature for consensus problems. We
illustrate the definition by considering a variety of algorithms. +
T
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. +
F
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. +
A
In the geometric theory of nonlinear control systems, the notion of a distribution and
the dual notion of codistribution play a central role. Many results in nonlinear control
theory require certain distributions to be integrable. Distributions (and codistributions)
are not generically integrable and, moreover, the integrability property is not likely to
persist under small perturbations of the system. Therefore, it is natural to consider the
problem of approximating a given codistribution by an integrable codistribution, and to
determine to what extent such an approximation may be used for obtaining approximate
solutions to various problems in control theory. In this note, we concentrate on the
purely mathematical problem of approximating a given codistribution by an integrable
codistribution. We present an algorithm for approximating an m-dimensional nonintegrable
codistribution by an integrable one using a homotopy approach. The method yields an
approximating codistribution that agrees with the original codistribution on an
m-dimensional submanifold E_0 of R^n. +
U
Uncertain semantics, representation nuisances, and necessary invariance properties of bootstrapping agents +
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. +
C
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.
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. +
O
In this chapter, we present a framework for online control customization that
makes use of finite-horizon, optimal control combined with real-time
trajectory generation and optimization. The results are based on a novel
formulation of receding-horizon optimal control that replaces the traditional
terminal constraints with a control Lyapunov function-based terminal cost.
This formulation leads to reduced computational requirements and allows proof
of stability under a variety of realistic assumptions on computation. By
combining these theoretical advances with advances in computational power for
real-time, embedded systems, we demonstrate the efficacy of online control
customization via optimization-based control. The results are demonstrated
using a nonlinear, flight control experiment at Caltech. +
D
In this letter we present a decomposition for control systems whose drift vector field
is the geodesic spray associated with an affine connection. With the geometric insight
gained with this decomposition, we are able to easily prove some special results for this
class of control systems. Examples illustrate the theory. +
O
On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage +
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. +
A
In this paper analysis of interconnected dynamical systems
is considered. A framework for the analysis of the stability
of interconnection is given. The results from Fax and
Murray that studies the SISO-case for a constant interconnection
matrix are genralized to the MIMO-case where
arbitrary interconnection is allowed. The analysis show existness
of a separation principle that is very useful in the
sense of the simplicity for stability analysis. Stability could
be checked graphically using a Nyquist-like criterion. The
problem with time-delays and interconnection variation and
robustness appear to be natural special cases of the general
framework, and hence, simple stability criteria are derived
easly. +
E
In this paper various design techniques are applied to the trajectory tracking problem for a mobile
robot with trailers. Using simulations and experiments, we evaluate linear and nonlinear designs
on the basis of implementation issues, stability and performance. After a careful design of their
gains, the various feedback controllers have very close performance measures. In both the
simulations and the experiments, all the controllers show a strong dependence on the knowledge
of the reference trajectory. The flatness of the system is exploited in precomputing this quantity. +
In this paper we analyze the effects of fluid noise, actuator bandwidth,
magnitude saturation and rate limits on rotating stall control by
studying a two dimensional system which is the approximation
of the dynamics on the attracting saddle-sink connections of the three
state low $B$ parameter Moore Greitzer model together with the
dynamics of the bleed valve controller. We show that the region of
attraction to the stabilized rotating stall
equilibria is seriously restrained by the fluid noise level, the
actuator bandwidth, magnitude saturation and rate limits. The
bandwidth and rate requirement for a fixed extension of stable region
is estimated by calculating the stable manifold of the saddle fixed
point of the two dimensional system. +
