Property:Abstract
From Murray Wiki
Jump to navigationJump to search
This is a property of type Text.
T
We regard the internal configuration of a deformable body, together with
its position and orientation in ambient space, as a point in a trivial
principal fiber bundle over the manifold of body deformations.
In the presence of a symmetry which leads to a conservation law, the
self-propulsion of such a body due to cyclic changes in shape is
described by the corresponding mechanical connection on the configuration
bundle. In the presence of viscous drag sufficient to negate inertial
effects, the viscous connection takes the place of the mechanical connection.
Both connections may be represented locally in terms of the variables
describing the body's shape. In the presence of both inertial and
viscous effects, the equations of motion may be written in terms of the
two local connection forms as an affine control system with drift on
the manifold of configurations and body momenta. We apply techniques
from nonlinear control theory to the equations in this form to obtain
criteria for a particular form of accessibility. +
D
We study a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A new decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The iterative algorithm is implemented on a multi-hop network and is designed to handle communication delays. The convergence of the algorithm is proved for communication networks with bounded delays. An explicit bound, which depends on the communication delays, on the convergence rate is given. A numerical comparison with a decentralized primal algorithm shows that the dual algorithm converges faster, with less communication. +
O
We study a simple pursuit scenario in which the
pursuer has potential access to an additional off-board global
sensor. However, the global sensor can be used for either of
two purposes: to improve the state estimate of the pursuer, or
to obtain more data about the trajectory being tracked. The
problem is to determine the variation in the performance of
the system as the global sensor changes its behavior. We use a
stochastic strategy to optimize over the transmission pattern
of the global sensor. +
S
Synthesizing Reactive Test Environments for Autonomous Systems: Testing Reach-Avoid Specifications with Multi-Commodity Flows +
We study automated test generation for verifying discrete decision-making modules in autonomous systems. We utilize linear temporal logic to encode the requirements on the system under test in the system specification and the behavior that we want to observe during the test is given as the test specification which is unknown to the system. First, we use the specifications and their corresponding non-deterministic Bu ̈chi automata to generate the specification product automaton. Second, a virtual product graph representing the high-level interaction between the system and the test environment is constructed modeling the product automaton encoding the system, the test environment, and specifications. The main result of this paper is an optimization problem, framed as a multi-commodity network flow problem, that solves for constraints on the virtual product graph which can then be projected to the test environment. Therefore, the result of the optimization problem is reactive test synthesis that ensures that the system meets the test specifications along with satisfying the system specifications. This framework is illustrated in simulation on grid world examples, and demonstrated on hardware with the Unitree A1 quadruped, wherein dynamic locomotion behaviors are verified in the context of reactive test environments. +
U
We study the continuous-time consensus problem where nodes on a graph attempt to reach average consensus. We consider communication graphs that can be decomposed into a hierarchical structure and present a consensus scheme that exploits this hierarchical topology. The scheme consists of splitting the overall graph into layers of smaller connected subgraphs.
Consensus is performed within the individual subgraphs starting with those of the lowest layer of the hierarchy and moving upwards. Certain ``leader'' nodes bridge the layers of the hierarchy. By exploiting the increased convergence speed of the smaller subgraphs, we show
how this scheme can achieve faster overall convergence than the standard single-stage consensus algorithm running on the full graph topology. The result presents some fundamentals on how the communication architecture influences the global performance of a networked system. Analytical
performance bounds are derived and simulations provided to illustrate the effectiveness of the scheme. +
A
We study the dynamic and static input output behavior of several primitive genetic interactions and their e↵ect on the performance of a genetic signal di↵erentiator. In a simplified design, several requirements for the linearity and time-scales of processes like transcription, translation and competitive promoter binding were introduced. By ex- perimentally probing simple genetic constructs in a cell-free experimental environment and fitting semi-mechanistic models to these data, we show that some of these require- ments can be verified, while others are only met with reservations in certain operational regimes. Analyzing the linearized model of the resulting genetic network we conclude that it approximates a di↵erentiator with relative degree one. Taking also the discovered non-linearities into account and using a describing function approach, we further deter- mine the particular frequency and amplitude ranges where the genetic di↵erentiator can be expected to behave as such. +
D
We study the dynamic stability of low Reynolds number swimming near a plane wall from a control-theoretic viewpoint. We consider a special class of swimmers having a constant shape, focus on steady motion parallel to the wall, and derive conditions under which it is passively stable without sensing or feedback. We study the geometric structure of the swimming equation and highlight the relation between stability and reversing symmetry of the dynamical system. Finally, our numerical simulations reveal the existence of stable periodic motion. The results have implications for design of miniature robotic swimmers, as well as for explaining the attraction of micro-organisms to surfaces. +
J
We study the dynamics of the relative motion of
satellites in the gravitational field of the Earth, including
the effects of the bulge of the Earth (the $J_2$ effect). Using
Routh reduction and dynamical systems ideas, a method is found
that locates orbits such that the cluster of satellites remains
close with very little dispersing, even with no controls. The use of
controls in the context of this natural dynamics is studied to maintain and
achieve precision formations. +
O
We study the effect of quantization on the performance
of a scalar dynamical system. We provide an expression
for calculation of the LQR cost of a dynamical system for
a general quantizer. Using the high-rate approximation, we
evaluate it for two commonly used quantizers: uniform and
logarithmic. We also provide a lower bound on performance
of the optimal quantizer based on entropy arguments and
consider the case when the channel drops data packets
stochastically. +
We study the problem of using a small number
of mobile sensors to monitor various threats in a geographical
area. Using some recent results on stochastic sensor scheduling,
we propose a stochastic sensor movement strategy. We present
simple conditions under which it is not possible to maintain a
bounded estimate error covariance for all the threats. We also
study a simple sub-optimal algorithm to generate stochastic
trajectories. Simulations are presented to illustrate the results. +
We study the synthesis problem of a LQR controller when the matrix describing the control
law is additionally constrained to lie in a particular vector space. Our motivation is the use of
such control laws to stabilize networks of autonomous agents in a decentralized fashion; with
the information
ow being dictated by the constraints of a pre-specified topology. We formulate
the problem as an optimization problem and provide numerical procedures to solve it. Then we
apply the technique to the decentralized vehicle formation control problem and show that the
topology can have a significant effect on the optimal cost. We also discuss the issue of optimal
topology. +
A
We study the synthesis problem of an LQR controller when the matrix describing the control law is
constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize
networks of autonomous agents in a decentralized fashion; with the information flow being dictated by
the constraints of a pre-specified topology. In this paper, we consider the finite-horizon version of the
problem and provide both a computationally intensive optimal solution and a sub-optimal solution that
is computationally more tractable. Then we apply the technique to the decentralized vehicle formation
control problem and show that the loss in performance due to the use of the sub-optimal solution is not
huge; however the topology can have a large effect on performance. +
L
When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents' trajectories (i.e. confidence tubes that contain trajectories with probability ), which can then be used to guarantee safety with probability . However, almost all existing works consider . The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with , and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low . Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for . These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems. +
I
Identifying and exploiting tolerance to unexpected jumps in synthesized strategies for GR(1) specifications +
When used as part of a hybrid controller, finite- memory strategies synthesized from LTL specifications rely on an accurate dynamics model in order to ensure correctness of trajectories. In the presence of uncertainty about this underlying model, there may exist unexpected trajectories that manifest as unexpected transitions under control of the strategy. While some disturbances can be captured by augmenting the dynamics model, such approaches may be conservative in that bisimulations may fail to exist for which strategies can be synthesized. In this paper, we characterize the tolerance of such hybrid controllers - synthesized for generalized reactivity(1) specifications- to disturbances that appear as unexpected jumps (transitions) to states in the discrete strategy part of the con- troller. As a first step, we show robustness to certain unexpected transitions that occur in a finite-manner, i.e., despite a certain number of unexpected jumps, the sequence of states obtained will still meet a stricter specification and hence the original specification. Additionally, we propose algorithms to improve robustness by increasing tolerance to additional disturbances. A robot gridworld example is presented to demonstrate the application of the developed ideas and also to obtain empirical computational and memory cost estimates. +
E
When used as part of a hybrid controller, finite-memory strategies synthesized from linear-time temporal logic (LTL) specifications rely on an accurate dynamics model in order to ensure correctness of trajectories. In the presence of uncertainty about the underlying model, there may exist unexpected trajectories that manifest as unexpected transitions under control of the strategy. While some disturbances can be captured by augment- ing the dynamics model, such approaches may be con- servative in that bisimulations may fail to exist for which strategies can be synthesized. In this paper, we consider games of the GR(1) fragment of LTL, and we character- ize the tolerance of hybrid controllers to perturbations that appear as unexpected jumps (transitions) to states in the discrete strategy part of the controller. As a first step, we show robustness to certain unexpected transi- tions that occur in a finite manner, i.e., despite a certain number of unexpected jumps, the sequence of states ob- tained will still meet a stricter specification and hence the original specification. Additionally, we propose al- gorithms to improve robustness by increasing tolerance to additional disturbances. A robot gridworld example is presented to demonstrate the application of the de- veloped ideas and also to perform empirical analysis. +
R
While complex dynamic biological networks control gene expression in all living organisms, the forward engineering of comparable synthetic networks remains challenging. The current paradigm of characterizing synthetic networks in cells results in lengthy design-build-test cycles, minimal data collection, and poor quantitative characterization. Cell-free systems are appealing alternative environments, but it remains questionable whether biological networks behave similarly in cell-free systems and in cells. We characterized in a cell-free system the 'repressilator,' a three-node synthetic oscillator. We then engineered novel three, four, and five-gene ring architectures, from characterization of circuit components to rapid analysis of complete networks. When implemented in cells, our novel 3-node networks produced population-wide synchronized oscillations and 95% of 5-node oscillator cells oscillated for up to 72 hours. Oscillation periods in cells matched the cell-free system results for all networks tested. An alternate forward engineering paradigm using cell-free systems can thus accurately capture cellular behavior. +
M
While the use of formal synthesis for robotics problems in which the environment may act adversarially provides for exactârather than probabilisticâcorrectness of controllers, such methods are impractical when the adversary can move freely in a large portion of the workspace. As is well-known, this is due to exponential growth in the state space with the addition of each new problem variable. Furthermore, such an approach is overly conservative because most configurations will not be reached in typical runs. Rather than entirely abandon the discrete game view, we propose a combined method that ensures exact satisfaction of a given specification, expressed in linear temporal logic, while providing a lower bound on robot-obstacle distance throughout execution. Our method avoids explicit encoding of the moving obstacle and thus substantially reduces the reactive synthesis problem size, while allowing other nondeterministic variables to still be included in the specification. Our approaches centers on modeling obstacle motion as changes in the presence of a virtual static obstacle, and performing incremental synthesis in response. The algorithm is tested in application to a planar surveillance task. +
Metabolic engineering of Pseudomonas putida for production of vanillylamine from lignin-derived substrates +
Whole-cell bioconversion of technical lignins using Pseudomonas putida strains overexpressing amine transaminases (ATAs) has the potential to become an eco-efficient route to produce phenolic amines. Here, a novel cell growth-based screening method to evaluate the in vivo activity of recombinant ATAs towards vanillylamine in P. putida KT2440 was developed. It allowed the identification of the native enzyme Pp-SpuC-II and ATA from Chromobacterium violaceum (Cv-ATA) as highly active towards vanillylamine in vivo. Overexpression of Pp-SpuC-II and Cv-ATA in the strain GN442ΔPP_2426, previously engineered for reduced vanillin assimilation, resulted in 94- and 92-fold increased specific transaminase activity, respectively. Whole-cell bioconversion of vanillin yielded 0.70 ± 0.20 mM and 0.92 ± 0.30 mM vanillylamine, for Pp-SpuC-II and Cv-ATA, respectively. Still, amine production was limited by a substantial re-assimilation of the product and formation of the by-products vanillic acid and vanillyl alcohol. Concomitant overexpression of Cv-ATA and alanine dehydrogenase from Bacillus subtilis increased the production of vanillylamine with ammonium as the only nitrogen source and a reduction in the amount of amine product re-assimilation. Identification and deletion of additional native genes encoding oxidoreductases acting on vanillin are crucial engineering targets for further improvement. +
R
With the advent of powerful computing and efficient computational algorithms,
real-time solutions to constrained optimal control problems are nearing a reality. In
this thesis, we develop a computationally efficient Nonlinear Trajectory Generation
(NTG) algorithm and describe its software implementation to solve, in real-time,
nonlinear optimal trajectory generation problems for constrained systems. NTG is
a nonlinear trajectory generation software package that combines nonlinear control
theory, B-spline basis functions, and nonlinear programming. We compare NTG
with other numerical optimal control problem solution techniques, such as direct
collocation, shooting, adjoints, and differential inclusions.
We demonstrate the performance of NTG on the Caltech Ducted Fan testbed.
Aggressive, constrained optimal control problems are solved in real-time for hover-
to-hover, forward flight, and terrain avoidance test cases. Real-time trajectory
generation results are shown for both the two-degree of freedom and receding
horizon control designs. Further experimental demonstration is provided with the
station-keeping, reconfiguration, and deconfiguration of micro-satellite formation
with complex nonlinear constraints. Successful application of NTG in these cases
demonstrates reliable real-time trajectory generation, even for highly nonlinear
and non-convex systems. The results are among the first to apply receding horizon
control techniques for agile flight in an experimental setting, using representative dynamics and computation. +
Q
Without accounting for the limited availability of shared cellular resources, the standard model of gene expression fails to reliably predict experimental data obtained in vitro. To overcome this limitation, we develop a dynamical model of gene expression explicitly modeling competition for scarce resources. In addition to accurately describing the experimental data, this model only depends on a handful of easily identifiable parame- ters with clear physical interpretation. Based on this model, we then characterize the combinations of protein concentrations that are simultaneously realizable with shared resources. As application examples, we demonstrate how the results can be used to explain similarities/differences among different in vitro extracts, furthermore, we illustrate that accounting for resource usage is essential in circuit design considering the toggle switch. +
