Property:Abstract
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E
In this paper we apply some recently developed control laws for
stabilization of mechanical systems with nonholonomic constraints to
an experimental system consisting of a mobile robot towing a trailer.
We verify the applicability of various control laws which have
appeared in the recent literature, and compare the performance of
these controllers in an experimental setting. In particular, we show
that time-periodic, non-smooth controllers can be used to achieve
exponential stability of a desired equilibrium configuration, and that
these controllers outperform smooth, time-varying control laws. We
also point out several practical considerations which must be taken
into account when implementing these controllers. +
A
A hovercraft robot that uses insect-inspired visual autocorrelation for motion control in a corridor +
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. +
C
Communication and Sensing Trade-Offs in Decentralized Mobile Sensor Networks: A Cross-Layer Design Approach +
In this paper we characterize the impact of imperfect communication
on the performance of a decentralized mobile sensor network.
We first examine and demonstrate the trade-offs between communication
and sensing objectives, by determining the optimal sensor configurations
when introducing imperfect communication. We further illustrate the
performance degradation caused by non-ideal communication links in
a decentralized mobile sensor network. To address this, we propose a
decentralized motion-planning algorithm that considers communication
effects. The algorithm is a cross-layer design based on the proper interface
of physical and application layers. Simulation results will show the
performance improvement attained by utilizing this algorithm. +
E
Estimation Over Wireless Sensor Networks: Tradeoff between Communication, Computation and Estimation Qualities +
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. +
F
In this paper we consider nonlinear systems with steady-state or Hopf bifurcations for
which the bifurcated modes are linearly uncontrollable. The goal is to find state
feedbacks such that the bifurcation for the closed loop system is supercritical, and at
the same time, the linearly controllable subsystem is asymptotically stable. Necessary and
sufficient conditions for the non-existence of sufficiently smooth state feedbacks have
been obtained under certain nondegeneracy conditions. For the cases when those conditions
are not satisfied, we give explicit constructions of the feedbacks. The construction has
the following separation property: for any linear state feedback such that the
controllable subsystem is asymptotically stable, we could construct gains in the nonlinear
state feedbacks such that the closed loop system is asymptotically stable at the
bifurcation point. +
O
Optimal Sensor Hop Selection: Sensor Energy Minimization and Network Lifetime Maximization with Guaranteed System Performance +
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. +
In this paper we consider task scheduling when
sensing and controlling over a network with packet dropping
links. We find optimum ways of allocating limited computing
resources for estimation and control of a number
of linear dynamical systems with different characteristics
over communication links with different qualities. We find
theoretical expressions relating the optimum sampling rates to
the characteristics of the communication links and dynamics of
the plants.When considering resource allocation for estimation
of the plants, we derive optimum ways of task scheduling for
two performance metrics: decay rate and the asymptotic value
of the estimation error variance. When scheduling the control
tasks, we consider rate of convergence of the state and the
overall control cost as performance measures. The work lays
the theoretical foundations for considering the impact of both
limited computing and communication resources on estimation
and control. +
C
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. +
T
In this paper we consider the problem of generating feasible motions
for a towed cable, flight control system that has been proposed for
use in remote sensor applications. Using the fact that the system is
differentially flat, we illustrate how to construct feasible
trajectories for the system and demonstrate the strengths and
limitations of this approach. Simulations of the full dynamics are
included to illustrate the proposed techniques. A significant
limitation of the current approach is the numerical instability of the
algorithm, resulting in the need for careful tuning of parameters to
achieve convergence. +
O
In this paper we consider the problem of estimating discrete
variables in a class of hybrid systems where we assume that the continuous
variables are available for measurement. Using lattice and order
theory we develop a framework for constructing an observer on an enlarged
space of variables with lattice structure, which updates only two
variables at each step. We apply our ideas to a multi-robot system example,
the RoboFlag Drill. +
G
Global Dynamical Structure Reconstruction from Reconstructed Dynamical Structure Subnetworks: Applications to Biochemical Reaction Networks +
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. +
M
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. +
K
In this paper we describe the response of a Kinetic Monte Carlo model to
time-varying growth conditions. We vary temperature and partial pressure
sinusoidally and identify behavior typical of low-dimensional nonlinear
systems. In particular, the frequency content of the roughness response is
sensitive to the presence of steps in the surface. +
A
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. +
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. +
E
In this paper we evaluate the actuator rate requirements for control of rotating stall
using a bleed valve and provide tools for predicting these requirements. Modification of
both the stable and unstable parts of the compressor characteristic via addition of
continuous air injection serves to reduce the requirement of a bleed valve used for the
purpose of rotating stall stabilization. Analytical tools based on low order models (2-3
states) and simulation tools based on a reduced order model (37 states) are described. A
bleed actuator rate limit study is presented to compare the actuator requirements
predicted by theory, simulation, and experiment. The comparisons show that the predictions
obtained from theory and simulations share the same trend as the experiments, with
increasing accuracy as the complexity of the underlying model increases. Some insights on
the design of a bleed-compressor pair are given. +
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. +
In this paper we give a formulation of differential flatness---a concept originally
introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence
between exterior differential systems. Systems which are differentially flat have several
useful properties which can be exploited to generate effective control strategies for
nonlinear systems. The original definition of flatness was given in the context of
differentiable algebra, and required that all mappings be meromorphic functions. Our
formulation of flatness does not require any algebraic structure and allows one to use
tools from exterior differential systems to help characterize differentially flat systems.
In particular, we shown that in the case of single input control systems (i.e.,
codimension 2 Pfaffian systems), a system is differentially flat if and only if it is
feedback linearizable via static state feedback. However, in higher codimensions feedback
linearizability and flatness are *not* equivalent: one must be careful with the role of
time as well the use of prolongations which may not be realizable as dynamic feedbacks in
a control setting. Applications of differential flatness to nonlinear control systems and
open questions will be discussed. +
T
In this paper we introduce the Caltech
Multi-Vehicle Wireless Testbed (MVWT), a platform for testing
decentralized control methodologies for multiple vehicle
coordination and formation stabilization. The testbed consists of
eight mobile vehicles, an overhead vision system providing
GPS-like position information and wireless Ethernet for
communications. Each vehicle rests on omni-direction casters and
is powered by two high-performance ducted fans. Thus, a unique
feature of our testbed is that the vehicles have second order
dynamics, requiring real-time feedback algorithms to stabilize the
system while performing cooperative tasks. The testbed will be
used by various research groups at Caltech and elsewhere as a
means to validate theoretical advances in multiple-vehicle
coordination and control, networked control systems, real time
networking and high confidence distributed computation. +
N
In this paper we investigate methods for steering systems with nonholonomic
constraints between arbitrary configurations. Early work by Brockett derives the optimal
controls for a set of canonical systems in which the tangent space to the configuration
manifold is spanned by the input vector fields and their first order Lie brackets. Using
Brockett's result as motivation, we derive suboptimal trajectories for systems which are
not in canonical form and consider systems in which it takes more than one level of
bracketing to achieve controllability. These trajectories use sinusoids at integrally
related frequencies to achieve motion at a given bracketing level. We define a class of
systems which can be steered using sinusoids (chained systems) and give conditions under
which a class of two-input systems can be converted into this form. +
