Property:Abstract
From Murray Wiki
Jump to navigationJump to search
This is a property of type Text.
R
This paper details the application of a constrained receding horizon control techniques to
stabilize an indoor vectored-thrust flight experiment, known as the Caltech Ducted Fan, subjected to step commands. The result of the experiment sheds light on the theoretical stability
of the receding horizon control strategy as well as validates some efficient computation techniques for solving nonlinear optimal control problems with constraints. The receding horizon
control problem is formulated as a constrained optimal control problem, which was solved with
an e±cient computational method developed and implemented by Milam et al., that combines
nonlinear control theory, B-spline basis functions, and nonlinear programming. Characteristic
issues including non-zero computational times, convergence property, choice of horizon length
and terminal cost are discussed. The study confirms the applicability of real-time receding
horizon control for constrained systems with fast dynamics. +
This paper discusses a Cooperative Path Planning (CPP) design
methodology for multi-vehicle systems and a Nonlinear
Trajectory Generation (NTG) algorithm. Three scenarios
of multi-vehicle tasking are proposed at the CPP framework.
The NTG algorithm is, then, used to generate realtime
trajectory for desired vehicle activities. Given system
dynamics and constraints, the NTG algorithm first finds trajectory
curves in a lower dimensional space and, then, parameterizes
the curves by the B-spline basis. The coefficients of the B-splines are further solved by the sequential
quadratic programming to satisfy the optimization objectives
and constraints. The NTG algorithm has been implemented
to generate real-time trajectories for a group of
cooperative vehicles in the presence of changing missions
and constraints. +
C
This paper discusses a design methodology of cooperative
trajectory generation for multi-robot systems.
The trajectory of achieving cooperative tasks, i.e., with
temporal constraints, is constructed by a nonlinear trajectory
generation (NTG) algorithm. Three scenarios
of multi-robot tasking are proposed at the cooperative
task planning framework. The NTG algorithm is, then,
used to generate real-time trajectory for desired robot
activities. Given robot dynamics and constraints, the
NTG algorithm first finds trajectory curves in a lower
dimensional space and, then, parameterizes the curves
by a set of B-spline representations. The coe�cients
of the B-splines are further solved by the sequential
quadratic programming to satisfy the optimization objectives
and constraints. The NTG algorithm has been
implemented to generate real-time trajectories for a
group of cooperative robots in the presence of spatial
and temporal constraints. Finally, an illustrated example
of cooperative task planning with temporal constraints
is presented. +
L
This paper explores low observability flight path planning of unmanned air vehicles (UAVs)
in the presence of radar detection systems. The probability of detection model of an aircraft
near an enemy radar depends on aircraft attitude, range, and configuration. A detection model
is coupled with a simplified aircraft dynamics model. The Nonlinear Trajectory Generation
(NTG) software package developed at Caltech is used. The NTG algorithm is a gradient descent
optimization method that combines three technologies: Bsplines, output space collocation and
nonlinear optimization tools. Implementations are formulated with temporal constraints that
allow periods of high observability interspersed with periods of low observability. Illustrative
examples of optimized routes for low observability are presented. +
A
This paper explores the problem of finding a real--time optimal tra jectory for unmanned air vehicles (UAV) in order to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the Nonlinear Tra jectory Generation (NTG) method developed by Milam et al. The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of NTG on the proposed low--observable tra jectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously--differentiable input-output mapping. Artificial Neural Networks (ANNs) as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of ANNs against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate UAV
trajectories optimized for both detectability and time. +
S
This paper explores the stability analysis problem for nonlinear systems which have general
linear feedback interconnections. Systems are often modeled in this manner in the study of
decentralized control because many communication topologies can be modeled and analyzed
using connections to graph theory. We present necessary conditions for stability of a classification
of interconnected systems, and we give some examples to provide insight into this problem.
These conditions are related to positive definiteness of matrices associated with the feedback
interconnection, and specialize to the common case where the Laplacian matrix of a graph
represents the communication topology of the system. +
L
This paper explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the behavior of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems. +
F
This paper focuses on RNA flux regulation for in vitro synthetic gene networks and considers architectures that can be scaled to an arbitrary number of species. Feedback loops are designed based on negative autoâregulation (which can minimize the potentially harmful amount of molecules not used to form useful products) and crossâactivation (which can maximize the overall output flux): transcription rate matching can be achieved through proper feedback constants; negative feedback is faster and maintains stability. A possible experimen- tal implementation of a three and four genes negative feedback architecture is also numerically studied. +
C
This paper focuses on a new geometric approach to fully actuated control
systems on the Riemannian manifold S^2. Our control laws exploit the basic
and intuitive notions of geodesic direction and of distance between points,
and generalize the classical proportional plus derivative feedback (PD)
without the need of arbitrary local coordinate charts. Even for the
stability analysis, the appropriate Lyapunov function relies upon the notion
of distance and its properties. This methodology then applies to spin-axis
stabilization of a spacecraft actuated by only two control torques:
discarding the rotation about the unactuated axis, a reduced system is
considered, whose state is in fact defined on the sphere. For this reduced
attitude stabilization problem our approach allows us not only to deal
optimally with the inevitable singularity, but also to achieve simplicity,
versatility and (coordinate independent) adaptive capabilities. +
R
This paper gives a brief introduction to some of the experimental
facilities at Caltech being used for instruction and research. Two
experiments are described: a flight control experiment using a vector
thrust engine, and a low-speed, axial flow compressor rig. A common
hardware and software infrastructure is used to control these
experiments, allowing easy transition from instructional to research
use. +
T
This paper gives a survey of current and emerging techniques for motion control of
nonlinear mechanical systems, motivated by applications in robotic locomotion. For this
class of systems, internal changes of shape and/or application of body fixed forces are
the mechanism by which the robot mov es in its environment and the geometric mechanical
properties of the system are crucial in understanding how specific gaits for generating
motion can be obtained. +
G
This paper gives a survey of some recent results on control of systems with magnitude
and rate limits, motivated by problems in real-time trajectory generation and tracking for
unmanned aerial vehicles. Two problems are considered: stabilization using ``nonlinear
wrappers'' to rescale a given control law and real-time trajectory generation using
differential flatness. For both problems, simplified versions of the general problem are
studied using tools from differential geometry and nonlinear control to give insights into
the limitations imposed by magnitude and rate limits and provide insights into
constructive solutions to the trajectory generation and tracking problems. +
U
This paper introduces a new computationally
inexpensive approach to perception and modeling of the
environment that allows fusion of sensory range data of
various types and fidelities while explicitly taking into account
a complete description of uncertainty of the range measurements.
This approach makes use of known sensor uncertainty
models to create a single 2.5D digital elevation map whose
accuracy is robust to sensor noise and spurious data. This
approach is particularly suitable for real-time application in
high speed and highly unstructured outdoor environments
for which reasonably accurate and timely vehicle state estimates
are available. Experimental results are presented in
which LADAR range measurements and state estimates are
combined according to this approach. We provide qualitative
comparison to other classes of environment modeling. +
O
This paper introduces the concept of outer flatness,
a derivative of differential flatness.
Outer flatness describes a
system that can be split
in 2 subsytems, a non-flat inner system and a flat outer system.
The outputs of the outer system are the tracking outputs of interest.
The inputs of the outer system are the outputs of the inner system,
and not subject to our direct control.
The inputs of the inner system are the real actuator inputs.
This system structure is also present in backstepping and dynamic
inversion.
We present two theorems on exponential and bounded tracking for
outer flat systems, based on Lyapunoff arguments.
We validate the approach with simulations and experiments
on a model helicopter.
<p> +
S
This paper investigates the results of distributing the delay of a single feedback system. To distribute the delayed feedback, the single delay is replaced by the sum of two distinct delays with the same effective delay. The statistical properties of the new distribution function in the feedback, namely the sum of two delta functions, are used to quantify the effectiveness of delay distribution. We show that the distribution is effective in reducing the magnitude of the open loop transfer function, thereby, decreasing the gain-crossover frequency and improving the phase margin. Finally, inspired by Orosz et al., we demonstrate an example of how these results can be used to design a controller using delays. +
This paper investigates the stability of linear systems with stochastic delay in discrete time. Stability of the mean and second moment of the non-deterministic system is determined by a set of deterministic discrete time equations with distributed delay. A theorem is provided that guarantees convergence of the state with convergence of the second moment, assuming the delays are identically independently distributed. The theorems are applied to a scalar equation where the stability of the equilibrium is determined. +
R
This paper investigates the use of efficient computational algorithms for the
computation of a nominal trajectory for fast transition between flight modes. We use
differential flatness of an approximate model of the longitudinal dynamics of a thrust
vectored aircraft to achieve fast switching between flight modes. We investigate some
methods to compensate for the discrepancy between the full aerodynamic model and the
approximate flat model, and analyze their performance. Simulations and experimental data
for a thrust vectored flight control experiment at Caltech are provided to validate the
approach. +
This paper is a very brief outline of an invited poster session giving a
first-year progress report on a research program with the above title being
carried out in the Control and Dynamical Systems (CDS) department at Caltech.
This 5-year grant funded by the AFOSR Partnership for Research Excellence
Transition (PRET) Program has a special emphasis on transitioning new methods
to industrial practice and thus involves a high level of industrial
participation. The focus of our program is fundamental research in general
methods of analysis and design of complex uncertain nonlinear systems, from
creating new mathematical theory to working to make that theory help engineers
solve a variety of real industrial problems. Caltech's Control and Dynamical
Systems department was created with precisely this goal, which is shared by our
industrial collaborators, led by Honeywell. Further details will be available
at the poster session. +
O
This paper is concerned with the distributed averaging problem subject to a quantization constraint. Given a group of agents associated with scalar numbers, it is assumed that each pair of agents can communicate with each other with a prescribed probability, and that the data being exchanged between them is quantized. In this part of the paper, it is proved that the stochastic gossip algorithm proposed in a recent paper leads to reaching the quantized consensus. Some important properties of the system in the steady-state (after reaching the consensus) are also derived. The results developed here hold true for any arbitrary quantization, provided the tuning parameter of the gossip algorithm is chosen properly. The expected value of the convergence time bounded in the second part of the paper. +
Q
This paper is concerned with the distributed averaging problem over a given undirected graph. To enable every vertex to compute the average of the initial numbers sitting on the vertices of the graph, the policy is to pick an edge at random and update the values on its ending vertices based on some rules, but only in terms of the quantized data being exchanged between them. Our recent paper showed that the quantized consensus is reached under a simple updating protocol which deploys a fixed tuning factor. The current paper allows the tuning factor to be time-dependent in order to achieve two goals. First, this makes it possible to study the numerical stability of the protocol with a fixed tuning factor under a small perturbation of this parameter. Furthermore, exploiting a time-varying tuning factor facilitates the implementation of the consensus protocol and pushes the steady state of the system towards an equilibrium point, as opposed to making it oscillatory. The current paper is an important extension of our recent work, which generalizes a finite-dimensional problem toan infinite-dimensional one that is more challenging in nature. +
