Property:Abstract
From Murray Wiki
Jump to navigationJump to search
This is a property of type Text.
S
This article provides a review of control protocol synthesis techniques that incorporate methodologies from formal methods and control theory to provide correctness guarantee for different types of autonomous systems, including those with discrete and continuous state space. The correctness of the system is defined with respect to a given specification expressed as a formula in linear temporal logic to precisely describe the desired properties of the system. The formalism presented in this article admits non-determinism, allowing uncertainties in the system to be captured. A particular emphasis is on alleviating some of the difficulties, e.g., heterogeneity in the underlying dynamics and computational complexity, that naturally arise in the construction of control protocols for autonomous systems. +
R
This dissertation addresses the problem of control and kinematic
planning for constrained robot systems. An example of a system of
this type is a multifingered robot hand grasping an object. The
individual fingers act as robot manipulators and are constrained by
their contact with the object. If the contacts allow rolling between
the object and the fingertips, it is possible for the constraints to
be nonholonomic. That is, the constraints may not restrict the
reachable configurations of the system, but rather, constrain only the
allowable velocities of the system.
<p>
Using the multifingered hand as a motivating example, this
dissertation presents a detailed analysis of the kinematics, dynamics,
and control of robot systems with contact constraints. In particular,
it presents a unified derivation of the dynamics of robot manipulators
with Pfaffian velocity constraints, including the nonholonomic case.
This derivation allows control laws to be specified which are provably
stable for an entire class of systems, including unconstrained robots,
robot hands, and other systems of multiple robots performing a
coordinated task. A method for building complex controllers which
respects this class of constraints is also developed using a set of
simple primitives which allow hierarchical control structures to be
created in an organized fashion.
<p>
Finally, the nonholonomic motion planning problem is introduced and
discussed in detail. Using tools from differential geometric control
theory, it is possible to classify and analyze systems with
nonholonomic constraints. A brief review of the necessary tools along
with a review of the current literature is presented. A practical
method for steering nonholonomic systems using sinusoids is derived
and applied to several kinematic systems with contact constraints. +
E
This dissertation lays the foundation for practical exponential
stabilization of driftless control systems. Driftless systems have
the form $$\dot x = X_1(x)u_1+\cdots +X_m(x)u_m, \quad x\in\real^n$$.
Such systems arise when modeling mechanical systems with nonholonomic
constraints. In engineering applications it is often required to
maintain the mechanical system around a desired configuration. This
task is treated as a stabilization problem where the desired
configuration is made an asymptotically stable equilibrium point. The
control design is carried out on an approximate system. The
approximation process yields a nilpotent set of input vector fields
which, in a special coordinate system, are homogeneous with respect to
a non-standard dilation. Even though the approximation can be given a
coordinate-free interpretation, the homogeneous structure is useful to
exploit: the feedbacks are required to be homogeneous functions and
thus preserve the homogeneous structure in the closed-loop system.
The stability achieved is called {\em $\rho$-exponential stability}.
The closed-loop system is stable and the equilibrium point is
exponentially attractive. This extended notion of exponential
stability is required since the feedback, and hence the closed-loop
system, is not Lipschitz. However, it is shown that the convergence
rate of a Lipschitz closed-loop driftless system cannot be bounded by
an exponential envelope.
<p>
The synthesis methods generate feedbacks which are smooth on
\rminus. The solutions of the closed-loop system are proven to be
unique in this case. In addition, the control inputs for many
driftless systems are velocities. For this class of systems it is
more appropriate for the control law to specify actuator forces
instead of velocities. We have extended the kinematic velocity
controllers to controllers which command forces and still
$\rho$-exponentially stabilize the system.
<p>
Perhaps the ultimate justification of the methods proposed in this
thesis are the experimental results. The experiments demonstrate the
superior convergence performance of the $\rho$-exponential stabilizers
versus traditional smooth feedbacks. The experiments also highlight
the importance of transformation conditioning in the feedbacks. Other
design issues, such as scaling the measured states to eliminate
hunting, are discussed. The methods in this thesis bring the
practical control of strongly nonlinear systems one step closer.
<p>
M
This paper applies some previously studied extended
Kalman filter techniques for planar road geometry
estimation to the domain of autonomous navigation of offhighway
vehicles. In this work, a clothoid model of the road
geometry is constructed and estimated recursively based on
road features extracted from single-axis LADAR range measurements.
We present a method for feature extraction of the
road centerline in the image plane, and describe its application
to recursive estimation of the road geometry. We analyze
the performance of our method against simulated motion of
varied road geometries and against recorded data from previous
autonomous navigation runs. Our method accomodates full 6
DOF motion of the vehicle as it navigates, constructs consistent
estimates of the road geometry with respect to a fixed global
reference frame, and requires an estimate of the sensor pose
for each range measurement. +
R
This paper bridges the advances in computer science and control to allow automatic synthesis of complex dynamical systems which are guaranteed, by construction, to satisfy the desired properties even in the presence of adversary. The desired properties are expressed in the language of temporal logic. With its expressive power, a wider class of properties than safety and stability can be specified. The resulting system consists of a discrete planner which plans, in the abstracted discrete domain, a set of transitions of the system to ensure the correct behaviors and a continuous controller which continuously implements the plan. For a system with certain structure, we present an approach, based on a receding horizon scheme, to overcome computational difficulties in the synthesis of a discrete planner and allow more complex problems to be solved. +
E
Exponential Stabilization of Driftless Nonlinear Control Systems via Time-varying, Homogeneous Feedback +
This paper brings together results from a number of different areas in
control theory to provide an algorithm for the synthesis of locally
exponentially stabilizing control laws for a large class of driftless
nonlinear control systems. The exponential stabilization relies on the
use of feedbacks which render the closed loop vector field homogeneous
with respect to a dilation. These feedbacks are generated from a
modification of Pomet's algorithm for smooth feedbacks. Converse
Liapunov theorems for time-periodic homogeneous vector fields
guarantee that local exponential stability is maintained in the
presence of higher order (with respect to the dilation) perturbing
terms.
<p> +
R
This paper concerns the average consensus problem with the constraint of quantized communication between nodes. A broad class of algorithms is analyzed, in which the transmission strategy, which decides what value to communicate to the neighbors, can include various kinds of rounding, probabilistic quantization, and bounded noise. The arbitrariness of the transmission strategy is compensated by a feedback mechanism which can be interpreted as a self-inhibitory action. The result is that the average of the nodes state is not conserved across iterations, and the nodes do not converge to a consensus; however, we show that both errors can be made as small as desired. Bounds on these quantities involve the spectral properties of the graph and can be proved by employing elementary techniques of LTI systems analysis. +
D
This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus we mean in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises minimal number of local observations of randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically using local information as suggested by Olshevsky and Tsitsiklis. +
S
This paper considers distributed control of interconnected multi-agent systems. The dynamics of the individual agents are not required to be homogeneous and the interaction topology is described by an arbitrary directed graph. We derive the sensitivity transfer functions between every pair of agents and we analyze stability and performance of non-homogeneous systems, showing that the low frequency behavior is influenced not only by topology, but also by static gain and poles of the agents. +
O
This paper considers how a team of mobile sensors
should cooperatively move so as to optimally categorize a
single moving target from their noisy sensor readings. The
cooperative control procedure is based on the development of
a cost function that quantifies the teamâs classification error.
The robotsâ motions are then chosen to minimize this function.
We particularly investigate the case where the sensor noise and
class distributions are Gaussian. In this case, we can derive a
duality principle which states that optimal classification will be
realized when the covariance of the target estimate is minimized.
That is, in this case, optimal estimation leads naturally to
optimal classification. We extend previous work to develop a
distributed discrete-gradient search algorithm that guides the
teamâs location motions for purposes of optimal estimation and
classification. The concepts developed are validated through
numerical studies. +
N
This paper considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for a planar robotic fish that is propelled using the carangiform style of locomotion. Our experimental apparatus consists of a freely translating and rotating flat plate and a two-link actuated tail. We develop a model for the fish's propulsion that is based on quasi-steady fluid flow. Using this model, we predict system response to sinusoidal motions of the tail joints and
compare these predictions to the experimental results. We then propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment. +
A
This paper considers the fundamental design and modeling of the Caltech ducted fan.
The Caltech ducted fan is a scaled model of the longitudinal axis of a flight vehicle. The
purpose of the ducted fan is the research and development of new nonlinear flight guidance
and control techniques for Uninhabited Combat Aerial Vehicles. It is shown that critical
design relations must be satisfied in order that the ducted fan's longitudinal dynamics
behave similar to those of an flight vehicle. Preliminary flight test results illustrate
the flying qualities of the ducted fan. +
E
This paper considers the problem of estimation over
communication networks. Suppose a sensor is taking
measurements of a dynamic
process. However the process needs to be estimated at a
remote
location connected to the sensor through a network of
communication links that drop
packets stochastically. We provide a framework for
computing the
optimal performance in the sense of expected error
covariance. Using
this framework we characterize the dependency of the
performance on
the topology of the network and the packet dropping
process. For
independent and memoryless packet dropping processes we
find the
steady-state error for some classes of networks and obtain
lower and
upper bounds for the performance of a general network. We
also
illustrate how this framework can be used in the synthesis
of
networks for the purpose of estimation. Finally we find a
necessary
and sufficient condition for the stability of the estimate
error
covariance for general networks with spatially correlated
and Markov
type dropping process. This interesting condition has a
max-cut
interpretation. +
A
This paper considers the problem of motion planning for a car-like robot (i.e., a
mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We
present a fast and exact planner for our mobile robot model, based upon recursive
subdivision of a collision-free path generated by a lower-level geometric planner that
ignores the motion constraints. The resultant trajectory is optimized to give a path that
is of near-minimal length in its homotopy class. Our claims of high speed are supported by
experimental results for implementations that assume a robot moving amid polygonal
obstacles. The completeness and the complexity of the algorithm are proven using an
appropriate metric in the configuration space R2 x S1 of the robot. This metric is defined
by using the length of the shortest paths in the absence of obstacles as the distance
between two configurations. We prove that the new induced topology and the classical one
are the same. Although we concentration upon the car-like robot, the generalization of
these techniques leads to new theoretical issues involving sub-Riemannian geometry and to
practical results for nonholonomic motion planning. +
R
This paper considers the problem of real time trajectory generation and tracking for
nonlinear control systems. We employ a two degree of freedom approach that separates the
nonlinear tracking problem into real time trajectory generation followed by local
(gain-scheduled) stabilization. The central problem which we consider is how to generate,
possibly with some delay, a feasible state space and input trajectory in real time from an
output trajectory that is given online. We propose two algorithms that solve the real time
trajectory generation problem for differentially flat systems with (possibly non-minimum
phase) zero dynamics. One is based on receding horizon point to point steering, the other
allows additional minimization of a cost function. Both algorithms explicitly address the
tradeoff between stability and performance and we prove convergence of the algorithms for
a reasonable class of output trajectories. To illustrate the application of these
techniques to physical systems, we present experimental results using a vectored thrust
flight control experiment built at Caltech. A brief introduction to differentially flat
systems and its relationship with feedback linearization is also included. +
S
Synthesis of Correct-by-construction Control Protocols for Hybrid Systems Using Partial State Information +
This paper considers the problem of synthesizing output-feedback control laws for a class of discrete-time hybrid systems in order for the trajectories of the system to satisfy certain high-level specifications expressed in linear temporal logic. By leveraging ideas from robust interpretation of temporal logic formulas and bounded-error estimation, we identify a subclass of systems for which it is possible to reduce the problem to a state-feedback form. In particular, we use locally superstable hybrid observers to resolve the partial information at the continuous level. This allows us to use recent results in temporal logic planning to synthesize the desired controllers based on two-player perfect- information games. The overall control architecture consists of a hybrid observer, a high-level switching protocol and a low-level continuous controller. We demonstrate the proposed framework in a case study on designing control protocols for an aircraft air management system. +
B
This paper considers the problem of synthesizing correct-by-construction robotic controllers in environments with uncertain but fixed structure. âEnvironmentâ has two notions in this work: a map or âworldâ in which some controlled agent must operate and navigate (i.e. evolve in a configuration space with obstacles); and an adversarial player that selects con- tinuous and discrete variables to try to make the agent fail (as in a game). Both the robot and the environment are subjected to behavioral specifications expressed as an assume-guarantee linear temporal logic (LTL) formula. We then consider how to efficiently modify the synthesized controller when the robot encounters unexpected changes in its environment. The crucial insight is that a portion of this problem takes place in a metric space, which provides a notion of nearness. Thus if a nominal plan fails, we need not resynthesize it entirely, but instead can âpatchâ it locally. We present an algorithm for doing this, prove soundness, and demonstrate it on an example gridworld. +
O
This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own numbers in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. In the first part of the paper, it was shown that the quantized consensus is reached by means of a stochastic gossip algorithm proposed in a recent paper, for any arbitrary quantization. The current part of the paper considers the expected value of the time at which the quantized consensus is reached. This quantity (corresponding to the worst case) is upper and lower bounded in terms of the topology of the graph, for uniform quantization. In particular, it is shown that these bounds are related to the principal minors of the weighted Laplacian matrix. A convex optimization is also proposed to determine the set of probabilities (used to pick a pair of agents) which leads to the fast convergence of the gossip algorithm. +
T
This paper demonstrates the effectiveness of sim- ple control-theoretic tools in generating simulation-guided ex- periments on a synthetic in vitro oscillator. A theoretical analysis of the behavior of such system is motivated by high cost, time consuming experiments, together with the excessive number of tuning parameters. A simplified model of the synthetic oscillator is chosen to capture only its essential features. The model is analyzed using the small gain theorem and the theory of describing functions. Such analysis reveals what are the parameters that primarily determine when the system can admit stable oscillations. Experimental verification of the theoretical and numerical findings is carried out and confirms the predicted results regarding the role of production and degradation rates. +
This paper describes TuLiP, a Python-based software tool- box for the synthesis of embedded control software that is provably correct with respect to an expressive subset of lin- ear temporal logic (LTL) specifications. TuLiP combines routines for (1) finite state abstraction of control systems, (2) digital design synthesis from LTL specifications, and (3) receding horizon planning. The underlying digital de- sign synthesis routine treats the environment as adversary; hence, the resulting controller is guaranteed to be correct for any admissible environment profile. TuLiP applies the re- ceding horizon framework, allowing the synthesis problem to be broken into a set of smaller problems, and consequently alleviating the computational complexity of the synthesis procedure, while preserving the correctness guarantee. +
