Property:Abstract
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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. +
D
This paper describes a synthetic in vitro genetic circuit programmed to work as an insulating device. This circuit is composed of nucleic acids, which can be designed to interact according to user defined rules, and of few proteins that perform catalytic functions. A model of the circuit is derived from first principle biochemical laws. This model is shown to exhibit time-scale separation that makes its output insensitive to downstream time varying loads. Simulation results show the circuit effectiveness and represent the starting point for future experimental testing of the device. +
R
Reduction of Bleed Valve Bandwidth Requirements for Control of Rotating Stall using Continuous Air Injection +
This paper describes a technique for reducing the actuator rate
requirement in active control of rotating stall and surge on
compressors. Actuation of the compressor characteristic, via the use
of continuous air injection at the rotor face in a single-stage, low
speed axial compressor, has been experimentally verified to provide a
method of reducing the actuator rate requirement of bleed valve
control of rotating stall. With a compressor rotor frequency of 100
Hz, active control of stall with a high speed bleed valve is achieved
only when the compressor characteristic is actuated. Furthermore, the
experiments show that the bleed valve rate requirement is reduced from
approximately 145 Hz to below 10 Hz when the amount of compressor
characteristic actuation is increased. Theoretical tools based on a
low order model (1-3 states) and simulations based on a reduced order
distributed model (37 states) have been developed to estimate the gain
and rate requirements of the bleed controller. All of the analytical
formulas and simulations share the same qualitative trends with
respect to the second and third derivatives of the compressor
characteristic function evaluated at the peak, and the experiments.
The agreement implies that bleed valve control of rotating stall
depends crucially on the rate limit of the bleed valve which in turn
depends on both the stable and the unstable part of the compressor
characteristic. Actuation of the compressor characteristic is
concluded to be a valuable tool in circumventing the rate limitation
of bleed valves for control of stall. By combining the compressor
characteristic identification tools and the analytic relations,
insights for designing a compressor-bleed pair are provided. +
A
This paper describes algorithms to generate trajectories
for differentially flat systems with zero dynamics.
Zero dynamics in flat systems occur when the flat outputs
are not the tracking outputs. This means that the output
trajectories can be fully parametrized by the flat outputs,
but that there is some additional freedom left.
This freedom can be exploited to minimize a cost criterion.
We parametrize the differentially
flat outputs by basis functions, and solve for the parameters
so as to track a prescribed trajectory approximately
while minimizing a cost function.
We focus on implementation issues and point out the computational
cost involved in the various problems. +
E
Extending Exponential Stabilizers for Nonholonomic Systems from Kinematic Controllers to Dynamic Controllers +
This paper describes an approach for extending (time-varying)
exponential stabilizers for nonholonomic systems from controllers which
command input velocity to controllers which command input torques. Due
to the nondifferentiable nature of exponential stablizers, additional
structure is required in order to ensure that the extended controllers
generate continuous control actions. In this paper we show how to
extend homogeneous controllers which use a nonstandard dilation adapted
to the problem. +
D
This paper describes the application of differential flatness
techniques from nonlinear control theory to mechanical (Lagrangian)
systems. Systems which are differentially flat have several useful
properties which can be exploited to generate effective control
strategies for nonlinear systems. For the special case of mechanical
control systems, much more geometric information is present and the
purpose of this paper is to explore the implications and features of
that class of systems. We concentrate on several worked examples
which illustrate the general theory and present a detailed catalog of
known examples of differentially flat mechanical systems. +
This paper describes the design, modeling, synthesis and preliminary validation of a protein concentration regulator circuit. The circuit is designed to maintain the level of a target protein to a reference level, specified by the amount of another protein. This is implemented using a single negative feedback loop that inhibited the production of the target protein once its concentration was equal to the reference amount. A mathematical model consisting of a set of ODEs is derived from mass action laws and Hill function approximations of protein production. Steady-state analysis of the model is used to predict parameter sensitivity and experimental behavior. We implemented this circuit in ''E. coli'' using scaffold-based sequestration and transcriptional activation. Preliminary experimental results show the system matching predictions from our model and performing the expected task. +
I
Interfacing TuLiP with the JPL Statechart Autocoder: Initial progress toward synthesis of flight software from formal specifications +
This paper describes the implementation of an in- terface connecting the two tools : the JPL SCA (Statechart Autocoder) and TuLiP (Temporal Logic Planning Toolbox) to enable the automatic synthesis of low level implementation code directly from formal specifications. With system dynamics, bounds on uncertainty and formal specifications as inputs, TuLiP synthesizes Mealy machines that are correct-by-construction. An interface is built that automatically translates these Mealy machines into UML statecharts. The SCA accepts the UML statecharts (as XML files) to synthesize flight-certified2 implementation code. The functionality of the interface is demonstrated through three example systems of varying com- plexity a) a simple thermostat b) a simple speed controller for an autonomous vehicle and c) a more complex speed controller for an autonomous vehicle with a map-element. In the thermostat controller, there is a specification regarding the desired temperature range that has to be met despite disturbance from the environment. Similarly, in the speed-controllers there are specifications about safe driving speeds depending on sensor health (sensors fail unpredictably) and the map-location. The significance of these demonstrations is the potential circumventing of some of the manual design of statecharts for flight software/controllers. As a result, we expect that less testing and validation will be necessary. In applications where the products of synthesis are used alongside manually designed components, extensive testing or new certificates of correctness of the composition may still be required. +
A
This paper describes the implementation and testing of Alice, the California Institute of Technology’s entry in the 2005 DARPA Grand Challenge. Alice utilizes a highly networked control system architecture to provide high performance, autonomous driving in unknown en- vironments. Innovations include a vehicle architecture designed for efficient testing in harsh environments, a highly sensory-driven approach to fuse sensor data into speed maps used by real-time trajectory optimization algorithms, health and contingency management algorithms to manage failures at the component and system level, and a software logging and display envi- ronment that enables rapid assessment of performance during testing. The system successfully completed several runs in the National Qualifying Event, but encountered a combination of sens- ing and control issues in the Grand Challenge Event that led to a critical failure after traversing approximately 8 miles. +
This paper describes the use of a domain-specific language, and an accompanying software tool, in constructing correct- by-construction control protocols for aircraft electric power systems. Given a base topology, the language consists of a set of primitives for standard specifications. The accompanying tool converts these primitives into formal specifica- tions, which are used to synthesize control protocols. We can then use TuLiP, a Python-based software toolbox, to synthesize centralized and distributed controllers. For sys- tems with no time involved in the specifications, this tool also provides an option to output specifications into a SAT-solver compatible format, thus reducing the synthesis problem to a satisfiability problem. We provide the results of our synthesis procedure on a range of topologies. +
C
This paper describes the use of time-delayed feedback to regulate the behavior of biological networks. The general ideas are demonstrated on specific transcriptional regulatory and neural networks. It is shown that robust yet tunable controllers can be constructed that provide the biological systems with model-engineered inputs. The results indicate that time delay modulation may serve as an efficient bio-compatible control tool. +
