There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

/pdf/information-flow-and-cooperative-control-of-vehicle-4ws61wioze.pdf

Information flow and cooperative control of vehicle formations

In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

/pdf/event-triggered-real-time-scheduling-of-stabilizing-control-t1gebqsndp.pdf

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

/pdf/coverage-control-for-mobile-sensing-networks-3gs75qafnm.pdf

Coverage control for mobile sensing networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

http://www.seas.ucla.edu/~tabuada/Papers/Hierarchical.pdf

Hierarchical trajectory refinement for a class of nonlinear systems

Trajectory generation and motion planning for nonlinear control systems is an important and difficult problem. In this paper, we provide a constructive method for hierarchical trajectory generation and hierarchical motion planning. The approach is based on the recent notion of /spl Phi/-related control systems. Given a control affine system satisfying certain assumptions, we project the trajectory planning problem onto a /spl Phi/-related control system of smaller dimension. Trajectories designed for the smaller, abstracted system are guaranteed, by construction, to be feasible for the original system. Constructive procedures are provided for refining trajectories of the coarser system to the more detailed system.

/pdf/hierarchical-trajectory-generation-for-a-class-of-nonlinear-1494eii65y.pdf

Hierarchical trajectory generation for a class of nonlinear systems

The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify analysis and synthesis for these models. In system theory, a similar notion is also of interest in order to develop modular analysis and design tools for purely continuous or hybrid control systems. We introduce two notions of bisimulation for nonlinear systems. We present a differential-algebraic characterization of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions. Furthermore, we also show that all bisimilar systems of different dimension are of this form.

/pdf/bisimilar-control-affine-systems-gooe4lp2ft.pdf

Bisimilar control affine systems

An upcoming frontier for distributed computing might literally save lives in future military operations. In civilian scenarios, significant efficiencies were gained from interconnecting devices into networked services and applications that automate much of everyday life from smart homes to intelligent transportation. The ecosystem of such applications and services is collectively called the Internet of Things (IoT). Can similar benefits be gained in a military context by developing an IoT for the battlefield? This paper describes unique challenges in such a context as well as potential risks, mitigation strategies, and benefits.

Will Distributed Computing Revolutionize Peace? The Emergence of Battlefield IoT

Feedback control laws are predominantly implemented on digital platforms as periodic tasks. Although periodicity simplifies the analysis and design of the implementation, new applications call for more efficient utilization of available resources such as processor utilization. To address this issue, new implementation paradigms, such as event-triggered and self-triggered control, have recently been proposed. These policies allow for a dynamic allocation of resources, since the execution times of the control task are defined according to the current state of the system. In this paper we continue our exploratory journey in the field of self-triggered control for nonlinear systems. In our previous work, we exploited the geometry of homogeneous and polynomial control systems to identify one dimensional manifolds along which the execution times scaled in a predictable manner. In this paper we complement our previous work by focusing on manifolds where the times remain constant. By merging both ideas new self-trigger conditions are derived, outperforming existing techniques.

Paulo Tabuada

Papers

Hierarchical trajectory refinement for a class of nonlinear systems

Hierarchical trajectory generation for a class of nonlinear systems

Bisimilar control affine systems

Will Distributed Computing Revolutionize Peace? The Emergence of Battlefield IoT

Isochronous manifolds in self-triggered control