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.

Given a control system and a desired property, an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail. We consider the abstraction problem for Hamiltonian control systems, that is, we preserve the Hamiltonian structure during the abstraction process. We show how the mechanical structure of Hamiltonian control systems can be exploited to simplify the abstraction computations and we provide conditions under which the local accessibility properties of the abstracted Hamiltonian system are equivalent to the local accessibility properties of the original Hamiltonian control system.

/pdf/abstractions-of-hamiltonian-control-systems-459zt1i5nu.pdf

Abstractions of Hamiltonian control systems

Satellite Attitude Control Problem, pp 393-432 in Control of Complex Systems (Edd.: K. Åström, P. Albertos, M. Blanke, A. Isidori, W. Schaufelberger)

Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lyapunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a "relaxation" of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.

Robustness of Control Barrier Functions for Safety Critical Control

We develop a network synthesis scenario, which is built around a concrete perimeter surveillance application, yet we believe captures a number of the challenges and requirements that are common to other tactical communication and computational network applications. The proposed scenario addresses the problem of binary population identification within a perimeter: our goal is to synthesize a sensing and computing network that classifies people moving within a given perimeter into one of two categories (e.g., friend or foe). We discuss several open challenges that we organize across the following clusters: sensor placement, communication network provisioning and optimization, computational task placement, dynamic re-synthesis and resilience under adversarial settings. We also briefly discuss approaches that attempt to address such challenges.

Network synthesis for tactical environments: scenario, challenges, and opportunities

Persistent surveillance with aerial vehicles (drones) subject to connectivity and power constraints is a relatively uncharted domain of research. To reduce the complexity of multi-drone motion planning, most state-of-the-art solutions ignore network connectivity and assume unlimited battery power. Motivated by this and advances in optimization and constraint satisfaction techniques, we introduce a new persistent surveillance motion planning problem for multiple drones that incorporates connectivity and power consumption constraints. We use a recently developed constrained optimization tool (Satisfiability Modulo Convex Optimization (SMC)) that has the expressivity needed for this problem. We show how to express the new persistent surveillance problem in the SMC framework. Our analysis of the formulation based on a set of simulation experiments illustrates that we can generate the desired motion planning solution within a couple of minutes for small teams of drones (up to 5) confined to a 7 × 7 × 1 grid-space.

Paulo Tabuada

Papers

Abstractions of Hamiltonian control systems

Satellite Attitude Control Problem, pp 393-432 in Control of Complex Systems (Edd.: K. Åström, P. Albertos, M. Blanke, A. Isidori, W. Schaufelberger)

Robustness of Control Barrier Functions for Safety Critical Control

Network synthesis for tactical environments: scenario, challenges, and opportunities

Persistent Connected Power Constrained Surveillance with Unmanned Aerial Vehicles