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.

Coverage control for mobile sensing networks

A survey of multi-agent formation control

The paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape. A new technique based on complex Laplacian is introduced to address the problems of which formation shapes specified by inter-agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability. Concerning the first question, we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex Laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter-agent specification of the formation shape is 2-rooted. Concerning the second question, a distributed and linear control law is developed based on the complex Laplacian specifying the target formation shape, and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed-loop system at desired locations are given. Moreover, we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re-design and change their control laws.

Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian

A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings While many previous works focused on the bearing rigidity of two-dimensional frameworks, a first contribution of this paper is to extend these results to arbitrary dimensions It is shown that a framework in an arbitrary dimension can be uniquely determined up to a translation and a scaling factor by the bearings if and only if the framework is infinitesimally bearing rigid In this paper, the proposed bearing rigidity theory is further applied to the bearing-only formation stabilization problem where the target formation is defined by inter-neighbor bearings and the feedback control uses only bearing measurements Nonlinear distributed bearing-only formation control laws are proposed for the cases with and without a global orientation It is proved that the control laws can almost globally stabilize infinitesimally bearing rigid formations Numerical simulations are provided to support the analysis

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Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.

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Dynamic Vehicle Routing for Robotic Systems

This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally.

Stabilisation of infinitesimally rigid formations of multi-robot networks

This paper proposes a local gradient control law to stabilize a group of robots to a target formation. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold describing the target formation.

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Stabilization of infinitesimally rigid formations of multi-robot networks

Mobile autonomous robots present an interesting example within the subject of distributed control systems. There are several motor-driven wheeled robots that are autonomous in that their actions are subject only to sensor inputs and pre-loaded programs; there is no leader and no supervisor. The problem is to design the onboard controllers so that the robots perform a useful cooperative task. For example, suppose the robots all have antennas, forming an antenna array, and the collective task is to shape and point the radiated beam of the array. This requires the robots to form a certain geometric pattern. Previous work in this area has focussed mainly on the rendezvous problem, where the desired task is to meet at a common location (without navigational instruments). In this paper the task is to form a prescribed geometric arrangement, such as a regular polygon. The arrangement is defined by a rigid graph with link lengths. Nonlinear control laws are developed and the closed-loop equilibria are studied in detail.

Laura Krick

Papers

Stabilisation of infinitesimally rigid formations of multi-robot networks

Stabilization of infinitesimally rigid formations of multi-robot networks

Getting Mobile Autonomous Robots to Form a Prescribed Geometric Arrangement