A Distributed Technique for Localization of Agent Formations from Relative Range Measurements

Autonomous agents deployed or moving on land for the purpose of carrying out coordinated tasks need to have good knowledge of their absolute or relative position. For large formations it is often impractical to equip each agent with an absolute sensor such as GPS, whereas relative range sensors measuring inter-agent distances are cheap and commonly available. In this setting, the paper considers the problem of autonomous, distributed estimation of the position of each agent in a networked formation, using noisy measurements of inter- agent distances. The underlying geometrical problem has been studied quite extensively in various fields, ranging from molecular biology to robotics, and it is known to lead to a hard non-convex optimization problem. Centralized algorithms do exist that work reasonably well in finding local or global minimizers for this problem (e.g. semidefinite programming relaxations). Here, we explore a fully decentralized approach for localization from range measurements, and we propose a computational scheme based on a distributed gradient algorithm with Barzilai-Borwein stepsizes. The advantage of this distributed approach is that each agent may autonomously compute its position estimate, exchanging information only with its neighbors, without need of communicating with a central station and without needing complete knowledge of the network structur

A distributed optimization framework for localization and formation control: applications to vision-based measurements

Multiagent systems have been a major area of research for the last 15 years. This interest has been motivated by tasks that can be executed more rapidly in a collaborative manner or that are nearly impossible to carry out otherwise. To be effective, the agents need to have the notion of a common goal shared by the entire network (for instance, a desired formation) and individual control laws to realize the goal. The common goal is typically centralized, in the sense that it involves the state of all the agents at the same time. On the other hand, it is often desirable to have individual control laws that are distributed, in the sense that the desired action of an agent depends only on the measurements and states available at the node and at a small number of neighbors. This is an attractive quality because it implies an overall system that is modular and intrinsically more robust to communication delays and node failures

Distributed stabilization control of rigid formations with prescribed orientation

Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in both 2-D and 3-D spaces. The proposed controllers involve the commonly-used gradient descent control for shape stabilization, and an additional term to control the directions of certain relative position vectors associated with certain chosen agents. In this control framework, we show the minimal number of agents which should have knowledge of a global coordinate system (2 agents for a 2-D rigid formation and 3 agents for a 3-D rigid formation), while all other agents do not require any global coordinate knowledge or any coordinate frame alignment to implement the proposed control. The exponential convergence to the desired rigid shape and formation orientation is also proved. Typical simulation examples are shown to support the analysis and performance of the proposed formation controllers.Comment: This paper was submitted to Automatica for publication. Compared to the submitted version, this arXiv version contains complete proofs, examples and remarks (some of them are removed in the submitted version due to space limit.

Bearing rigidity theory and its applications for control and estimation of network systems: Life beyond distance rigidity

Distributed control and location estimation of multiagent systems have received tremendous research attention in recent years because of their potential across many application domains [1], [2]. The term agent can represent a sensor, autonomous vehicle, or any general dynamical system. Multiagent systems are attractive because of their robustness against system failure, ability to adapt to dynamic and uncertain environments, and economic advantages compared to the implementation of more expensive monolithic systems