7,152 research outputs found
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.
Formation Control of Rigid Graphs with a Flex Node Addition
This paper examines stability properties of distance-based formation control
when the underlying topology consists of a rigid graph and a flex node
addition. It is shown that the desired equilibrium set is locally
asymptotically stable but there exist undesired equilibria. Specifically, we
further consider two cases where the rigid graph is a triangle in 2-D and a
tetrahedral in 3-D, and prove that any undesired equilibrium point in these
cases is unstable. Thus in these cases, the desired formations are almost
globally asymptotically stable.Comment: The full version of this paper with general extensions has been
submitted to a journal for publicatio
Bearing-Based Formation Maneuvering
This paper studies the problem of multi-agent formation maneuver control
where both of the centroid and scale of a formation are required to track given
velocity references while maintaining the formation shape. Unlike the
conventional approaches where the target formation is defined by inter-neighbor
relative positions or distances, we propose a bearing-based approach where the
target formation is defined by inter-neighbor bearings. Due to the invariance
of the bearings, the bearing-based approach provides a natural solution to
formation scale control. We assume the dynamics of each agent as a single
integrator and propose a globally stable proportional-integral formation
maneuver control law. It is shown that at least two leaders are required to
collaborate in order to control the centroid and scale of the formation whereas
the followers are not required to have access to any global information, such
as the velocities of the leaders.Comment: To appear in the 2015 IEEE Multi-Conference on Systems and Control
(MSC2015); this is the final versio
A Unified Dissertation on Bearing Rigidity Theory
This work focuses on the bearing rigidity theory, namely the branch of
knowledge investigating the structural properties necessary for multi-element
systems to preserve the inter-units bearings when exposed to deformations. The
original contributions are twofold. The first one consists in the definition of
a general framework for the statement of the principal definitions and results
that are then particularized by evaluating the most studied metric spaces,
providing a complete overview of the existing literature about the bearing
rigidity theory. The second one rests on the determination of a necessary and
sufficient condition guaranteeing the rigidity properties of a given
multi-element system, independently of its metric space
Bearing-based formation control with second-order agent dynamics
We consider the distributed formation control problem for a network of agents using visual measurements. We propose solutions that are based on bearing (and optionally distance) measurements, and agents with double integrator dynamics. We assume that a subset of the agents can track, in addition to their neighbors, a set of static features in the environment. These features are not considered to be part of the formation, but they are used to asymptotically control the velocity of the agents. We analyze the convergence properties of the proposed protocols analytically and through simulations.Published versionSupporting documentatio
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