41,361 research outputs found
Bearing rigidity and formation stabilization for multiple rigid bodies in SE(3)
In this work, we first distinguish different notions related to bearing rigidity in graph theory and then further investigate the formation stabilization problem for multiple rigid bodies. Different from many previous works on formation control using bearing rigidity, we do not require the use of a shared global coordinate system, which is enabled by extending bearing rigidity theory to multi-agent frameworks embedded in the three dimensional special Euclidean group SE(3) and expressing the needed bearing information in each agent's local coordinate system. Here, each agent is modeled by a rigid body with 3 DOFs in translation and 3 DOFs in rotation. One key step in our approach is to define the bearing rigidity matrix in SE(3) and construct the necessary and sufficient conditions for infinitesimal bearing rigidity. In the end, a gradient-based bearing formation control algorithm is proposed to stabilize formations of multiple rigid bodies in SE(3)
Bearing Rigidity Theory: characterization and control of mixed formations and localization
The bearing rigidity theory is applied to mixed formations composed by agents having heterogeneous domains. Necessary and sufficient conditions are provided for the characterization of infinitesimally bearing rigid formations. The stabilization problem for such formations is addressed and a distributed solution proposed and validated through simulations. A location recovery algorithm for fully-actuated formations embedded in SE(3) is presented along with analytical proofs.ope
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 Distributed Control and Estimation of Multi-Agent Systems
This paper studies the distributed control and estimation of multi-agent
systems based on bearing information. In particular, we consider two problems:
(i) the distributed control of bearing-constrained formations using relative
position measurements and (ii) the distributed localization of sensor networks
using bearing measurements. Both of the two problems are considered in
arbitrary dimensional spaces. The analyses of the two problems rely on the
recently developed bearing rigidity theory. We show that the two problems have
the same mathematical formulation and can be solved by identical protocols. The
proposed controller and estimator can globally solve the two problems without
ambiguity. The results are supported with illustrative simulations.Comment: 6 pages, to appear in the 2015 European Control Conferenc
Distributed scaling control of rigid formations
Recently it has been reported that biased range-measurements among
neighboring agents in the gradient distance-based formation control can lead to
predictable collective motion. In this paper we take advantage of this effect
and by introducing distributed parameters to the prescribed inter-distances we
are able to manipulate the steady-state motion of the formation. This
manipulation is in the form of inducing simultaneously the combination of
constant translational and angular velocities and a controlled scaling of the
rigid formation. While the computation of the distributed parameters for the
translational and angular velocities is based on the well-known graph rigidity
theory, the parameters responsible for the scaling are based on some recent
findings in bearing rigidity theory. We carry out the stability analysis of the
modified gradient system and simulations in order to validate the main result.Comment: 6 pages In proceedings 55th Conference on Decision and Control, year
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