Decentralized rigidity maintenance control with range measurements for multi-robot systems

Abstract

Abstract-This work proposes a fully decentralized strategy for maintaining the formation rigidity of a multi-robot system using only range measurements, while still allowing the graph topology to change freely over time. In this direction, a first contribution of this work is an extension of rigidity theory to weighted frameworks and the rigidity eigenvalue, which when positive ensures the infinitesimal rigidity of the framework. We then propose a distributed algorithm for estimating a common relative position reference frame amongst a team of robots with only range measurements in addition to one agent endowed with the capability of measuring the bearing to two other agents. This first estimation step is embedded into a subsequent distributed algorithm for estimating the rigidity eigenvalue associated with the weighted framework. The estimate of the rigidity eigenvalue is finally used to generate a local control action for each agent that both maintains the rigidity property and enforces additional constraints such as collision avoidance and sensing/communication range limits and occlusions. As an additional feature of our approach, the communication and sensing links among the robots are also left free to change over time while preserving rigidity of the whole framework. The proposed scheme is then experimentally validated with a robotic testbed consisting of 6 quadrotor UAVs operating in a cluttered environment.

Human-Collaborative Schemes in the Motion Control of Single and Multiple Mobile Robots

“…A graph has an algebraic representation given by the adjacency and the incidence matrixes, denoted with A and E, respectively (see, e.g., [1], [2] for the formal definitions of these and all the algebraic graph concepts mentioned in this chapter). Another matrix that plays an important role in the control of networks of robots is the Laplacian matrix L = E T E ∈ R N×N , which is always positive semidefinite, i.e., with all real and non-negative eigenvalues.…”

“…The main algebraic object of what is called infinitesimal rigidity [2] is the so called rigidity matrix R (G , p 1 , . . .…”

“…The authors in [2] present a distributed algorithm that ensures the preservation of the rigidity resorting to local relative distance measurements only. Experiments are shown in which multiple human operators can interact with the group of robots providing velocity references while the group of aerial robots preserves the required degree of rigidity in an autonomous way.…”

Formation Tracking of Heterogeneous Mobile Agents Using Distance and Area Constraints

“…Control of formations specified only by interagent angles has been studied by Basiri et al [9]. Formation and communication changes have also been studied to find suitable control laws that maintain rigidity in Zelazo et al [10]. Experimental work is found in Fidan et al [11] using local video cameras and Antonelli et al [12] with laser range finder devices.…”

Bearing rigidity theory in SE(3)

“…Main notions about distance rigidity are illustrated in [5]- [7]: these works explain how distance constraints for a framework can be summarized into a unique matrix whose rank A. Franchi is with LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France, afranchi@laas.fr determines the infinitesimal rigidity properties of the system, providing a necessary and sufficient condition. In such a context, a framework is generally represented by means of the bar-and-joint model where agents are represented as points joined by bars whose fixed lengths enforce the interagent distance constraints.…”