Dynamic Control of Mobile Multirobot Systems: The Cluster Space Formulation

Abstract

The formation control technique called cluster space control promotes simplified specification and monitoring of the motion of mobile multirobot systems of limited size. Previous paper has established the conceptual foundation of this approach and has experimentally verified and validated its use for various systems implementing kinematic controllers. In this paper, we briefly review the definition of the cluster space framework and introduce a new cluster space dynamic model. This model represents the dynamics of the formation as a whole as a function of the dynamics of the member robots. Given this model, generalized cluster space forces can be applied to the formation, and a Jacobian transpose controller can be implemented to transform cluster space compensation forces into robot-level forces to be applied to the robots in the formation. Then, a nonlinear model-based partition controller is proposed. This controller cancels out the formation dynamics and effectively decouples the cluster space variables. Computer simulations and experimental results using three autonomous surface vessels and four land rovers show the effectiveness of the approach. Finally, sensitivity to errors in the estimation of cluster model parameters is analyzed. INDEX TERMSCluster space, multirobot systems, dynamic control, formation control, marine robotics.

Quaternions and Dual Quaternions: Singularity-Free Multirobot Formation Control

“…In previous work, implementations of a cluster space (CS) controller relied on the use of an inverse cluster space Jacobian matrix for the case of rateresolved robots or on cluster space Jacobian transpose matrices for dynamic control architectures [5]. Such configurations allow for a controller to operate directly on the cluster space variables and their errors, but suffer from limitations related to representation singularities.…”

“…Earlier work by the authors have not addressed this topic in detail, as most of the work [5][6][7][8] dealt with wheeled ground robots or marine autonomous surface vessels, where the formation operates in a common plane. This characteristic either limits the existence of singular poses or allows then to be easily avoided by choosing alternative definitions to operate around singularity-free poses.…”

“…This allows to conceptualize the formation as a full degree of freedom virtual kinematic mechanism that can be intuitively specified, controlled, and monitored by an operator or an autonomous supervisor. The cluster space approach has been successfully implemented in a wide variety of robotic platforms, ranging from land rovers to marine surface vessel systems [5], and for target applications such as escorting/patrolling [6] and multirobot object manipulation [7].…”

Distributed formation control of multiple unmanned aerial vehicles over time-varying graphs using population games

“…The equilibrium point condition in (8) shows that all the portion of decision makers for the follower agents i ∈ F converges to values such that the formation references are met for all the coordinate positions and yaw angle d ∈ D (see Figure 1). Besides, the portion of decision makers p d l , for all d ∈ D, and for the fictitious strategy, adopts a value that satisfies the simplex ∆ d .…”

“…For instance, a review of different control techniques has been presented in [3], where approaches and issues such as consensus, optimization aspects, distributed tasks assignment and estimation have been discussed. In [8], a cluster-space formulation has been presented for control purposes of multi-agent systems. In [13], formation of UAVs is addressed with optimal control using only information from a fixed neighborhood set.…”