Centralized and Decentralized Multi-Robot Control Methods using the Cluster Space Control Framework Ignacio Mas and Christopher Kitts Abstract— The cluster space control technique promotes sim- plified specification and monitoring of the motion of mobile multi-robot systems. Previous work has established the concep- tual foundation of this approach and has experimentally verified and validated its use. In this publication, we summarize the defi- nition of the cluster space framework for planar robots and study some of the most common formation control methods found in the literature from the cluster space perspective. In doing this, we show that our proposed formation control framework can be implemented in various ways; as a centralized or distributed system, and with different levels of scalability depending on the particular cluster definition chosen. In particular, lead- follower, potential functions and virtual structures approaches are analyzed with the intent of addressing the generality and flexibility of the cluster space formation control approach. Experimental results illustrate the different implementations which are then compared and contrasted. Index Terms— cluster space, multi-robot systems, formation control, distributed control. I. I NTRODUCTION Robotic systems offer many advantages to accomplishing a wide variety of tasks given their strength, speed, precision, repeatability, and ability to withstand extreme environments. Whereas most robots perform these tasks in an isolated man- ner, interest is growing in the use of tightly interacting multi- robot systems to improve performance in current applications and to enable new capabilities. Potential advantages of multi- robot systems include redundancy, increased coverage and throughput, flexible reconfigurability and spatially diverse functionality. For mobile systems, one of the key technical considerations is the technique used to coordinate the motions of the individual vehicles. A wide variety of techniques have been and continue to be explored, drawing on work in control theory, robotics, and biology [1] and applicable for robotic ap- plications throughout land, sea, air, and space. Notable work in this area includes the use of leader-follower techniques, in which follower robots control their position relative to a designated leader [2], [3]. A variant of this is leader-follower chains, in which follower robots control their position relative to one or more local leaders, which, in turn, are following This work has been sponsored through a variety of funding sources to include Santa Clara University Technology Steering Committee grant TSC131 and National Science Foundation Grant No. CNS-0619940. The authors are with the Robotic Systems Laboratory, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, USA iamas,ckitts@scu.edu other local leaders in a network that ultimately is led by a designated leader. For example, a follower robot might position itself with respect to the local leader by sensing and controlling its relative distance and bearing to that leader, or by maintaining its relative distance between two local leaders [4]. Several approaches employ artificial attraction/repulsion fields as a construct to establish formation-keeping forces for individual robots within a formation. For example, potential fields may be used to implement repulsive forces among neighboring robots and between robots and objects in the field in order to symmetrically surround an object to be transported [5]. Potential fields and behavioral motion primitives have also been used to compute reactive robot drive commands that balance the need to arrive at the final destination, to maintain relative locations within the formation, and to avoid obstacles [6], [7]. As another example, the virtual bodies and artificial potentials (VBAPs) approach uses potential fields to maintain the relative distances both between neighboring robots as well as between robots and reference points, or ’virtual leaders’, that define the ’virtual body’ of the formation [8], [9]. This approach has been successfully demonstrated in field tests of underwater robots performing a distributed sampling mission [10]. The motivation of the proposed cluster space approach is to promote the simple specification and monitoring of the motion of a mobile multi-robot system. This strategy conceptualizes the n-robot system as a single entity, a cluster, and desired motions are specified as a function of cluster attributes, such as position, orientation, and geometry. These attributes guide the selection of a set of independent system state variables suitable for specification, control, and moni- toring. These state variables form the system’s cluster space. The particular selection of such variables play an essential role in the dynamic behavior of the system as well as in the different resulting control architectures, for example, in centralized or distributed approaches. Previous work presented a generalized framework for de- veloping the cluster space approach for a system of n robots, each with m degrees of freedom (DOF)[11]. This framework has been successfully demonstrated for both holonomic and non-holonomic centralized systems with limited numbers of rovers, including automated trajectory control [12] and potential field-based obstacle avoidance [13]. The method has also been implemented for formations of marine surface