Model-Based Nonlinear Cluster Space Control of Mobile Robot Formations

Multi-robot systems have the potential to improve application-specific performance by offering redundancy, increased coverage and throughput, flexible reconfiguration, and/or spatially diverse functionality (Kitts & Egerstedt, 2008). For mobile systems, a driving consideration is the method by which the motions of the individual vehicles are coordinated. Centralized approaches have been successfully demonstrated (Yamaguchi & Arai, 1994; Tan & Lewis, 1996) and have been found to be useful for material transport, regional synoptic sampling, and sensing techniques where active stimulus and/or signal reception are spatially distributed (Hashimoto et al., 1993; Rus et al., 1995; Tang et al., 2006). Such approaches, however, typically suffer from limited scalability and the need for global information. As an alternative, decentralized approaches have been shown to hold great promise in addressing scalability and limited information exchange (Siljak, 1991; Ikeda, 1989; Yang et al., 2005); such approaches often employ control strategies that are behavioral (Balch & Hybinette, 2000; Flinn, 2005; Khatib, 1985), biologically-inspired (Murray, 2007), optimization-based (Dunbar & Murray, 2006), or potential field-based (Leonard & Fiorelli, 2001; Ogren et al., 2004; Justh & Krishnaprasad, 2004; Stipanovic et al., 2004). In this chapter, we present our work relating to the cluster space control technique for multi-robot systems, specifically its implementation using a nonlinear, model-based controller in both kinematic and dynamic forms. The cluster space state representation provides a simple means of specifying and monitoring the geometry and motion characteristics of a cluster of mobile robots without sacrificing flexibility in specifying formation constraints or limiting the ability to fully articulate the formation (Kitts & Mas, 2009). The cluster space control 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 monitoring. These state variables form the system’s cluster space. Cluster space state variables are related to robot-specific state variables through a formal set of kinematic transforms. These transforms allow cluster commands to be converted to robot-specific commands, and for sensed robot-specific state data to be converted to cluster space state data. With the formal kinematics defined, the controller is composed such that desired motions are specified and control compensations are computed in the cluster space. For a kinematic controller, suitable for robots with negligible dynamics such as many low-speed wheeled robots, compensation commands are transformed to robot space through the inverse Jacobian relationship. For a dynamic controller, appropriate for clusters of marine and aerial 4