Model-Based Nonlinear Cluster Space Control of Mobile Robot Formations

IGNACIO MAS; CHRISTOPHER KITTS; ROBERT LEE

Multi-Robot Systems, Trends and Development

InTech Publisher

Año: 2011; p. 53 - 70

Multi-robot systems have the potential to improve application-specific performance byoffering redundancy, increased coverage and throughput, flexible reconfiguration, and/orspatially diverse functionality. For mobile systems, a drivingconsideration is the method by which the motions of the individual vehicles are coordinated. In this chapter, we present ourwork relating to the cluster space control technique for multi-robot systems, specifically itsimplementation using a nonlinear, model-based controller in both kinematic and dynamicforms. The cluster space state representation provides a simple means of specifying andmonitoring the geometry and motion characteristics of a cluster of mobile robots withoutsacrificing flexibility in specifying formation constraints or limiting the ability to fullyarticulate the formation. The cluster space control strategy conceptualizesthe n-robot system as a single entity, a cluster, and desired motions are specified as afunction of cluster attributes, such as position, orientation, and geometry. These attributesguide 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 spacestate variables are related to robot-specific state variables through a formal set of kinematictransforms. These transforms allow cluster commands to be converted to robot-specificcommands, and for sensed robot-specific state data to be converted to cluster space statedata. With the formal kinematics defined, the controller is composed such that desiredmotions are specified and control compensations are computed in the cluster space. For akinematic controller, suitable for robots with negligible dynamics such as many low-speedwheeled robots, compensation commands are transformed to robot space through the inverseJacobian relationship. For a dynamic controller, appropriate for clusters of marine and aerial robots, compensation commands are transformed to robot space through a Jacobian transposerelationship. In either case, the resulting robot-level commands are transformed to actuatorcommands through a vehicle-level inverse Jacobian. In the following sections, we review the cluster spacecontrol strategy to include its formulation, the development of the appropriate kinematicrelationships, and the composition of its control architecture. We also present the developmentof a kinematic and a dynamic nonlinear, model-based partitioned controller. For each case, wepresent experimental results that verify these techniques and demonstrate the capabilities ofthe cluster space control approach.