On a Class of Hierarchical Formations of Unicycles and Their Internal Dynamics

Abstract

Abstract-This paper studies a class of hierarchical formations for an ordered set of + 1 unicycle robots: the first robot plays the role of the leader and the formation is induced through a constraint function , so that the position and orientation of the th robot depends only on the pose of the preceding ones. We study the dynamics of the formation with respect to the leader's reference frame by introducing the concept of reduced internal dynamics, we characterize its equilibria and provide sufficient conditions for their existence. The discovered theoretical results are applied to the case in which the constraint induces a formation where the th robot follows a convex combination of the positions of the previous 1 vehicles. In this case, we prove that if the curvature of the leader's trajectory is sufficiently small, the positions and orientations of the robots, relative to the leader's reference frame, are confined in a precise polyhedral region.

Mobile Formation Coordination and Tracking Control for Multiple Nonholonomic Vehicles

“…For example, the formation shape stabilization problem where the follower maintains a desired distance and orientation with respect to its leader's coordinate frame is studied in [22], and the formation control problem that the follower maintains a desired relative position with respect to its leader's coordinate frame is studied in [23]. As an extension of the leader-follower scheme, the formation shapes in [24], [25], [26] are specified in the follower's coordinate frame. For example, a desired distance and orientation of the leader's barycenter with respect to the follower's coordinate frame is used in [24], [25], and the formation shape in [26] is specified by a desired relative position of the leader's barycenter with respect to the follower's coordinate frame.…”

A New Characterization of Mobility for Distance-Bearing Formations of Unicycle Robots

“…It is finally worth pointing out here that an early attempt towards a characterization of the mobility of leader-follower formations of unicycles was made in [20]. However, the analysis in [20] departs from ours, since it does not leverage the nonslip condition for centered wheels, but the more abstract, system-theoretic notion of internal dynamics.…”

Rendezvous of Nonholonomic Robots via Output-Feedback Control Under Time-Varying Delays

“…which define a first-order model often used in the literature on control of nonholonomic systems -see e.g., [14], [27]- [29] and [15]. In such model the control inputs are the velocities v and ω.…”

“…This is a typical two-stage formation problem. In the first, a rendezvous algorithm is required for the stabilization of the agents [11]- [13] and in the second a formation-tracking controller is employed [14]- [15].…”