Stabilizing and Maneuvering Angle Rigid Multiagent Formations With Double-Integrator Agent Dynamics

Abstract

This paper studies formation stabilization and maneuvering of mobile agents governed by double-integrator dynamics. The desired formation is described by a set of tripleagent angles. A carefully chosen such set of angle constraints guarantees that the desired formation is angle rigid. To achieve the desired angle rigid formation, a stabilization control law is proposed using only local velocity and direction measurements. We show that the closed-loop dynamics of the formation, when each agent is modeled by a double-integrator, are closely related to the corresponding one in single-integrator agent dynamics. Sufficient conditions are constructed to guarantee the closedloop stability for identical and distinct velocity damping gains, respectively. To guide an angle rigid formation to move with the desired translational velocity, orientation and scale, formation maneuvering laws are then proposed. Simulation examples are also provided to validate the results.

Maneuvering Angle Rigid Formations With Global Convergence Guarantees

“…Although the proposed bearing-constrained formation maneuvering law in [13] also only needs at least 2 leaders, it requires all the agents' coordinate frames to have the same orientation. Compared with [24] and [27], no inter-agent communication is required in ( 15) and (40). A requirement of the 3D maneuvering algorithm (40) is that the desired formation should satisfy Assumption 2, which holds when .…”

“…Under a leader-follower framework, the bearing-constrained formation tracking problem has been investigated in [21], [22], where the translational formation maneuvering is achieved by using relative position and absolute velocity measurements. Unlike the distance and bearing rigid formations alone, angle rigid formations can undergo simultaneously translational, rotational and scaling maneuvering because any angle constraints are invariant under these three types of formation maneuvering motions [7], [23], [24]. With the advantage of having more formation maneuvering freedoms, angle rigid formation maneuvering algorithms have been designed in [7] for single-integrator agents, and in [25] for double-integrator agents.…”