In this work, we present solutions to the flocking and target interception problems of multiple nonholonomic unicycletype robots using the distance-based framework. The control laws are designed at the kinematic level and are based on the rigidity properties of the graph modeling the sensing/communication interactions among the robots. An input transformation is used to facilitate the control design by converting the nonholonomic model into the single integrator-like equation. We assume only a subset of the robots know the desired, time-varying flocking velocity or the target's motion. The resulting control schemes include distributed, variable structure observers to estimate the unknown signals. Our stability analyses prove convergence to the desired formation while tracking the flocking velocity or the target motion. The results are supported by experiments.

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In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance and area-based scheme for the formation control of n-agent systems in two dimensions using directed graphs and the singleintegrator model. We show that under certain conditions on the edge lengths of the triangulated desired formation, the control ensures almost-global convergence to the correct formation.

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SUMMARYIn this paper, we present a new leader–follower type solution to the translational maneuvering problem for formations of multiple, non-holonomic wheeled mobile robots. The solution is based on the graph that models the coordination among the robots being a spanning tree. Our control law incorporates two types of position errors: individual tracking errors and coordination errors for leader–follower pairs in the spanning tree. The control ensures that the robots globally acquire a given planar formation while the formation as a whole globally tracks a desired trajectory, both with uniformly ultimately bounded errors. The control law is first designed at the kinematic level and then extended to the dynamic level. In the latter, we consider that parametric uncertainty exists in the equations of motion. These uncertainties are accounted for by employing an adaptive control scheme. The main contributions of this work are that the proposed control scheme minimizes the number of control links and global position measurements, and accounts for the uncertain vehicle dynamics. The proposed formation maneuvering controls are demonstrated experimentally and numerically.