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The paper proposes a new geometric approach to the stabilization of a hierarchical formation of unicycle robots. Hierarchical formations consist of elementary leader-follower units disposed on a rooted tree: each follower sees its relative leader as a fixed point in its own reference frame. Robots' linear velocity and trajectory curvature are forced to satisfy some given bounds. The major contribution of the paper is to study the effect of these bounds on the admissible trajectories of the main leader. In particular, we provide recursive formulas for the maximum velocity and curvature allowed for the main leader, so that the robots can achieve the desired formation while respecting their input constraints. An original formation control law is proposed and the asymptotic stabilization is proved. Simulation experiments illustrate the theory and show the effectiveness of the proposed designs.
Date of Publication: Oct. 2009