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We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslovs problem, which is defined as the motion of a rigid body with a vanishing projection of the body frame angular velocity on a given direction $boldsymbol{xi}$. We derive the optimal control formulation, first for an arbitrary group, and then in the classical realization of Suslovs problem for the rotation group $SO(3)$. We show that it is possible to control the system using the constraint $boldsymbol{xi}(t)$ and demonstrate numerical examples in which the system tracks quite complex trajectories such as a spiral.
In contrast to the Euler-Poincar{e} reduction of geodesic flows of left- or right-invariant metrics on Lie groups to the corresponding Lie algebra (or its dual), one can consider the reduction of the geodesic flows to the group itself. The reduced ve
Multiagent systems consist of agents that locally exchange information through a physical network subject to a graph topology. Current control methods for networked multiagent systems assume the knowledge of graph topologies in order to design distri
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and Hamilton-Dirac dynamica
In this paper we present necessary and sufficient conditions to guarantee the existence of invariant cones, for semigroup actions, in the space of the $k$-fold exterior product. As consequence we establish a necessary and sufficient condition for con
This paper considers the distributed sampled-data control problem of a group of mobile robots connected via distance-induced proximity networks. A dwell time is assumed in order to avoid chattering in the neighbor relations that may be caused by abru