ترغب بنشر مسار تعليمي؟ اضغط هنا

Constraint Control of Nonholonomic Mechanical Systems

70   0   0.0 ( 0 )
 نشر من قبل Stuart Rogers
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

178 - Mikhail V. Deryabin 2007
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 ctor field has a remarkable hydrodynamic interpretation: it is a velocity field for a stationary flow of an ideal fluid. Right- or left-invariant symmetry fields of the reduced field define vortex manifolds for such flows. Consider now a mechanical system, whose configuration space is a Lie group and whose Lagrangian is invariant to left translations on that group, and assume that the mass geometry of the system may change under the action of internal control forces. Such system can also be reduced to the Lie group. With no controls, this mechanical system describes a geodesic flow of the left-invariant metric, given by the Lagrangian, and thus its reduced flow is a stationary ideal fluid flow on the Lie group. The standard control problem for such system is to find the conditions, under which the system can be brought from any initial position in the configuration space to another preassigned position by changing its mass geometry. We show that under these conditions, by changing the mass geometry, one can also bring one vortex manifold to any other preassigned vortex manifold.
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 buted control laws for achieving desired global system behaviors. However, this assumption may not be valid for situations where graph topologies are subject to uncertainties either due to changes in the physical network or the presence of modeling errors especially for multiagent systems involving a large number of interacting agents. Motivating from this standpoint, this paper studies distributed control of networked multiagent systems with uncertain graph topologies. The proposed framework involves a controller architecture that has an ability to adapt its feed- back gains in response to system variations. Specifically, we analytically show that the proposed controller drives the trajectories of a networked multiagent system subject to a graph topology with time-varying uncertainties to a close neighborhood of the trajectories of a given reference model having a desired graph topology. As a special case, we also show that a networked multi-agent system subject to a graph topology with constant uncertainties asymptotically converges to the trajectories of a given reference model. Although the main result of this paper is presented in the context of average consensus problem, the proposed framework can be used for many other problems related to networked multiagent systems with uncertain graph topologies.
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 l systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler-Poincare-Suslov equations with advected parameters and the implicit Lie-Poisson-Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin-Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.
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 trollability of a class of bilinear control systems.
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 pt changes of positions when updating information from neighbors. Distributed sampled-data control laws are designed based on nearest neighbour rules, which in conjunction with continuous-time dynamics results in hybrid closed-loop systems. For uniformly and independently initial states, a sufficient condition is provided to guarantee synchronization for the system without leaders. In order to steer all robots to move with the desired orientation and speed, we then introduce a number of leaders into the system, and quantitatively establish the proportion of leaders needed to track either constant or time-varying signals. All these conditions depend only on the neighborhood radius, the maximum initial moving speed and the dwell time, without assuming a prior properties of the neighbor graphs as are used in most of the existing literature.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا