论文标题
非体力学机械系统的几何最佳轨迹跟踪
Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems
论文作者
论文摘要
我们通过将问题重新塑造为最佳最佳控制问题来研究非独立系统的轨迹的跟踪。选择成本函数是为了最大程度地减少非实体系统轨迹和所需的参考轨迹之间的位置和速度的误差，这两者都随着定义非物质约束的分布而演变。该问题是从几何框架中研究的。最佳条件是由蓬蒂拉金的最大原理和各种观点确定的，该原理允许构建几何积分器。示例和数值模拟显示以验证结果。
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the distribution which defines the nonholonomic constraints. The problem is studied from a geometric framework. Optimality conditions are determined by the Pontryagin Maximum Principle and also from a variational point of view, which allows the construction of geometric integrators. Examples and numerical simulations are shown to validate the results.
