论文标题
利用最佳控制
Path Planning in a Riemannian Manifold using Optimal Control
论文作者
论文摘要
我们考虑对象在Riemannian歧管中的运动计划，其中对象从初始点转移到了最终点，利用最佳控制。考虑到Pontryagin最小化原理，我们计算将对象从初始点转向到最终点所需的最佳控件。在时间t方面求解了最佳对照，并显示出具有标准1的情况，这将是弧形长度参数化的极端轨迹（是pontryagin原理的解决方案）的情况。极端轨迹被认为是里曼尼亚歧管上的大地测量学。因此，我们计算了Riemannian结构的大地曲率和高斯曲率。
We consider the motion planning of an object in a Riemannian manifold where the object is steered from an initial point to a final point utilizing optimal control. Considering Pontryagin Minimization Principle we compute the Optimal Controls needed for steering the object from initial to final point. The Optimal Controls were solved with respect to time t and shown to have norm 1 which should be the case when the extremal trajectories, which are the solutions of Pontryagin Principle, are arc length parametrized. The extremal trajectories are supposed to be the geodesics on the Riemannian manifold. So we compute the geodesic curvature and the Gaussian curvature of the Riemannian structure.
