Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomposition, potential fields or sampling-based. In this work, we focus on using numerical optimization, which is understudied for solving motion planning problems. This lack of interest in the favor of sampling-based methods is largely due to the non-convexity introduced by narrow passages. We address this shortcoming by grounding the solution in differential geometry. We demonstrate through a series of experiments on 3 Dofs and 6 Dofs narrow passage problems, how modeling explicitly the underlying Riemannian manifold leads to an efficient interior-point non-linear programming solution.

中文翻译：

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解决窄通道运动规划问题的内点法

运动规划问题的算法解决方案已经被研究了五年。自 1969 年 A* 的发展以来，已经研究了许多方法，传统上分为网格分解、势场或基于采样的方法。在这项工作中，我们专注于使用数值优化来解决运动规划问题。对基于采样的方法缺乏兴趣主要是由于狭窄的通道引入的非凸性。我们通过在微分几何中解决这个问题来解决这个缺点。我们通过对 3 自由度和 6 自由度窄通道问题的一系列实验证明，显式建模底层黎曼流形如何导致有效的内点非线性规划解决方案。