Feasible Path Search Algorithm on Two Dimensional Manifold S²

Spherical Barrier Free RRT path search method (SBF-RRT) can be solved the problem of the feasible path search on two-dimensional manifold S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. SBF-RRT algorithm is based on RRT algorithm, an area uniform sampling model based on Monte Carlo integration method can be solved the problem of uniform random sampling on two-dimensional manifold S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. The approximate distance measurement function of two-dimensional manifold surface distance between two points on manifold S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> can be obtained by arc segment proportional segmentation method. The angle cutting method can be solved the new node generation model on S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> surface. The continuous interpolation method can be solved the directed connection problem between two points on the manifold S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. The feasibility and effectiveness of the SBF-RRT algorithm have been verified through simulation experiments. The SBF-RRT algorithm can be searched for a feasible path on the two-dimensional manifold S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>.