  Multi-goal path finding (MGPF) aims to find a closed and collision-free path
to visit a sequence of goals orderly. As a physical travelling salesman
problem, an undirected complete graph with accurate weights is crucial for
determining the visiting order. Lack of prior knowledge of local paths between
vertices poses challenges in meeting the optimality and efficiency requirements
of algorithms. In this study, a multi-task learning model designated Prior
Knowledge Extraction (PKE), is designed to estimate the local path length
between pairwise vertices as the weights of the graph. Simultaneously, a
promising region and a guideline are predicted as heuristics for the
path-finding process. Utilizing the outputs of the PKE model, a variant of
Rapidly-exploring Random Tree (RRT) is proposed known as PKE-RRT. It
effectively tackles the MGPF problem by a local planner incorporating a
prioritized visiting order, which is obtained from the complete graph.
Furthermore, the predicted region and guideline facilitate efficient
exploration of the tree structure, enabling the algorithm to rapidly provide a
sub-optimal solution. Extensive numerical experiments demonstrate the
outstanding performance of the PKE-RRT for the MGPF problem with a different
number of goals, in terms of calculation time, path cost, sample number, and
success rate.
