Aiming at the problem of low solution success rate due to high node coupling degree in multi-robot path robust planning, a Coupling degree matrix based k-Robust Safe Interval Path Planning (CkR-SIPP) algorithm based on coupling degree matrix is proposed. Firstly, according to the path planning scheme, the coupling degree information of global map nodes is collected to form the coupling degree matrix, which is constantly updated during the planning process. Secondly, A safe interval is introduced to avoid conflicts between robots, and A* algorithm with k time expansion is used as the low-level path planning algorithm for multi-robots, where k is the set robust factor, which can deal with the robust planning problem in the spatio-temporal relationship of multi-robots. At the same time, the information in the coupling degree matrix is fed back to the A* algorithm with k time extension as a routing constraint, and the nodes with high coupling degree are avoided as far as possible. Finally, simulation tests are carried out on the Benchmark map, and the results show that the proposed CkR-SIPP algorithm can effectively improve the scheme reliability of multi-robot path k-robust planning system, which is 19.2% higher than the kR-SIPP algorithm.