In order to solve the problem of low success rate due to high coupling degree, the concept of a coupling degree matrix is proposed and a safe interval multi-robot path k robust planning(CkR-SIPP) algorithm based on coupling degree matrix is presented. 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 the 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, the path planning of all robots is completed in the order of high priority to low priority. Simulation tests on the Benchmark map show that the proposed CkR-SIPP algorithm is superior to both the kR-CBS algorithm and the IkR-CBS algorithm, with an average improvement of 19.2% over the kR-SIPP algorithm, which can effectively improve the scheme reliability of the multi-robot path k-robust planning system.