A new method in robot path generation is presented using an analysis of the characteristics of multi-robot collision avoidance. The research is based on the concept of the collision map, where the collision between two robots is presented by a collision region and a crossing curve TLVSTC (traveled length versus servo time curve). Analytic collision avoidance is considered by translating the collision region in the collision map. The 4 different translations of collision regions correspond to the 4 parallel movements of the actual original robot path in the real world. This analysis is applied to path modifications where the analysis of collision characteristics is crucial and the resultant path for collision avoidance is generated. Also, the correlations between the translations of the collision region and robot paths are clarified by analyzing the collision/non-collision areas. The influence of the changes of robot velocity is investigated analytically in view of collision avoidance as an example.