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In this paper, we proposed a method to estimate the destination of walking persons from their walking patterns, for avoidance of collision accidents between pedestrians and robots in a human-robot coexistence environment. We adopted the hidden Markov model (HMM) as a model to represent walking patterns. We constructed a model for each movement pattern. A movement pattern was defined with a departure point and destination point of a person. Comparing the likelihood with the achieved model, we discriminated walking patterns for which the destination is unknown. We did some experiments in an actual environment to verify the availability of the proposed method. Results show that the discrimination ratio approached 80% within 2 s of observation.