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We presented and evaluated an approach based on HMM, GMR, and dynamical systems to allow robots to acquire new skills by imitation. Using HMM allowed us to get rid of the explicit time dependency that was considered in our previous work , by encapsulating precedence information within the statistical representation. In the context of separated learning and reproduction processes, this novel formulation was systematically evaluated with respect to our previous approach, LWR , LWPR , and DMPs . We finally presented applications on different kinds of robots to highlight the flexibility of the proposed approach in three different learning by imitation scenarios.