Interaction with human musicians is a challenging task for robots as it involves online perception and precise\r\nsynchronization. In this paper, we present a consistent and theoretically sound framework for combining\r\nperception and control for accurate musical timing. For the perception, we develop a hierarchical hidden Markov\r\nmodel that combines event detection and tempo tracking. The robot performance is formulated as a linear\r\nquadratic control problem that is able to generate a surprisingly complex timing behavior in adapting the tempo.\r\nWe provide results with both simulated and real data. In our experiments, a simple Lego robot percussionist\r\naccompanied the music by detecting the tempo and position of clave patterns in the polyphonic music. The robot\r\nsuccessfully synchronized itself with the music by quickly adapting to the changes in the tempo
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