![]() The control architecture has an automatic parameter estimation process that is usually employed for optimization of the imitation stage. The MSR we have developed for controlling ROMI is a feature extractor for learning to imitate human players in a duet. In this paper we introduce the robotic device ROMI together with its control architecture, the Musical State Representation "MSR" and focus on parameter estimation for imitation of duo players by ROMI. ROMI's intelligent control architecture also has the ability to provide player identification and performance training. The presented RObotic Musical Instrument "ROMI", is aimed at jointly playing two instruments that belong to two different classes of acoustic instruments and improvises while assisting others in an orchestral performance. The last images formed are reflections of the refelctions reflection.A new approach to musical improvisation based on controlled relaxation of imitation parameters by a robotic acoustic musical device, is presented in this paper. The second reflections are the images formed of the reflections of the The first reflection is the reflection of the objects. Let's take a 60-60-60 degree triangle mirror systemĪnd look at the resulting reflection. Three mirror system has more complicated math but it all boils down to reflections and reflactions of reflections. In each of the segments only one image formed is real so the actual number of images is (n+1)-1=n, so n=(360/ θ)-1 (8). If α= θ, it means that 360 is a multiple of θ, then (n+1) θ=360, and n+1=(360/ θ), where n+1 is equal to number of segments the whole 360 degrees is divided by the images of the mirrors. So, θ has to be less than 360°, n(θ)+α=360, where α is the angle at the top is less than θ. The images only overlap when the angle at the top is equal to θ and the images do not form when the angle at the top is less than θ. ![]() When an object is placed between the two mirrors there are images through mirror 1 and mirror 2 and mirror images of these images through 1’ and 2’.Īlso, remember the mirror images have their own images in the mirrors 1’’ and 2’’ and so on until the point where two images get overlapped or their rays get overlapped. ![]() This continues to the other end throughout 360 degrees. Mirror 2’’ is the mirror image of mirror 2 through the imaged mirror 1’ and mirror 1’’ is the mirror image of mirror 1 through imaged mirror 2’. The mirrors 1 and 2 are at some angle, θ, and 2’ is the image of mirror 2 through mirror 1.Īlso, 1’ is the mirror image of mirror 1 through mirror 2. Points are determined by dividing 180° by the angle between the mirrors.Īs the angle decreases the number of folds increase. Using this table, we can see that folds are determined by dividing 360° by the angle between the two mirrors and subtracting one. See table two for the number of folds create as the angle is change. Using this applet to find the number of folds at different angles, we can derive a relationship between the angle between the mirrors and number of folds formed. In this applet we can manipulate the angels between the mirrors and find the number of reflections or folds present when changing the angle of the mirror. To make this easier there is an online physics applet we can use to simulate a 2-mirror system. It is difficult to create this mirror system in real life if you don't have two mirrors and a designated space between the mirrors that produce known angles. The smaller the angle the higher number of reflections, those reflections are called folds. In the 2-mirror system the angle between the two mirror surfaces determines the number reflections that make up the image. The 2-mirror system is the most common system used in kaleidoscopes.
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