Fig. 5

Convergence of the adaptive oscillator with simulated and experimental data. The two left graphs of both panels (simulated data and experimental data) display the oscillator input (left: simulated; right: actual position of the patient; black line) and the learned position by the adaptive oscillator (red line) as x and x _osc (top) and y and y _osc (bottom) as a function of time. The top right panel displays the actual movement in space (x and y axes) and the trajectory being estimated by the adaptive oscillator during 3 s. The bottom right panel displays the adaptive oscillator state variables as a function of time as the offsets φ _{x,o s c} , and φ _{y,o s c} and the amplitude α _osc in [cm], the phase ϕ _osc in [rad] and the angular velocity ω _osc in [rad/s]. After two cycles, the oscillator synchronizes with the actual signal and gives a smooth version of the input circle (left: simulated; right: drawn by the patient)