Design of a nonlinear adaptive natural oscillator: Towards natural dynamics exploitation in cyclic tasks

In this paper, we present the dynamical equations of a nonlinear adaptive natural oscillator (NANO) in order to exploit the natural dynamics in robotic systems. The presented oscillator tries to minimize an energy-based cost function by adapting the shape and frequency of the reference trajectory. Stability, convergence, and optimality of this oscillator are guaranteed analytically. Moreover, the performance of this oscillator is investigated by applying it to three different types of robotic models; i.e., the pendulum, the adaptive-toy, and the hopper-leg.