A programmable central pattern generator with bounded output

Abstract Despite extensive studies on cyclic tasks in robotics, definitive solutions for the problem of trajectory generation for periodic motions have not been achieved so far. In this paper, we present an approach for online trajectory generation from a library of desired periodic trajectories. The proposed approach consists of a Central Pattern Generator (CPG) architecture ensuring entrainment of any periodic trajectory, smooth motion modulation and observing position and velocity limits of the robot. The proposed CPG is composed of a synchronized network of novel bounded output oscillatory systems. Every oscillatory system is a three-dimensional dynamical system encoding a one-dimensional periodic function as a stable limit cycle. We also use the state transformation method to bound the oscillator’s output and its first time derivative. Finally, we present a synchronization technique to construct a synchronized network of the proposed oscillators for generating multi dimensional periodic functions. Using Lyapunov based arguments, we prove that the proposed CPG ensures stability, convergence, and synchronization of the desired trajectory. The soundness of the proposed oscillator and the resulting CPG are validated both in simulations and experiments on the humanoid robot iCub.