:This research proposes an algorithm for the online reference joint trajectory generation for biped walking assuming a library of desired trajectories. The proposed algorithm is a central pattern generator (CPG) whose steady state response can match any desired trajectory. For this purpose, at first, a non-integrated CPG comprising a synchronized network of oscillators is presented. To this end, a 3-dimensional oscillator is designed whose limit cycle can match any one-dimensional periodic signal. Then, the oscillator dynamic is modified by a state transformation method for generating a bounded output. Finally, a synchronized network of the proposed bounded output oscillators is presented for generating multi-dimensional periodic signals. The performance of the non-integrated CPG for generating the reference joint trajectory for free arm motion, as well as, walking is studied by conducting a few simulations and experiments on the humanoid robot iCub. The results show that the non-integrated CPG is not suitable for walking, because the reference trajectory generated for different joints is not always synchronous. Therefore, at second, a (2n+1)-dimensional bounded output oscillator is designed whose limit cycle can match any n-dimensional periodic signal. Then, an integrated CPG consisting of only one such an oscillator is presented. The Lyapunov arguments prove that both proposed CPGs ensure the stability and convergence of the multi-dimensional periodic signal. Moreover, the stability and convergence of the desired signal are independent of the CPG parameters. Thus, the parameter tuning is not required for generating the desired trajectory. Besides that, the output of the proposed CPGs is bounded, and hence the generated reference joint trajectory complies with the joint position and velocity constraints of the robot. Finally, the integrated CPG is modified for integrating with the sensory feedback while the stability and convergence of the desired trajectory are preserved. Keywords:Online Trajectory Generation, Central Pattern Generator, Programmable Oscillator, Bounded Position and Velocity, Synchronization, Biped
