Selective learning with a forgetting factor for robotic motion control

A class of learning control algorithms with a forgetting factor 1>α>0 and without differentiation of velocity signals is proposed, which updates the input by u_k+1=(1-α) u_k+αu ₀+Φe_k, where u_k and e_k stand for command input and velocity error at kth exercise, respectively. The robustness of this learning control with respect to reinitialization errors, fluctuation of dynamics, and measurement noise is studied. It is shown that the exponential passivity of displacement robot dynamics plays a crucial role in the uniform boundedness of transient behaviors and the convergence in the progress of learning. A method called selective learning, which updates u₀ in the long-term memory by selecting the best command among the past several trials, is proposed. It is claimed that this method accelerates the speed of convergence