Iterative Learning-Based Trajectory Optimization Using Fourier Series Basis Functions

This letter presents an iterative, online trajectory optimization algorithm for systems performing repetitive processes. While typical iterative learning techniques are formulated for tracking control applications, a precise definition of the tracking reference is required. In repetitive applications where the optimal tracking reference is not fully defined, there exists an opportunity to improve system performance by altering the
trajectory
of the system based on information rich signals from previous cycles. In this letter, we develop an algorithm to optimize the parameterized trajectory of a system in real time utilizing constrained optimization of a cost function generated from the performance values of the previous cycle. Simulation results are used to illustrate the implementation of this iterative trajectory optimization framework while also benchmarking the performance against a norm optimal iterative learning controller with perfect system knowledge.