Data-driven differential dynamic programming using Gaussian processes

We present a Bayesian nonparametric trajectory optimization framework for systems with unknown dynamics using Gaussian Processes (GPs), called Gaussian Process Differential Dynamic Programming (GPDDP). Rooted in the Dynamic Programming principle and second-order local approximations of the value function, GPDDP learns time-varying optimal control policies from sampled data. Based on this framework, we propose two algorithms for implementations. We demonstrate the effectiveness and efficiency of the proposed framework using three numerical examples.