iRiSC: Iterative Risk Sensitive Control for Nonlinear Systems with Imperfect Observations

This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with computational complexity similar to the iterative linear quadratic regulator algorithm. The proposed algorithm introduces feasibility gaps to allow the initialization with non-feasible trajectories. Moreover, an approximation for the expectation of the general nonlinear cost is proposed to enable an iterative line search solution to the planning problem. The optimal estimator is also derived along with the controls minimizing the general stochastic nonlinear cost. Finally extensive simulations are carried out to show the increased robustness the proposed framework provides when compared to the risk neutral iLQG counter part. To the authors' best knowledge, this is the first algorithm that computes risk aware optimal controls that are a function of both the process noise and measurement uncertainty.