Minimal parametric sensitivity trajectories for nonlinear systems

Trajectory optimization techniques can be used to minimize error norms on both state and controls with respect to a reference. However, without sufficient control authority, resulting controllers can be sensitive to variations in model parameters. This paper presents a method to incorporate parametric sensitivity in optimal control calculations to develop optimally insensitive trajectories which can be better tracked under open loop and limited gain feedback conditions. As it builds on existing nonlinear optimal control theory, the approach can be easily implemented and applies to a variety of system types. The effectiveness of the technique is demonstrated using a simplified vehicle model. Controllers developed are capable of tracking highly aggressive and dynamically infeasible paths while minimizing sensitivity to variations in modeled friction.