Real-Time Atmospheric Entry Trajectory Computation Using Parametric Sensitivities

The real-time generation of optimal trajectories and controls for nonlinear systems is a technology of interest to many applications. The online solution of an optimal control Problem (OCP) is often not computationally feasible on current embedded systems hardware. We present a method to generate a near-optimal control sequence and the corresponding state trajectory based on the parametric sensitivity Analysis (PSA) of nonlinear programs (NLPs) which does not require performing the classical gradient based NLP process online and hence reduces the computational load. The OCP is transcribed into a parametric NLP which is solved offline for a nominal set of parameters. Additionally the parametric sensitivities of the optimal solution with respect to different types of perturbations are computed at discrete points along the nominal trajectory. The sensitivities are used online in a Taylor expansion of the nominal solution and an iterative feasibility and optimality restoration to compute a new near-optimal control sequence and trajectory from an off-nominal state to the terminal set without solving a NLP. This process is repeated iteratively in the neighborhood of the nominal trajectory. The proposed method is demonstrated for the guided, hypersonic entry of a small capsule into the Martian atmosphere. The PSA algorithm is used as feed forward command and trajectory generation to provide the input for a dragenergy tracking controller