A fast guidance algorithm for an autonomous navigation system

Abstract

In the present paper a fast and robust algorithm is presented for optimization of finite thrust orbit transfers. Generally optimal nominal trajectories are designed very accurately on ground solving two point boundary value problems with hard numerical work and computational time. Of course, an on board guidance system is needed to take into account the many perturbations occurring during the transfer trajectory. Two approaches are generally followed: in the first a steering program is actuated each time the navigation system detects sensible errors from the nominal trajectory. This guidance (perturbative guidance) is not optimal. The second approach (adaptive guidance) is to design a new optimal trajectory starting from the current state to the required final condition. This guidance is optimal but it requires the on board solution of two point boundary value problems any time it is necessary to update the trajectory. Therefore, complex algorithms and computational times, related to the convergence of the numerical solutions, are needed. In the present paper a method to reduce the complexity of adaptive guidance systems is described: the main point is to reduce the required two-point boundary value problems to differential problems with initial conditions only. This allows to design a fast and easy guidance law, suitable for on-board computers with a restricted storage capability, as in the case of small satellites and small launchers. The algorithm is robust, allowing rather large deviation from the nominal trajectory, and avoiding the use of uncontrolled iterative routines. This method is applied to an easy example: an in plane guidance law maximizing the final horizontal velocity.