Unscented Optimal Control for Space Flight

The routine use of pseudospectral (PS) optimal control techniques in space applications1 has generated new opportunities for performance enhancement. One of these opportunities is related to the interaction of an outer guidance loop with inner control loops. In current flight applications, knowledge of the initial state vector, padded with high conservatism, is considered necessary to maintain overall controllability and stability of the flight guidance and control system. Although in-flight knowledge of the state vector is possible with the proper use of sensors and estimation techniques, the junction conditions during flight segmentation are not known to a sufficient precision during the design phase and pre-flight planning operations. In order to manage this uncertainty, the current practice is to generate an optimal guidance trajectory based on a mean value of the junction state vector and flow down the anticipated flight perturbations to inner-loop requirements of tracking and stability. In turn, the capability margins of the inner control loop are passed up to the table of guidance requirements for the outer loop. This practice of uncertainty management not only breeds overly conservative designs, it also adds significantly to the cost of both design and operations of a space system. This is because the design process involves repeated iterations between the inner and outer loops which adds to increased cost and delayed schedules. Furthermore, the operational cost is unnecessarily increased through several human-in-the-loop tests and pre-flight verifications that are driven by the need to keep the operational conditions within the design specifications. Despite all these checks and tests, the actual flight perturbations may indeed stress the control system beyond its capabilities leading to very costly failures. In this paper, we pose the fundamental question: is it possible to better design a guidance solution that accounts for uncertainties in the junction conditions? One approach is to generate a field of extremals and select the appropriate solution based on in-flight conditions. While this is technically possible, this approach generates new problems on methods to interpolate between the 1 I. M. Ross and M. Karpenko, "A Review of Pseudospectral Optimal Control: From Theory to Flight," Annual Reviews in Control, Vol. 36, pp. 182-197, 2012.