Mapping 3D guidance performance using approximate optimal cost-to-go function

Being able to define and measure the performance of guidance systems is fundamental to their proper development. This task is particularly challenging for unmanned aerial vehicles operating in complex spatial environment like cities or mountains, both of which are operational theaters of predilection. Previous research mainly focuses on relative performance metrics. This paper, introduces a framework to derive absolute metrics. The approach is based on the idea that many guidance problems have a meaningful formulation as an optimal control problem. Hence the idea is that absolute performance metrics can be based on an approximation of the optimal control problem. In the following we approximate the vehicle dynamics using motion primitives. The choice of motion primitives is based on an analysis of the vehicle flight performance based on experimental data. As performance metric, we use the approximate cost-to-go maps and associated optimal states computed via dynamic programming for a cell-based world representation. The cost-to-go map, which can be computed for any environment described by Digital Terrain Elevation Data (DTED), provides a comprehensive insight into the interrelation of space, optimal behavior, as driven by a user specified performance index. The only limitation in the choice of performance index is that it should be a function of attributes of the finite state motion primitives. The paper illustrates the method applied to an unmanned R-MAX helicopter (10ft rotor diameter) operating in the down town of San Francisco. Three performance indexes are analyzed: time, energy and length.