Unscented Hypersonic Trajectory Optimization with a Heating-Rate Chance Constraint

The aerothermal load on an aerospace vehicle is one of the most critical conditions during hypersonic flight. To maximize performance, a typical hypersonic vehicle rides the maximum allowable value of the heating-rate constraint during a portion of its flight. Because atmospheric density has high uncertainty, guiding a hypersonic vehicle along a deterministic optimal trajectory will violate the maximum heating-rate limit with an unacceptable probability. To address this problem, we pose the maximum heating rate on the vehicle as a chance constraint in a tychastic trajectory optimization problem (from Tyche, the Greek goddess of chance). To generate a tractable problem formulation, the chance constraint is mapped to a constraint on a deviation measure of the heating rate. The resulting tychastic problem is transcribed to a constrained unscented trajectory optimization problem and solved by a guess-free, spectral algorithm. The validity of the entire approach is independently verified via a Monte Carlo analysis. Sample numerical results demonstrate how risk can be reduced from unsafe (i.e., 70% risk) to safe (i.e., near 0% risk) operations.