Spiral-diving trajectory optimization for hypersonic vehicles by second-order cone programming

Spiral maneuvering targets are well known to be very difficult to intercept due to its high maneuverability and unpredictability. This paper focuses on the optimization of a spiral-diving trajectory for a hypersonic vehicle to strike a stationary target. Second-order cone programming (SOCP), a subclass of convex optimization, is applied to achieve this optimization task. First, based on a detailed analysis of spiraling nature, the dynamics are partially reconstructed to better formulate the spiraling motion. Then, a nonconvex optimal control problem is formulated with the maximum impact velocity as a performance index. Constraints on the states, controls, and terminal conditions are helping to shape a feasible and practical spiraling trajectory. This nonconvex problem is convexified and subsequently discretized in a suitable form so that it can be easily solved in polynomial time using the existing primal-dual interior-point algorithm. In addition, a relaxation technique is used to convexify control constraints and is theoretically proved to be valid. The high reliability and efficiency of the successive SOCP method are verified by numerical examples and comparisons with other methods.