M.Sc Thesis

M.Sc StudentTsin Alon
SubjectFast Optimal Trajectory Shaping for TBM and LFA Interceptor
up to Hand Over
DepartmentDepartment of Mechanical Engineering
Supervisors PROF. Aharon Bar-Gill
Full Thesis textFull thesis text - English Version


A fast Algorithm for optimal trajectory shaping of an interceptor of ballistic and low-flying targets is proposed. The trajectory is planned from launch point (or any point during interceptor  flight) to a Hand Off (HO) point, where the interceptor locks on the target and begins the Homing stage. The optimality of the trajectory is designed to satisfy a cost function consisting of Minimum Flight Time and Minimum Interceptor Energy Loss considerations. The trajectory is additionally constrained by Interceptor maneuverability and by a velocity vector constraint at HO point. This Algorithm is an expansion of two similar works in the realm of general aviation in literature.

The algorithm consists of two parts - An offline part, that is calculated beforehand, and a real-time part that is designed to be run during real time interceptions.

The offline part divides the nD space, including the geometric 3D space, along with other state vector components around the launcher into a grid of discrete nodes. Subsequently, it simulates transition between neighboring nodes using a simplified 3DOF physical model of the interceptor combined with a Proportional Navigation guidance law and calculates the cost function of the transition. Then, a graph of interconnected nodes and costs of transition between viable nodes is created by the program.

The Real-time part of the algorithm finds the optimal trajectory between any two nodes in the previously created graph by using a problem-specific variant of the Dijkstra algorithms, which assures global optimality of the solution while maintaining low run-time values.

The algorithm is verified in several scenarios using the Matlab GPOPS "black box" routine. In addition, The algorithm has been implemented on several test scenarios. The results show that the algorithm can provide real-time, optimal trajectories for the interceptor while efficiently coping with No Flight Zones and allowing for in-flight trajectory updates.

The research presented here yields an algorithm that calculates globally optimal trajectories to HO points, engaging TBMs & LFAs. It's main features and contributions include (a) Construction of between-nodes transition costs by perceiving the (i) nodes as Virtual Targets, and employing an optimal guidance algorithm,

 (b) Efficient tackling of scenarios with non-analytic boundary conditions such as LFAs over DTM,

 (c) Versatility of application to a variety of missiles, design configuration tradeoffs for a missile and cost functions,

(d) Ease of application and fast run times.