Three-dimensional Vector Cooperative Guidance Law for Flight Vehicles with Time and Angle Constraints

A three-dimensional vector cooperative guidance law with integrated time and angle constraints is developed to address the coordinated attack problem targeting large strategic objectives by multiple flight vehicles. Initially, a twodimensional impact angle control guidance law is established under pure proportional navigation, utilizing optimal error dynamics theory. This law ensures that the terminal line -of-sight angle converges to the desired value while maintaining favorable initial performance characteristics. Subsequently, the two-dimensional guidance law is extended to threedimensional space via vector guidance method. A time constraint bias term is introduced to derive the dynamic expression of flight time error. By applying fixed - time convergence theory, a three-dimensional guidance law is obtained, which enables flight vehicles to impact the target at the desired time while satisfying impact angle constraints without the need for planar motion decoupling. Numerical simulations are conducted to validate the effectiveness of the proposed guidance law, demonstrating high guidance and cooperative accuracy in multi - flight -vehicle cooperative attack scenarios.