Minimum-Effort Guidance Using Quadratic Kinematics Approximation

A guidance law for intercepting a stationary target is derived based on solving the minimum effort optimal control problem with fixed time and a quadratic approximation of the kinematic equations. It is proven that this optimal control problem has, in general, a unique solution. Based on this solution, a guidance law is proposed that is shown to be implementable based on typically available sensor data, using a semi-analytic procedure. Numerical simulations show that the solution based on the second-order approximate kinematics matches closely the solution based on the original nonlinear kinematics that can only be obtained by numerical optimization.