Optimal Generalized Vector Explicit (GENEX) Homing Guidance of Nonholonomic Systems

The problem of optimal homing guidance is investigated for a target-missile intercept mission and under the general setting that the missile dynamics are constrained rather than of point mass. A nonholonomic missile model is derived in the Cartesian space, and based on the nonholonomic constraint that missile's Cartesian velocity components are changed through steering. For the nonholonomic kinematic model, the generalized vector explicit guidance (GENEX) problem is solved by applying the Pontryagin's minimum principle. The resulting fifth-order two-point boundary value problem is shown to be solvable as the nonlinearly designed GENEX guidance law. An illustrative example is presented to demonstrate that the nonlinearly designed GENEX guidance law provides better performance than the existing linearly designed one. Furthermore, it is shown that the proportional navigation time-to-go estimate commonly used in practice is not optimal even for missiles of linear point mass model. This comparative study shows not only the effectiveness of nonlinear GENEX guidance law but also future research directions for nonholonomic missile control.