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This paper investigates the optimization approach to generate waypoints for the Mars landing problem in the context of employing the zero-effort-miss/zero-effort-velocity feedback guidance algorithm. For a power-limited engine, the waypoint optimization problem in the presence of state constraints is converted to an equivalent standard quadratic programming problem, which can be solved efficiently. In the case with a thrust-limited engine, by introducing a continuously differentiable function to approximate the standard saturation function, the optimal waypoint can be determined using open-source optimization software. This novel idea exploits parameter optimization techniques for feedback control implementation, thus, it can combine the advantages of open-loop and closed-loop methods to achieve near-optimal performance with acceptable robustness, while meeting various practical constraints and requirements.

This paper presents a comprehensive review of spacecraft guidance algorithms for asteroid intercept and rendezvous missions. Classical proportional navigation (PN) guidance is reviewed first, followed by pulsed PN guidance, augmented PN guidance, predictive feedback guidance, Lambert guidance, and other guidance laws based on orbit perturbation theory. Optimal feedback guidance laws satisfying various terminal constraints are also discussed. Finally, the zero-effort-velocity (ZEV) error, analogous to the well-known zero-effort-miss (ZEM) distance, is introduced, leading to a generalized ZEM/ZEV guidance law. These various feedback guidance laws can be easily applied to real asteroid intercept and rendezvous missions. However, differing mission requirements and spacecraft capabilities will require continued research on terminal-phase guidance laws.

High-speed intercept missions, which include kinetic impactors and nuclear penetration devices, may be required to mitigate the threat from a near-Earth object. Various guidance laws, including the pulsed proportional navigation (PPN) guidance and advanced predictive guidance, are examined for the autonomous terminal-phase guidance and control of asteroid interceptors. The asteroid Apophis is used as an illustrative example to show that current technology can be used for high-speed intercept missions. A mission scenario based on a 2-dimensional orbital intercept model is simulated using classical, modified, and predictive guidance laws. Simulations show that intercept is possible even using the simple PPN guidance law for small target asteroids with an acceptable margin of error. The mission scenario is also simulated with a high-fidelity simulation program, called CLEON. The study results verify the applicability of the various guidance laws examined, and also confirm the suitability of the CLEON software for asteroid intercept mission design.

The new vision for advanced missions to asteroids, including soft landing, presents many challenges that have essential differences from previous experiences with planetary landing. This paper focuses on two subjects pertaining to asteroid proximity operations: highaccuracy modeling of the gravitational environment and fuel-efficient guidance and control algorithm design. Both a spherical harmonic expansion method and a polyhedron shape model are used for modeling the gravitational environment of an irregular-shaped asteroid. The effects of Coriolis and centripetal accelerations are also examined. The ZEM/ZEV (Zero-Effort-Miss/Zero-Effort-Velocity) feedback guidance algorithm is in general not an optimal control scheme, however it is conceptually simple and easy to implement, and in many cases it approaches optimality. Two mission phases, orbital transfer between observational orbits and soft landing, are numerically simulated using different implementations of the ZEM/ZEV algorithm. These simulations show that the ZEM/ZEV algorithm is suitable for asteroid proximity operations, and important considerations for using the algorithm are discussed.