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Near-Earth asteroid (NEA) 99942 Apophis provides a typical example for the evolution of asteroid orbits that lead to Earth-impacts after a close Earth-encounter that results in a resonant return. Apophis will have a close Earth-encounter in 2029 with potential very close subsequent Earth-encounters (or even an impact) in 2036 or later, depending on whether it passes through one of several less than 1 km-sized gravitational keyholes during its 2029-encounter. A pre-2029 kinetic impact is a very favorable option to nudge the asteroid out of a keyhole. The highest impact velocity and thus deflection can be achieved from a trajectory that is retrograde to Apophis orbit. With a chemical or electric propulsion system, however, many gravity assists and thus a long time is required to achieve this. We show in this paper that the solar sail might be the better propulsion system for such a mission: a solar sail Kinetic Energy Impactor (KEI) spacecraft could impact Apophis from a retrograde trajectory with a very high relative velocity (75-80 km/s) during one of its perihelion passages. The spacecraft consists of a 160 m × 160 m, 168 kg solar sail assembly and a 150 kg impactor. Although conventional spacecraft can also achieve the required minimum deflection of 1 km for this approx. 320 m-sized object from a prograde trajectory, our solar sail KEI concept also allows the deflection of larger objects. For a launch in 2020, we also show that, even after Apophis has flown through one of the gravitational keyholes in 2029, the solar sail KEI concept is still feasible to prevent Apophis from impacting the Earth, but many KEIs would be required for consecutive impacts to increase the total Earth-miss distance to a safe value
Interplanetary trajectories for low-thrust spacecraft are often characterized by multiple revolutions around the sun. Unfortunately, the convergence of traditional trajectory optimizers that are based on numerical optimal control methods depends strongly on an adequate initial guess for the control function (if a direct method is used) or for the starting values of the adjoint vector (if an indirect method is used). Especially when many revolutions around the sun are re-
quired, trajectory optimization becomes a very difficult and time-consuming task that involves a lot of experience and expert knowledge in astrodynamics and optimal control theory, because an adequate initial guess is extremely hard to find. Evolutionary neurocontrol (ENC) was proposed as a smart method for low-thrust trajectory optimization that fuses artificial neural networks and evolutionary algorithms to so-called evolutionary neurocontrollers (ENCs) [1]. Inspired by natural archetypes, ENC attacks the trajectoryoptimization problem from the perspective of artificial intelligence and machine learning, a perspective that is quite different from that of optimal control theory. Within the context of ENC, a trajectory is regarded as the result of a spacecraft steering strategy that maps permanently the actual spacecraft state and the actual target state onto the actual spacecraft control vector. This way, the problem of searching the optimal spacecraft trajectory is equivalent to the problem of searching (or "learning") the optimal spacecraft steering strategy. An artificial neural network is used to implement such a spacecraft steering strategy. It can be regarded as a parameterized function (the network function) that is defined by the internal network parameters. Therefore, each distinct set of network parameters defines a different network function and thus a different steering strategy. The problem of searching the optimal steering strategy is now equivalent to the problem of searching the optimal set of network parameters. Evolutionary algorithms that work on a population of (artificial) chromosomes are used to find the optimal network parameters, because the parameters can be easily mapped onto a chromosome. The trajectory optimization problem is solved when the optimal chromosome is found. A comparison of solar sail trajectories that have been published by others [2, 3, 4, 5] with ENC-trajectories has shown that ENCs can be successfully applied for near-globally optimal spacecraft control [1, 6] and that they are able to find trajectories that are closer to the (unknown) global optimum, because they explore the trajectory search space more exhaustively than a human expert can do. The obtained trajectories are fairly accurate with respect to the terminal constraint. If a more accurate trajectory is required, the ENC-solution can be used as an initial guess for a local trajectory optimization method. Using ENC, low-thrust trajectories can be optimized without an initial guess and without expert attendance.
Here, new results for nuclear electric spacecraft and for solar sail spacecraft are presented and it will be shown that ENCs find very good trajectories even for very difficult problems. Trajectory optimization results are presented for 1. NASA's Solar Polar Imager Mission, a mission to attain a highly inclined close solar orbit with a solar sail [7] 2. a mission to de ect asteroid Apophis with a solar sail from a retrograde orbit with a very-high velocity impact [8, 9] 3. JPL's \2nd Global Trajectory Optimization Competition", a grand tour to visit four asteroids from different classes with a NEP spacecraft