Massimiliano Vasile

Preliminary design of multiple gravity-assist trajectories

In this paper the preliminary design of multiple gravity-assist trajectories is formulated as a global optimization problem. An analysis of the structure of the solution space reveals a strong multimodality, which is strictly dependent on the complexity of the model. On the other hand it is shown how an oversimplification could prevent finding potentially interesting solutions. A trajectory model, which represents a compromise between model completeness and optimization problem complexity is then presented. The exploration of the resulting solution space is performed through a novel global search approach, which hybridizes an evolutionary based algorithm with a systematic branching strategy. This approach allows an efficient exploration of complex solution domains by automatically balancing local convergence and global search. A number of difficult multiple gravity-assist trajectory design cases demonstrates the effectiveness of the proposed methodology.

Multicriteria comparison among several mitigation strategies for dangerous near-Earth objects

In this paper a comparative assessment of the effectiveness of different deviation methods for Near Earth Objects is presented. Specifically, solar collector, nuclear interceptor, kinetic impactor, low-thrust propulsion, mass driver and gravity tug are modelled and compared. For each method, a mathematical model is developed in order to compute the achievable deviation. A multi-criteria optmization method is then used to construct the set of Pareto optimal solutions, minimizing the mass of the spacecraft at departure from the Earth and the warning time, i.e., the time from launch to the foreseen impact of the asteroid with the Earth, while at the same time maximizing the deviation. A dominance criterion is defined and used to compare all the Pareto sets for all the various mitigation strategies. Finally a Technology Readiness Level factor is associated to each strategy in order to estimate the required technological development.

An Inflationary Differential Evolution Algorithm for Space Trajectory Optimization

In this paper, we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of differential evolution (DE) is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points toward which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard DE on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima.

Preliminary Design of Low-Thrust Multiple Gravity-Assist Trajectories

The availability of electric engines as primary sources of propulsion has opened the doors to new scenarios for future interplanetary missions, but has increased the complexity of trajectory design. This paper proposes a novel approach to the preliminary design of interplanetary trajectories characterized by a combination of low-thrust propulsion and multiple gravity-assist maneuvers. Low-thrust arcs are obtained by shaping the trajectory through a set of parameterized pseudoequinoctial elements. The characterization of the solution space for a particular set of planetary encounters and a range of launch dates is then performed through a global optimization method, blending a particular evolutionary algorithm with a deterministic domain decomposition technique. The effectiveness of the proposed approach is demonstrated through a number of examples of the design of low-thrust, gravity-assist interplanetary trajectories.

Analysis of Some Global Optimization Algorithms for Space Trajectory Design

In this paper, we analyze the performance of some global search algorithms on a number of space trajectory design problems. A rigorous testing procedure is introduced to measure the ability of an algorithm to identify the set of ²-optimal solutions. From the analysis of the test results, a novel algorithm is derived. The development of the novel algorithm starts from the redefinition of some evolutionary heuristics in the form of a discrete dynamical system. The convergence properties of this discrete dynamical system are used to derive a hybrid evolutionary algorithm that displays very good performance on the particular class of problems presented in this paper.

Optimal impact strategies for asteroid deflection

This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple analytical formulas are derived from proximal motion equations. The proposed analytical formulation allows for an analysis of the optimal direction of the deviating impulse transferred to the asteroid. This ideal optimal direction cannot be achieved for every asteroid at any time; therefore, an analysis of the optimal launch opportunities for deviating a number of selected asteroids was performed through the use of a global optimization procedure. The results in this paper demonstrate that the proximal motion formulation has very good accuracy in predicting the actual deviation and can be used with any deviation method because it has general validity. Furthermore, the characterization of optimal launch opportunities shows that a significant deviation can be obtained even with a small spacecraft.

Improved shaping approach to the preliminary design of low-thrust trajectories

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.

A hybrid multiagent approach for global trajectory optimization

In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers (corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with existing deterministic and stochastic global optimization methods.

Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach

A multi-objective problem is addressed consisting of finding optimal low-thrust gravity-assist trajectories for interplanetary and orbital transfers. For this, recently developed pruning techniques for incremental search space reduction – which will be extended for the current situation – in combination with subdivision techniques for the approximation of the entire solution set, the so-called Pareto set, are used. Subdivision techniques are particularly promising for the numerical treatment of these multi-objective design problems since they are characterized (amongst others) by highly disconnected feasible domains, which can easily be handled by these set oriented methods. The complexity of the novel pruning techniques is analysed, and finally the usefulness of the novel approach is demonstrated by showing some numerical results for two realistic cases.

Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earths orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.