A random sampling scheme for path planning
International Journal of Robotics Research
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Efficient algorithms for collision-free energy sub-optimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of way-points through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are energy-optimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasi-quadratic parameter optimization problem in terms of the way-points parameters. The mathematical structure of the problem is further exploited to develop gradient-based algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20).