A successful autonomous spacecraft must be able to navigate “intelligently”. Intelligent navigation entails finding and following collision-free paths through space which can be traversed in a reasonable time and which use a reasonable amount of fuel. Several spacecraft have been recently proposed for which intelligent navigation abilities are either desirable or necessary. Among these are NASA's AERCam, PSA, and ISS Inspector, ESA's Automated Transfer Vehicle (ATV), and DARPA's Orbital Express. These mission scenarios present challenging guidance problems, as the vehicles may in general start in different orbits from their targets. Trajectory planners for these vehicles must therefore combine “long range” orbital maneuvering, with its attendant nonlinear dynamics and fuel use constraints, and “short range” proximity operations where collision avoidance is paramount.; We describe a spacecraft trajectory planning algorithm based on the calculus of variations which can solve 6-DOF spacecraft docking and proximity operations problems. The design of a cost functional which trades off fuel use, obstacle clearance distance, and arrival time is discussed. The nonlinear orbital dynamic equations are treated as dynamic constraints. The Euler-Lagrange equations for this functional are derived, as are the Pontryagin criteria for the optimal control input given realistic saturating on-off thrusters. The collocation method is chosen to solve the attendant boundary-value problem, and a number of features added to further improve the algorithm's robustness. The manipulation of the Euler-Lagrange equations and the transversality condition into a form suitable for use with collocation methods is also discussed.; The algorithm is shown to be capable of solving “traditional” free-space path planning problems with complex-shaped, moving obstacles. Trajectories are also shown for a variety of orbital maneuvers, culminating in an end-to-end docking maneuver with a tumbling satellite. The computation effort needed to solve these problems is discussed, as are the tradeoffs between fuel use, obstacle clearance distance, and arrival time.
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