On-Line Generation of Quasi-Optimal Docking Trajectories

Satellites ’ rendezvous and docking is a challenging problem for space exploitation. Saving time, fuel, or any other resource, expressed for example as a combination of the two previous ones, is not a straightforward task if onboard calculation is required to make the control autonomous. A direct method for a rapid generation of near-optimal trajectories of proximity maneuvers onboard a flying vehicle (required to dock a target one), with predetermined thrust history along a master direction, is presented. The new direct method, already implemented and tested onboard for the case of a real aircraft by one of the authors, is based on three concepts: high-order polynomials from the virtual arc as reference functions for the spatial coordinates, preset sequence of a master control, reduction of the optimization problem to the determination of a small set of parameters. By doing this the remaining controls act as slaves, guarantying the chaser to move along the desired path. The master thrust has an on-off structure. Seeking of the optimum strategy is transformed to an nonlinear programming problem, then numerically solved through an ad hoc algorithm in accelerated time scale. Examples are reported in order to prove the rapidness of the approach to generate a sub-optimal docking trajectory. Abbreviations and Acronyms DMRP = direct method for rapid prototyping LVLH = local vertical local horizontal NLP = nonlinear programming OP = optimization parameter PMP = Pontryagin maximum principle Nomenclature ika = coefficients of reference polynomials g = acceleration due to gravity J, Jsc = performance index, scaled performance index k={x,y,z} = Cartesian coordinates in LVLH frame m = mass N = number of nodes n = polynomial order scO = slaves control constraint violation scaling factor ()kP τ = polynomial reference function for the Cartesian coordinates maxT = maximum thrust t = tim