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Optimal approach to and alignment with a rotating rigid body for capture

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Abstract

This paper addresses a feed-forward optimal control problem for one rigid body to approach to and align with another arbitrarily rotating rigid body, with an application to the satellite rendezvous problem. In particular, we focus on the satellite rendezvous strategy of finding an optimal trajectory, and the required thrust force profiles, which will guide the chasing spacecraft to approach the tumbling satellite such that the two vehicles will eventually have no relative rotation and thus a subsequent docking or capture operation can be safely performed with a normal docking or capture mechanism. Our approach is to model the system using rigid-body dynamics and apply Pontryagin’s Maximum Principle for the optimal control. A planar problem is presented as a case study, in which together with the Maximum Principle, the Lie algebras associated with the system are used to examine the existence of singular extremals for the time-optimal control problem. Also, optimal trajectories and the corresponding set of control force/torque profiles are numerically generated for the time/fuel-consumption optimal control problem.

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ, 08544, USA

    Zhanhua Ma

  2. Mechanical and Aerospace Engineering Department, New Mexico State University, Las Cruces, NM, 88003, USA

    Ou Ma & Banavara N. Shashikanth

Authors
  1. Zhanhua Ma
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  2. Ou Ma
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  3. Banavara N. Shashikanth
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Additional information

A shortened version of this paper was published in the Proceedings of the 2006 IEEE International Conference on Intelligent Robots and Systems, October 9–15, 2006, Beijing, pp. 4109–4114.

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Ma, Z., Ma, O. & Shashikanth, B.N. Optimal approach to and alignment with a rotating rigid body for capture. J of Astronaut Sci 55, 407–419 (2007). https://doi.org/10.1007/BF03256532

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