Quasi-Linear Optimization for Multiple-Spacecraft Clustering
- Paper number
IAC-05-C1.5.04
- Author
Dr. Hiroaki Umehara, National Institute of Information and Communications Technology, Japan
- Coauthor
Prof. Colin R. McInnes, University of Strathclyde, United Kingdom
- Year
2005
- Abstract
Distributed systems with a cluster of multiple artificial satellites have been considered to be beneficial for telecommunications. Therefore, advanced operations of a loose-cluster formation are desired, where a loose cluster means that each relative distance between satellites is not guided strictly although all satellites are controlled so as not to approach each other in a bounded region orbiting the earth. Both near-miss avoidance and fuel minimization are crucial requirements for a safe and efficient operation. Such an optimum control problem is formulated and solved by Umehara and McInnes (2005) in Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, pp.182-185, “Penalty-Function Guidance for Multiple-Satellite Cluster Formation”. Autonomy is another important requirement, however, unsolved owing to multiple minimal solutions, which disturbs the convergence during an iterative search for a truly fuel-minimum solution. The distribution of the minimal solutions with respect to arbitrarily given initial-state variables will have to be known as a first step to formulate an automatic and optimized control. Umehara and McInnes (2005) defined a non-quadratic penalty function for near-miss avoidance since no penalty was imposed during non near-miss state and since a class C2 function was required for applying the Newton-Raphson shooting search method. Accordingly, the nonlinear differential equations of costate variables were derived although the original state-variable equations of motion are linear. However, a class C2 is superfluous requirement if the time evolution of the sensitivity function is determined uniquely. Therefore, a piecewise-quadratic penalty function is introduced. The function value vanishes in excess of near-miss distance. If any mutual distance is judged as near miss, then a concave quadratic value of distance is imposed with off-set so that the penalty function is continuous in any distance value. For simplification, this paper considers multiple spacecraft in deep space without a gravitational field. This is the variable separable system and divided into two subsystems. If there are only two spacecraft, then the zero relative velocity at the final time corresponds to staying at fixed point in one subsystem. Then, it is sufficient to analyze another subsystem which has three dimensions of state and costate variables. Here, the Hamiltonian is a time-constant function although this includes piecewise penalty function, which results in reduction of one dimension. All extremum state-space points are searched for with arbitrarily given initial-state variables and final variables limited to a cluster configuration with zero relative velocity. Then, the existence and distribution of extremums are categorized by the initial and final state variables. Such an analysis will help us find a global feedback-like formulation with non-iterative algorithm.
- Abstract document
- Manuscript document
IAC-05-C1.5.04.pdf (🔒 authorized access only).
To get the manuscript, please contact IAF Secretariat.