Local Pursuit as a Bio-Inspired Computational Optimal Control Tool
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This paper explores the use of a bio-inspired control algorithm, termed ``local pursuit', as a numerical tool for computing optimal control-trajectory pairs in settings where analytical solutions are difficult to obtain. Inspired by the foraging activities of ant colonies, local pursuit has been the focus of recent work on cooperative optimization. It allows a group of agents to solve a broad class of optimal control problems (including fixed final time, partially-constrained final state problems) and affords certain benefits with respect to the amount of information (description of the environment, coordinate systems, etc.) required to solve the problem. Here, we present a numerical optimization method that combines local pursuit with the well-known technique of multiple shooting, and compare the computational efficiency and capabilities of the two approaches. The proposed method method can overcome some important limitations of multiple shooting by solving an optimal control problem ``in small pieces'. Specifically, the use of local pursuit increases the size of the problem that can be handled under a fixed set of computational resources. Furthermore, local pursuit can be effective in some situations where multiple shooting leads to an ill-conditioned nonlinear programming problem. The trade-off is an increase in computation time. We compare our pursuit-based method with direct multiple shooting using an example that involves optimal orbit transfer of a simple satellite.