Trajectory optimization using quantum computing

Alok Shukla () and Prakash Vedula ()
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Alok Shukla: The University of Oklahoma
Prakash Vedula: The University of Oklahoma

Journal of Global Optimization, 2019, vol. 75, issue 1, No 11, 199-225

Abstract: Abstract We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization of the optimization problem wherein we discretize not only independent variables (such as time) but also dependent variables. Our discretization scheme enables a reduction in computational cost through selection of coarse-grained states. It further facilitates the solution of the trajectory optimization problem via classical discrete search algorithms including deterministic and stochastic methods for obtaining a global optimum. This framework also allows us to efficiently use quantum computational algorithms for global trajectory optimization. We demonstrate that the discrete search problem can be solved by a variety of techniques including a deterministic exhaustive search in the physical space or the coefficient space, a randomized search algorithm, a quantum search algorithm or by employing a combination of randomized and quantum search algorithms depending on the nature of the problem. We illustrate our methods by solving some canonical problems in trajectory optimization. We also present a comparative study of the performances of different methods in solving our example problems. Finally, we make a case for using quantum search algorithms as they offer a quadratic speed-up in comparison to the traditional non-quantum algorithms.

Keywords: Trajectory optimization; Calculus of variations; Global optimization; Quantum computation; Randomized search algorithm; Brachistochrone problem; 49M25; 81P68 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00754-5

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