Numerical Trajectory Optimization with Swarm Intelligence and Dynamic Assignment of Solution Structure

Abstract

Particle swarm optimization is an evolutionary optimization method that relies on a group of potential solutions to explore the search space. Conceptually, each particle in the swarm uses its own memory, as well as the knowledge accumulated by the entire swarm, to iteratively converge on the optimal solution. It is relatively easy to implement and, unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, has been little explored. In this work, particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems, including thrust programming for minimum fuel, multiburn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of nonlinear mixed-integer programming problems with the swarming technique. A dynamic multistage-assignment penalty function is incorporated to enforce the associated constraints. For each test case, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy.