Computational Geometric Optimal Control of Connected Rigid Bodies in a Perfect Fluid

TL;DR

This paper develops a geometric numerical method to solve optimal control problems for connected rigid bodies in a fluid, accurately capturing their complex maneuvers while preserving the system's mathematical structure.

Contribution

It introduces a Lie group variational integrator for optimal control of connected rigid bodies in fluid, ensuring structure preservation and computational efficiency.

Findings

Accurate numerical solutions for complex maneuvers

Preservation of Hamiltonian structure and Lie group configuration

Efficient computation demonstrated through simulations

Abstract

This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space, and each joint has three rotational degrees of freedom. We assume that internal control moments are applied at each joint. We present a computational procedure for numerically solving this optimal control problem, based on a geometric numerical integrator referred to as a Lie group variational integrator. This computational approach preserves the Hamiltonian structure of the controlled system and the Lie group configuration manifold of the connected rigid bodies, thereby finding complex optimal maneuvers of connected rigid bodies accurately and efficiently. This is illustrated by numerical computations.