Variational integrators for optimal control of foldable drones

TL;DR

This paper develops variational integrators tailored for control-dependent Lagrangian systems on Lie groups, specifically applied to optimal control and path planning of foldable UAVs, preserving geometric invariants for improved numerical stability.

Contribution

It introduces a novel class of variational integrators for control-dependent systems on Lie groups and applies them to optimize foldable drone trajectories.

Findings

Validated the integrator's performance through simulations.

Preserved geometric invariants in UAV control simulations.

Enhanced stability and accuracy in optimal control of foldable drones.

Abstract

Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The general idea for those variational integrators is to discretize Hamilton's principle rather than the equations of motion and as a consequence these methods preserves some of the invariants of the original system (symplecticity, symmetry, good behavior of energy,...). In this paper, we construct variational integrators for control-dependent Lagrangian systems on Lie groups. These integrators are derived via a discrete-time variational principle for discrete-time control-dependent reduced Lagrangians. We employ the variational integrator into optimal control problems for path planning of foldable unmanned aerial vehicles (UAVs). Simulation are shown to validate the performance of the geometric integrator.