Momentum Preserving Simulation of Cooperative Multirotors With Flexible-Cable Suspended Payload

Abstract

In this paper, a momentum-preserving integration scheme is implemented for the simulation of single and cooperative multirotors with a flexible-cable suspended payload by employing a Lie group–based variational integrator (VI), which provides the preservation of the configuration manifold and geometrical constraints. Due to the desired properties of the implemented VI method, e.g., symplecticity, momentum preservation, and the exact fulfillment of the constraints, exponentially long-term numerical stability, and good energy behavior are obtained for more accurate simulations of aforementioned systems. The effectiveness of Lie group VI method with the corresponding discrete systems are demonstrated by comparing the simulation results of two example scenarios for the single and cooperative systems in terms of the preserved quantities and constraints, where a conventional fixed-step Runge–Kutta 4 (RK4) and variable-step integrator are utilized for the simulation of continuous-time models. It is shown that the implemented VI method successfully performs the simulations with a long-time stable behavior by preserving invariants of the system and the geometrical constraints, whereas the simulation of continuous-time models by RK4 and variable step are incapable of satisfying these desired properties, which inherently results in divergent and unstable behavior in simulations.