Biological flying, gliding, and falling creatures are capable of extraordinary forms of inertial maneuvering: free-space maneuvering based on fine control of their multibody dynamics, as typified by the self-righting reflexes of cats. However, designing inertial maneuvering capability into biomimetic robots, such as biomimetic unmanned aerial vehicles (UAVs) is challenging. Accurately simulating this maneuvering requires numerical integrators that can ensure both singularity-free integration, and momentum and energy conservation, in a strongly coupled system - properties unavailable in existing conventional integrators. In this work, we develop a pair of novel quaternion variational integrators (QVIs) showing these properties, and demonstrate their capability for simulating inertial maneuvering in a biomimetic UAV showing complex multibody-dynamics coupling. Being quaternion-valued, these QVIs are innately singularity-free; and being variational, they can show excellent energy and momentum conservation properties. We explore the effect of variational integration order (left-rectangle vs. midpoint) on the conservation properties of integrator, and conclude that, in complex coupled systems in which canonical momenta may be time-varying, the midpoint integrator is required. The resulting midpoint QVI is well-suited to the analysis of inertial maneuvering in a biomimetic UAV - a feature that we demonstrate in simulation - and of other complex dynamical systems.
翻译:生物飞行、滑翔和坠落生物能够进行非同寻常的惯性操控:在精细控制其多体动态的基础上自由空间操控,其典型特征是猫自右反射。然而,将惯性操控能力设计成生物模拟机器人,如生物模拟无人驾驶飞行器(UAVs)具有挑战性。精确地模拟这种操控需要数字集成器,这些集成器既能确保无奇异的整合,又能确保动力和节能,在一种紧密结合的系统中——现有传统集成器没有的特性。在这项工作中,我们开发一副新型的四元变异变变变异聚合器(QVIs)来显示这些特性,并展示它们在生物模拟超动性超动动机器人(UAV)中振动(Vial-Vinder)中点分析中点(Viroal-Virodral)中点的变异性变异性变异性变性变性变性系统的效果。