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Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum

机译：近似分析解决方案的损失春载倒置摆的双姿态动力学

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摘要

This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of nonnegligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.
机译：本文介绍了在非中央阻尼的存在下，在存在“双面”弹簧加载的倒置摆（B滑）的不可排序的双姿态动态的近似时域解决方案。我们首先介绍一种辅助系统，其行为在某些条件下大致相当于双姿势的B滑移。然后，我们通过两种不同方法导出了新系统动态的近似解：（i）更新的动量方法，可以处理有损和无损B滑移模型，以及（ii）基于扰动的方法只能导出对无损案件的解决方案。每种方法的预测性能通过综合数值分析表征。与数值集成相比，衍生的表示是非常有效的，因此，适用于在线规划，增加行走机器人的自主权。提出了步行步态控制的两个应用示例。所提出的解决方案可以用作各种领域的仪器工具，例如在生物力学中的腿机器人学和人类运动理解中的控制。

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