[论文解读] Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Articulated Soft Robots

Cosimo Della Santina, Dominic Lakatos+2 more|arXiv (Cornell University)|Jun 21, 2018

Soft Robotics and Applications参考文献 16被引用 12

一句话总结

本文提出了一种通过特征流形（Eigenmanifolds）利用非线性模态的控制策略，以在铰接式软体机器人中实现高效、稳定的周期性运动。通过结合PD反馈以吸引系统至模态流形，并采用简单的能量调节反馈律，该方法在2自由度分段软腿上激发了可重复的非线性振荡，尽管存在模型不确定性与耗散效应，仍实现了稳定且能量受控的振荡。

ABSTRACT

Inspired by the vertebrate branch of the animal kingdom, articulated soft robots are robotic systems embedding elastic elements into a classic rigid (skeleton-like) structure. Leveraging on their bodies elasticity, soft robots promise to push their limits far beyond the barriers that affect their rigid counterparts. However, existing control strategies aiming at achieving this goal are either tailored on specific examples, or rely on model cancellations -- thus defeating the purpose of introducing elasticity in the first place. In a series of recent works, we proposed to implement efficient oscillatory motions in robots subject to a potential field, aimed at solving these issues. A main component of this theory are Eigenmanifolds, that we defined as nonlinear continuations of the classic linear eigenspaces. When the soft robot is initialized on one of these manifolds, it evolves autonomously while presenting regular -- and thus practically useful -- evolutions, called normal modes. In addition to that, we proposed a control strategy making modal manifolds attractors for the system, and acting on the total energy of the soft robot to move from a modal evolution to the other. In this way, a large class of autonomous behaviors can be excited, which are direct expression of the embodied intelligence of the soft robot. Despite the fact that the idea behind our work comes from physical intuition and preliminary experimental validations, the formulation that we have provided so far is however rather theoretical, and very much in need of an experimental validation. The aim of this paper is to provide such an experimental validation using as testbed the articulated soft leg. We will introduce a simplified control strategy, and we will test its effectiveness on this system, to implement swing-like oscillations. We plan to extend this validation with a soft quadruped.

研究动机与目标

• 实验验证非线性模态在铰接式软体机器人中的理论框架。
• 证明可利用特征流形作为吸引子，实现稳定、周期性的振荡。
• 测试一种简化的能量调节策略，以在存在未建模动力学与系统不确定性的情况下，实现鲁棒且可重复的周期性运动。
• 评估该控制方法向更复杂系统（如软体四足机器人）扩展的可行性。

提出的方法

• 该方法采用坐标嵌入（X, ˙X）以在状态空间中定义一个二维不变子流形，即非线性特征流形。
• 应用类似PD的反馈控制律，通过多项式函数对X和˙X进行处理，以吸引系统轨迹趋近模态流形。
• 通过基于状态和能量阈值的离散开关式力矩脉冲，实现简化的能量调节律τE，模拟一种启动控制器（swing-up controller）的行为。
• 控制输入通过转置雅可比矩阵映射，并通过电机位移实现，以考虑串联驱动与串联弹性特性。
• 系统在瞬态阶段通过向系统注入能量以启动振荡。
• 该方法在具有上段杆件约束的2自由度分段软腿上进行了测试，实现了类似摆动的运动。

实验结果

研究问题

• RQ1 能否通过简化的控制策略在软体机器人系统中实验实现非线性模态？
• RQ2 所提出的控制框架在面对未建模动力学、参数失配与能量耗散时具有多高的鲁棒性？
• RQ3 当由于耗散效应而无法达到目标能量水平时，能量调节策略在多大程度上仍能维持稳定的振荡？
• RQ4 系统层面的非线性与非对称性如何影响模态流形跟踪的精度？
• RQ5 该控制方法是否可扩展至更复杂、高维的软体机器人系统（如四足机器人）？

主要发现

• 该控制策略在五组不同的增益值（0.2Nm至0.9Nm）下，成功在2自由度软腿上生成了稳定且可重复的非线性振荡，振荡幅度随增益提高而增大。
• 实际达到的能量水平由能量注入增益α与耗散效应之间的动态平衡决定，而非达到预设的目标能量水平。
• 系统在(θ, r)空间中对理想模态流形（r = X(θ, ˙θ)）表现出良好的跟踪性能，经过2秒瞬态后，实际轨迹与理想轨迹高度对齐。
• 在较高速度下，与流形的偏差增大，且振荡表现出不对称性，尤其在正δ值时更为明显，提示需要引入质量项的模型。
• 尽管简化，能量调节器仍有效将振荡维持在目标能量带[21J, 22J]内，即使由于耗散效应无法达到目标值。
• 实验表明，通过自适应调节α比优化特征流形更实际，以实现期望的振荡幅度。