Lift-off dynamics in a simple jumping robot
本文研究了一個垂直跳躍機器人(a 1D mass-spring system with an actuated mass)的動力特性嗜愈，該機器人主要是由驅(qū)動馬達港粱、質(zhì)心彈簧組成峭判。文章通過改變驅(qū)動力(馬達)的頻率、幅值來尋找跳躍的最優(yōu)表現(xiàn)划乖。通過分析離地跳躍模型，發(fā)現(xiàn)最有跳躍不是發(fā)生在機器人的共振頻率(resonant frequency) 秧秉。其中污桦，類似于蹲下來起跳(squat maneuver)的行為，最優(yōu)跳躍的頻率高于
书幕；類似于反向運動(counter-movement)新荤，最優(yōu)跳躍的頻率低于
。
Systematic variation of forcing parameters reveals complex dynamics which are sensitive to amplitude, phase and frequency.
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Introduction
- 本文分析簡單運動模型的意義：為復(fù)雜設(shè)備的簡單控制提供指導(dǎo)苟呐，揭露生物運動的原理痒芝。
Simple models have the ability to be fully analyzed and can thus provide guidance for simplifying control of more complex devices, and even reveal principles of biological locomotion.
- 研究背景：在越過復(fù)雜地形時，生物啟發(fā)的跳躍機器人是輪式機器人的一個替代掠抬。目前吼野，跳躍的最優(yōu)策略往往是基于經(jīng)驗來調(diào)試，瞬間行為(如離地跳躍)的動態(tài)系統(tǒng)分析(dynamics of transient behaviors)是相對少的两波。
In robotics, biologically inspired legged jumping robots have been constructed as an alternative to wheeled robots to better traverse rough terrain.
The initial movement strategies for optimal jumping are typically chosen by empirical tuning for steady state hopping or squat jumps. Systematic studies of the dynamics of transient behaviors, critical to issues of lift-off, are relatively scarce.
Experiment and model
- 硬件設(shè)計：線性馬達+彈簧+推力棒+空氣軸承(摩擦小)
The robot consisted of a linear motor actuator with a series spring rigidly attached to the bottom end of the actuator’s lightweight thrust rod. The actuator was mounted to an air bearing which allowed for 1D, and nearly frictionless, motion.
- 馬達(actuator)相對軸承(bearing)的力量有限瞳步，所以通過傾斜來減少重力，但我不太理解這番話蘊含的物理意思腰奋，無法想象軸承和馬達的位置關(guān)系是什么单起。猜測可能是
Due to power limitations in the actuator, the bearing was inclined at 15 degree relative to the horizontal, reducing gravitational acceleration to 0.276g.
- 馬達相對于驅(qū)動棒(thrust rod)底部的位置關(guān)系如下所示。
- 設(shè)計巧妙處劣坊，利用電路(open circuit)做傳感器嘀倒，統(tǒng)計跳躍時間和高度，簡單且精度高局冰。
To detect lift-off, a continuity sensor attached to the bottom of the metal spring measured an open circuit when the spring left the ground.
結(jié)合理論和實驗测蘑，作者提出一個機器人的動態(tài)模型，如下所示康二。
以及碳胳，和地面碰撞后的恢復(fù)系數(shù)。
A constant coefficient of restitution of 0.8 (measured from experiment) modeled the collision of the spring with the ground.
MC(my comment): 公式基于力學(xué)中的基本概念之一沫勿，使物體獲得加速度或形變的外因挨约，在動力學(xué)中它等于物體的質(zhì)量與加速度的乘積味混。=> F = ma
Lift off and jump height
- 只研究馬達運行一次的跳躍表現(xiàn)。
Since we were interested in rapid jumps from rest, actuator forcing was then restricted to only one cycle (N = 1). We systematically examined jumping height for
N = 1.
兩種跳躍模式
本節(jié)主要研究頻率(frequency) 和初始相位(initial phase offset)
對跳躍高度的影響诫惭。從跳躍高度圖發(fā)現(xiàn)翁锡，局部兩個最大值，對應(yīng)兩種跳躍行為模式(two distinct modes of jumping)夕土。
- 單次跳(single jump)
In the single jump mode, the robot compressed the spring and was propelled into the air.
- 突突跳(stutter jump)
In the stutter jump mode, the robot performed a small initial jump followed by a larger second jump.
重要結(jié)論：For large single jumps predominate while stutter jumps occurred at lower
and
.
Single jump vs Stutter jump
- 起跳時間：The time to lift-off was smaller for single jumps than stutter jumps.
Theory of transient mixing
看似簡單的等式一馆衔，因為參數(shù)
的線性，更像是一個分段線性動態(tài)系統(tǒng)(piecewise linear dynamical systems)隘弊，包含一系列復(fù)雜的行為哈踱。
基于等式一，理論分析為什么最佳跳躍不是發(fā)生在諧振頻率梨熙。
We are particularly interested in why optimal jumps occur only off resonance.
Single jump
基于對等式一的變形开镣，從模型中發(fā)現(xiàn)理論依據(jù)。
Moving off resonance, the prefactor favors higher f over lower, so the optimum f lies somewhat above
(resonance). This argument holds regardless of A.
Stutter jump
基于物理公式瞬時動能(instantaneous power) P = 外界力 F(external force) 乘以 質(zhì)心速度 V(the center-of-mass robot velocity)咽扇。
Single jump vs Stutter jump
- 最佳突突跳(stutter jump)的頻率帶寬(narrow frequency bandwidth)比較窄邪财。
This sensitivity to proper timing explains the narrow frequency bandwidth required to achieve optimal jump heights using the stutter jump mode.
- 最佳突突跳的頻率強依賴幅值，單次跳則沒有明顯依賴质欲。
A further consequence is a strong dependence of optimal f with respect to A.
- 和單次跳躍相比树埠，突突跳達到相同高度的消耗能量要少一個數(shù)量級。
Thus the stutter jump is energetically advantageous since it has a lower optimal f than the single jump. In fact, the stutter jump uses nearly an order of magnitude less power to achieve comparable jump height to the single jump.
Conclusion
Works have done
- 發(fā)現(xiàn)突突跳嘶伟，使用的能量少怎憋，但是跳躍高度高，性價比高九昧。
The system becomes hybrid for certain parameters as a stutter jump emerges. This mode achieves comparable jump height but uses less power.
- 研究成果和已有結(jié)論相符
Biologically, our model is in accord with a previous model of bipedal jumping which predicted that counter-movement achieves greater jump height than the squat jump. A quick single jump that resembles a squat jump is beneficial when a fast escape is essential, while a slower stutter jump similar to a counter-movement can achieve comparable jump height.
Works to do
- 研究其他影響因素绊袋，如系統(tǒng)固有性質(zhì)和環(huán)境的影響
how other factors, intrinsic and environmental, affect optimal performance
- A non-sinusoidal actuation could improve jump height, take off time, or efficiency.
- Animals jump off compliant surfaces (like tree branches) and from deformable substrates (like sand).
- 如何結(jié)合 Single jump 和 Stutter jump，取得更優(yōu)的表現(xiàn)铸鹰。
