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In this paper, a navigation method for a small size hopping rover with advantages on its mobility is discussed by considering with some uncertainties caused by jumping behavior and measurement error.

By extracting obstacles from environmental data and constructing triangular polygons it is possible to form paths. The algorithm considers with safety of collision with obstacles, roughness of terrain and failures of hopping action, and then could generate safer path based on A* algorithm.

# INTRODUCTION

One possibility is the introduction of a light and compact exploration robot agent, and it is possible that multiple types of agents work together in one system. Various roles (functions) can be played on various kinds of equipment, and all of them can constitute one exploration system.

By allocating the same function (equipment) to some or many of them, it is possible to ignore some percentage of the agent's loss rate, so that risk can be distributed to the system and the mission and there is a high possibility of obtaining higher efficiency.

However, its size causes problems on its traversability and measurement ability.

We have introduced hopping mobility to obtain higher traversability and wider measurement range.

Introduction of two types of rovers is being considered in the exploration system. One is a land-based agent and a stochastic existence region is given in the search region, contributing to the search of the ground surface. The other is hopping rover. the rover that makes path planning taking advantage of sensing from high places while moving the exploration area together with the ground moving rover plays an important role.

• 相比轮式机器人，在低重力环境下 (low gravitational environment)，可以通过跳跃的方式跳过障碍物，从而抄近路 (adopt a short-cut path)。

Especially under low gravitational environment such as other planet or satellite, it indicates higher performance, e.g.Thus, it can jump over a long distance upon terrains and obstacles, adopt a short-cut path without a detour of a wheeled type, and also measure an environment from higher position in the air of jumping trajectory.

# ISSUE AND OBJECTIVES

• 为什么导航问题需要研究：现有的导航研究，没有利用跳跃机器人的运动特性 (文章发表于2017)，所以需要进一步利用跳和远距离的优势来导航。

For a hopping rover, though a lot of jumping hardware designs have been studied, its software e.g. navigation algorithms have been discussed hardly. So, the navigation method hasn't been established by taking advantage of hopping mobility such as jumping over obstacles or a long distance yet.

In this paper, a navigation method for a small size hopping rover with advantages on its mobility is discussed with some risk considerations on its mobility and measured data.

# PATH PLANNING FOR HOPPING MOBILITY

## Selection of Jumping Target Position

The uncertainty factor of hopping rover's jumping motion is the initial speed change, jump distance, jumping direction, bound after landing, failure of leap.

### 如何环境建模

1. 连接被识别到的障碍物，构成不规则三角形的环境模型。

Each obstacle captured by sensing is connected and the observation area is divided into triangles

1. 在观测到的障碍物上使用狄洛尼三角剖分 (Delaunay triangulation)，可以获得每三个点的外心(outside heart)，即可能的落地点。

By using Delaunay triangulation on the observed obstacles, we can set the landing point.

> Delaunay三角剖分定义：平面上的点集P是一种三角剖分，使得P中没有点严格处于剖分后中任意一个三角形**外接圆**的**内部**(可以是圆上)。

Since the outer heart is equally distant from each vertex, it can be said that it is safe if a certain margin can be secured.

Safety distance is secured by creating a circumscribed circle (其实是 delaunay triangulation) so as not to include other obstacles in the circle

## Candidate Path Network

1. 通过连接外心，可以得到一个维诺图 (Voronoi diagram)。

The Voronoi diagram is a method of dividing the region by joining the outer centers formed by Delaunay triangulation.

MC: 什么是 Voronoi diagram？ Voronoi diagram

> 泰森多边形是对空间平面的一种剖分，其特点是多边形内的任何位置离该多边形的样点（如居民点）的距离最近，离相邻多边形内样点的距离远，且每个多边形内含且仅包含一个样点。

It can be confirmed that there are no obstacles on the sides of the Voronoi diagram enclosing the obstacles and safe nodes can be generated.

The error is generally given in the form of a normal distribution, which rides on the initial speed, the jumping angle, and the direction angle, respectively.

The position of the rover can be indicated as the existence probability, and generally takes a shape called an error ellipse.

MC: 通过椭圆来表示误差和不确定性，算是一个新奇的做法。

# SIMULATION OF PATH PLANNING

Even if the obstacle is the size of the black part of the figure.

Simulation was also carried out in the virtual lunar environment created based on the rock distribution collected by “Surveyor 7” of NASA.

When the occupancy rate of the obstacle in the error ellipse exceeds the threshold value, the rover performs self-position estimation.

# CONCLUSION

## The results of this research

• In consideration of the uncertainty of the hopping rover, we were able to determine a safe landing point.
• By performing self-position estimation in the virtual lunar environment, it was possible to induce Rover while suppressing position error.

## Works to do

• 路径规划限于2维，缺乏对障碍物和跳跃高度的考虑。
• 如何切分大的障碍物，而不仅仅是把障碍物作为质点考虑。
• 跳跃机器人的设计，物理构建，环境识别，以及规划好路径后，如何对跳跃行为进行控制，准确抵达目标点。

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Systematic variation of forcing parameters reveals complex dynamics which are sensitive to amplitude, phase and frequency.

# Introduction

• 本文分析简单运动模型的意义：为复杂设备的简单控制提供指导，揭露生物运动的原理。

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：在越过复杂地形时，生物启发的跳跃机器人是轮式机器人的一个替代。目前，跳跃的最优策略往往是基于经验来调试，瞬间行为(如离地跳跃)的动态系统分析(dynamics of transient behaviors)是相对少的。

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

• 硬件设计：线性马达+弹簧+推力棒+空气轴承(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.

• 马达(actuator)相对轴承(bearing)的力量有限，所以通过倾斜来减少重力，但我不太理解这番话蕴含的物理意思，无法想象轴承和马达的位置关系是什么。

Due to power limitations in the actuator, the bearing was inclined at 15 degree relative to the horizontal, reducing gravitational acceleration to 0.276g.

• 马达相对于驱动棒(thrust rod)底部的位置关系表达式，如下所示。

• 设计巧妙处，利用电路(open circuit)做传感器，统计跳跃时间和高度，简单且精度高。

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.

A constant coefficient of restitution of 0.8 (measured from experiment) modeled the collision of the spring with the ground.

# Lift off and jump height

• 只研究马达运行一次的跳跃表现。

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.

## 两种跳跃模式

• 单次跳(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.

## Single jump vs Stutter jump

• 起跳时间：The time to lift-off was smaller for single jumps than stutter jumps.

# Theory of transient mixing

• 看似简单的等式一，因为参数 $$\alpha$$ 的线性，更像是一个分段线性动态系统 (piecewise linear dynamical systems)，包含一系列复杂的行为。

• 基于等式一，理论分析为什么最佳跳跃不是发生在谐振频率。

We are particularly interested in why optimal jumps occur only off resonance.

## Single jump

Moving off resonance, the prefactor favors higher f over lower, so the optimum f lies somewhat above $$f_{0}$$ (resonance). This argument holds regardless of A.

## Single jump vs Stutter jump

• 最佳突突跳(stutter jump)的频率带宽(narrow frequency bandwidth)比较窄。 > This sensitivity to proper timing explains the narrow frequency bandwidth required to achieve optimal jump heights using the stutter jump mode.
• 最佳突突跳的频率强依赖幅值，单次跳则没有明显依赖。 > A further consequence is a strong dependence of optimal f with respect to A.
• 和单次跳跃相比，突突跳达到相同高度的消耗能量要少一个数量级。 > 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

• 发现突突跳，使用的能量少，但是跳跃高度高，性价比高。 > The system becomes hybrid for certain parameters as a stutter jump emerges. This mode achieves comparable jump height but uses less power.
• 研究成果和已有结论相符 > 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

• 研究其他影响因素，如系统固有性质和环境的影响 > 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).
• 如何结合 Single jump 和 Stutter jump，取得更优的表现。

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# 目标和方法

1. 从频谱仪中导出频谱仪 I/Q 数据；
2. 在 matlab 上编程实现基于 I/Q 数据的多帧 ASK 和 FSK 解调；
3. Matlab 解调结果和频谱仪基本吻合，并实现解调自动化。

# 导入 I/Q 数据

• Y 是一个复变量，包含了采样数据点的同相 I 分量和正交 Q 分量。
• InputCenter 显示了采样时的中心频率，据此可计算出实际频率分量。
• InputZoom 值为1，表示采集数据已下变频到基带。
• XDelta 为采样周期，由此可以计算出采样率 (fs=1/XDelta)。

## IQ 数据简介

I/Q 直角坐标图表示矢量的参数不是直接的幅值和瞬时相位，而是把它们投影在 I/Q 直角坐标轴上，采用 I 轴和 Q 轴的投影分量来确定矢量。

## 数据分析

• 输入信号的幅度 $$Am$$ 分析： $$Am=\sqrt{I^{2}+Q^{2}}$$ 。根据 I/Q 信号的每一个采样值，可以计算出对应采样时刻的幅度值。在测量时间内的所有幅度数值构成 I/Q 幅度数组，对应于“射频功率－时间曲线”。

• 输入信号的相对相位 $$\Phi m$$ 分析： $$\Phi m=arctan(Q/I)$$ 。根据 I/Q 信号的每一个采样值，可以计算出对应采样时刻的相对相位值。在测量时间内的所有 $$\Phi m$$ 数值构成 I/Q 相对相位数组 $$\Phi m$$

• 输入信号的频率 $$F m$$ 计算：$$F m = \frac{d(\Phi m)}{dt}$$ 。在测量时间内的所有 $$F m$$ 数值构成 I/Q 频率数组 $$F m$$，对应于频率曲线。

• 频谱计算：Spectrum = FFT(Y)。对 I/Q 数据 Y 进行傅里叶变换，即可计算出其频谱值。其中，Spectrum 为输入信号中频带宽内的频谱。

## 解调实例分析

### FSK 解调实现

FSK就是用数字信号去调制载波的频率，FSK解调一般采用两种方式：非相干解调和相干解调。

Matlab代码为：

ASK 是振幅键控方式，这种调制方式是根据信号的不同，调节正弦波的幅度。这里参考上述计算幅值 $$Am$$ 的公式，将频谱仪导入的 I/Q数据计算瞬时幅值。

Matlab 代码为：