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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。