Distance-Optimal Navigation in an Unknown

Environment Without Sensing Distances

Presenter: 林易增 2008/3/11

Outline

• Introduction

• Robot Model

• Gap Navigation Tree(GNT)

• Multiply Connected Environments

• Implementation

• Conclusion

INTRODUCTION

• More information is better?

• Abstract sensor

• Gap Navigation Tree(GNT)

• Bug Algorithms

Outline

• Introduction

• Robot Model

• Gap Navigation Tree(GNT)

• Multiply Connected Environments

• Implementation

• Conclusion

Robot Model(1/4)

• Gap Sensor

Robot Model(2/4)

• Definition

– – R

– q

R

Robot Model(3/4)

• cyclic ordering

1,..... kG g g

R

1 2 1,,..... ,.....k kg g g g g

Robot Model(4/4)

• Motion Primitives• chase(g)

g G : 0,1 R

sg G 0,1s

Outline

• Introduction

• Robot Model

• Gap Navigation Tree(GNT)

• Multiply Connected Environments

• Implementation

• Conclusion

GNT(1/10)

• Compressing the Sensor History

1 2 30 , ,g g gG

1 4 5 3' , , ,s g g g gG

1 4 5 3' , , ,s g g g gG

361' g,g,gsG

GNT(2/10)

• 一個新的 gap 出現：一個節點 g 被當成一個孩子增加到 root 中。

GNT(3/10)

• Gaps g1 和 g2 合併成一個 g ：節點 g1 和 g2 變成 g 節點的新孩子。

GNT(4/10)

• 一個 gap 消失：必須是一個葉子節點g ，則會被移除。

GNT(5/10)

• Gap g 分解成 g1 和 g2 ：如果 g 是一個葉子節點，則g1 和 g2 變成新的節點；否則他們已經存在且為 g的子節點。

GNT(6/10)• Critical events

• Complete?

GNT(7/10)

GNT(8/10)

GNT(9/10)

GNT(10/10)

Outline

• Introduction

• Robot Model

• Gap Navigation Tree(GNT)

• Multiply Connected Environments

• Implementation

• Conclusion

Multiply Connected Environments

• New Assumptions– Markers or pebbles

• Another Abstract sensor

Multiply Connected Environments

• Primitive:• Non-primitive• Block

Outline

• Introduction

• Robot Model

• Gap Navigation Tree(GNT)

• Multiply Connected Environments

• Implementation

• Conclusion

Implementation(1/3)

Implementation(2/3)

Implementation(3/3)

Conclusion

• two robots

• the robot is not a point

• GNT

• wrong gaps

• small gaps

• make the gap sensor more robust