Introduction to Information Science and Technology (IST) Part IV: - - PowerPoint PPT Presentation

▶
introduction to information science and technology ist
SMART_READER_LITE
LIVE PREVIEW

Introduction to Information Science and Technology (IST) Part IV: - - PowerPoint PPT Presentation

Mar 02, 2023 378 likes •1.03k views

Introduction to Information Science and Technology (IST) Part IV: Intelligent Machines and Robotics Planning Sren Schwertfeger / ShanghaiTech University 2 ShanghaiTech University - SIST - 23.05.2016 Autonomous mobile robots

slide-1
SLIDE 1

Introduction to Information Science and Technology (IST) Part IV: Intelligent Machines and Robotics Planning

Sören Schwertfeger / 师泽仁 ShanghaiTech University

slide-2
SLIDE 2
  • Autonomous mobile robots

move around in the

  • environment. Therefore ALL of

them:

  • They need to know where they

are.

  • They need to know where their

goal is.

  • They need to know how to get

there.

  • Different levels:
  • Control:
  • How much power to the motors to

move in that direction, reach desired speed

  • Navigation:
  • Avoid obstacles
  • Classify the terrain in front of you
  • Follow a path
  • Planning:
  • Long distance path planning
  • What is the way, optimize for certain

parameters

ShanghaiTech University - SIST - 23.05.2016

2

slide-3
SLIDE 3

General Control Scheme for Mobile Robot Systems

Sensing Acting Information Extraction Vision Path Execution Cognition & AI Path Planning Real World Environment Localization Map Building

Motion Control Navigation Perception

ShanghaiTech University - SIST - 23.05.2016

With material from Roland Siegwart and Davide Scaramuzza, ETH Zurich

Raw data Environment Model Local Map Position Global Map Actuator Commands Path

Lecture 3: Planning

3

slide-4
SLIDE 4

PATH FOLLOWING

Obstacle Avoidance

IST ShanghaiTech University - SIST - 19.05.2016

4

slide-5
SLIDE 5

Navigation, Motion & Motor Control

  • Navigation/ Motion Control:
  • Where to drive to next in order to reach goal
  • Output: motion vector (direction) and speed
  • For example:
  • follow path (Big Model)
  • go to unexplored area (Big Model)
  • drive forward (Small Model)
  • be attracted to goal area (Small Model)
  • Motion Control:
  • How use propulsion to achieve motion vector
  • Motor Control:
  • How much power to achieve propulsion (wheel

speed)

IST ShanghaiTech University - SIST - 19.05.2016

5

Planner Path Following/ Local Goal Global Goal Path (0.1Hz) Motion Control Navigation Goal (10Hz) Motor Control Wheel Speeds (1000 Hz)

1 2 3

slide-6
SLIDE 6

Obstacle Avoidance (Local Path Planning)

  • Goal: avoid collisions with obstacles
  • Usually based on local map
  • Often implemented as independent task
  • However, efficient obstacle avoidance should be
  • ptimal with respect to
  • the overall goal
  • the actual speed and kinematics of the robot
  • the on boards sensors
  • the actual and future risk of collision

IST ShanghaiTech University - SIST - 19.05.2016

6

slide-7
SLIDE 7

Obstacle Avoidance: Vector Field Histogram (VFH)

  • Environment represented in a grid (2 DOF)
  • cell values: probability of obstacle
  • Reduction in to 1 DOF histogram
  • Steering direction algorithm:
  • Find all openings for the robot to pass
  • Lowest cost function G

Borenstein et al.

target_direction = alignment of the robot path with the goal wheel_orientation = difference between the new direction and the currrent wheel orientation previous_direction = difference between the previously selected direction and the new direction

IST ShanghaiTech University - SIST - 19.05.2016

7

slide-8
SLIDE 8

Obstacle Avoidance: The Bubble Band Concept

  • Bubble = Maximum free space which can be reached without any risk of

collision

  • generated using the distance to the object and a simplified model of the robot
  • bubbles are used to form a band of bubbles which connects the start point with the goal

point

Khatib and Chatila

IST ShanghaiTech University - SIST - 19.05.2016

8

slide-9
SLIDE 9

Path Following

  • A path is generated by planning algorithm (next lecture)
  • Goal: Drive along that path
  • Path smoothing or
  • Local planner
  • Control onto the local path
  • For example:
  • Select goal point one meter ahead of path

9

Material from Martin Rufli

  • M. Rufli and R. Siegwart: Deformable Lattice Graphs

IST ShanghaiTech University - SIST - 19.05.2016

slide-10
SLIDE 10

MAPS

ShanghaiTech University - SIST - 23.05.2016

10

slide-11
SLIDE 11

Representation of the Environment

  • Environment Representation
  • Continuous Metric

→ x, y, θ

  • Discrete Metric

→ metric grid

  • Discrete Topological → topological grid
  • Environment Modeling
  • Raw sensor data, e.g. laser range data, grayscale images
  • large volume of data, low distinctiveness on the level of individual values
  • makes use of all acquired information
  • Low level features, e.g. line other geometric features
  • medium volume of data, average distinctiveness
  • filters out the useful information, still ambiguities
  • High level features, e.g. doors, a car, the Eiffel tower
  • low volume of data, high distinctiveness
  • filters out the useful information, few/ no ambiguities

ShanghaiTech University - SIST - 23.05.2016

11

slide-12
SLIDE 12

Map Representation: Approximate cell decomposition

  • Fixed cell decomposition => 2D grid map
  • Cells: probability of being occupied =>
  • 0 free; 0.5 (or 128) unknown; 1 or (255) occupied

ShanghaiTech University - SIST - 23.05.2016

12

slide-13
SLIDE 13

Map Representation: Occupancy grid

  • Fixed cell decomposition: occupancy grid example

Courtesy of S. Thrun

ShanghaiTech University - SIST - 23.05.2016 EE 100

13

slide-14
SLIDE 14

SLAM

Simultaneous Localization and Mapping

ShanghaiTech University - SIST - 23.05.2016

14

slide-15
SLIDE 15

Map Building: The Problems

  • 1. Map Maintaining: Keeping track of

changes in the environment e.g. disappearing cupboard

  • e.g. measure of belief of each

environment feature

  • 2. Representation and

Reduction of Uncertainty position of robot -> position of wall position of wall -> position of robot § Inconsistent map due to motion drift

?

ShanghaiTech University - SIST - 23.05.2016

15

slide-16
SLIDE 16

Cyclic Environments

  • Small local error accumulate to arbitrary large global errors!
  • This is usually irrelevant for navigation
  • However, when closing loops, global error does matter

ShanghaiTech University - SIST - 23.05.2016

16

slide-17
SLIDE 17

Raw Odometry …

ShanghaiTech University - SIST - 23.05.2016

Courtesy of S. Thrun

17

slide-18
SLIDE 18

Scan Matching: compare to sensor data from previous scan

ShanghaiTech University - SIST - 23.05.2016

Courtesy of S. Thrun

18

slide-19
SLIDE 19

SLAM overview

  • Let us assume that the robot

uncertainty at its initial location is zero.

  • From this position, the robot
  • bserves a feature which is

mapped with an uncertainty related to the sensor error model

ShanghaiTech University - SIST - 23.05.2016

19

slide-20
SLIDE 20

SLAM overview

  • As the robot moves, its pose

uncertainty increases under the effect of the errors introduced by the odometry

ShanghaiTech University - SIST - 23.05.2016

20

slide-21
SLIDE 21

SLAM overview

  • At this point, the robot observes two

features and maps them with an uncertainty which results from the combination of the measurement error with the robot pose uncertainty

  • From this, we can notice that the

map becomes correlated with the robot position estimate. Similarly, if the robot updates its position based

  • n an observation of an imprecisely

known feature in the map, the resulting position estimate becomes correlated with the feature location estimate.

ShanghaiTech University - SIST - 23.05.2016

21

slide-22
SLIDE 22

SLAM overview

  • The robot moves again and its

uncertainty increases under the effect of the errors introduced by the odometry

ShanghaiTech University - SIST - 23.05.2016

22

slide-23
SLIDE 23

SLAM overview

  • In order to reduce its uncertainty, the

robot must observe features whose location is relatively well known. These features can for instance be landmarks that the robot has already

  • bserved before.
  • In this case, the observation is called

loop closure detection.

  • When a loop closure is detected, the

robot pose uncertainty shrinks.

  • At the same time, the map is

updated and the uncertainty of other

  • bserved features and all previous

robot poses also reduce

ShanghaiTech University - SIST - 23.05.2016

23

slide-24
SLIDE 24

FAST SLAM Example

ShanghaiTech University - SIST - 23.05.2016

Courtesy of S. Thrun

24

slide-25
SLIDE 25

FAST SLAM example

ShanghaiTech University - SIST - 23.05.2016

Courtesy of S. Thrun

25

slide-26
SLIDE 26

ShanghaiTech University - SIST - 23.05.2016

Jacobs 3D Mapping – Plane Mapping

Experiment Lab Run: 29 3D point-clouds; size of each: 541 x 361 = 195,301

26

slide-27
SLIDE 27

3D Range Sensing Plane Extraction Planar Scan Matching Pose Graph ...

i j

T

j i

CT

j i

Relax Loop- Closing Errors

Jacobs 3D Mapping – Plane Mapping

ShanghaiTech University - SIST - 23.05.2016

27

slide-28
SLIDE 28

PLANNING

ShanghaiTech University - SIST - 23.05.2016

28

slide-29
SLIDE 29

General Control Scheme for Mobile Robot Systems

Sensing Acting Information Extraction Vision Path Execution Cognition & AI Path Planning Real World Environment Localization Map Building

Motion Control Navigation Perception

ShanghaiTech University - SIST - 23.05.2016

With material from Roland Siegwart and Davide Scaramuzza, ETH Zurich

Raw data Environment Model Local Map Position Global Map Actuator Commands Path 29

slide-30
SLIDE 30

The Planning Problem

  • The problem: find a path in the work space (physical space) from the initial

position to the goal position avoiding all collisions with the obstacles

  • Assumption: there exists a good enough map of the environment for

navigation.

C

  • f

f e e r

  • m

Corridor Bill’s office Topological Map

Coarse Grid Map (for reference only)

C

  • f

f e e r

  • m

Corridor Bill’s office Topological Map

Coarse Grid Map (for reference only)

ShanghaiTech University - SIST - 23.05.2016

30

slide-31
SLIDE 31

The Planning Problem

  • We can generally distinguish between
  • (global) path planning and
  • (local) obstacle avoidance.
  • First step:
  • Transformation of the map into a representation useful for planning
  • This step is planner-dependent
  • Second step:
  • Plan a path on the transformed map
  • Third step:
  • Send motion commands to controller
  • This step is planner-dependent (e.g. Model based feed forward, path following)

ShanghaiTech University - SIST - 23.05.2016

31

slide-32
SLIDE 32

Work Space (Map) à Configuration Space

ShanghaiTech University - SIST - 23.05.2016

  • State or configuration q can be described with k values qi
  • What is the configuration space of a mobile robot?

Work Space Configuration Space: the dimension of this space is equal to the Degrees of Freedom (DoF)

  • f the robot

32

slide-33
SLIDE 33
  • Mobile robots operating on a flat ground (2D) have 3 DoF: (x, y, θ)
  • Differential Drive: only two motors => only 2 degrees of freedom directly controlled (forward/ backward +

turn) => non-holonomic

  • Simplification: assume robot is holonomic and it is a point => configuration space is reduced to 2D (x,y)
  • => inflate obstacle by size of the robot radius to avoid crashes => obstacle growing

Configuration Space for a Mobile Robot

ShanghaiTech University - SIST - 23.05.2016

33

slide-34
SLIDE 34

Path Planning: Overview of Algorithms

  • 3. Graph Search
  • Identify a set edges between nodes within the

free space

  • Where to put the nodes?
  • 1. Optimal Control
  • Solves truly optimal solution
  • Becomes intractable for even moderately

complex as well as nonconvex problems

  • 2. Potential Field
  • Imposes a mathematical function over the

state/configuration space

  • Many physical metaphors exist
  • Often employed due to its simplicity and

similarity to optimal control solutions

Source: http://mitocw.udsm.ac.tz

ShanghaiTech University - SIST - 23.05.2016

34

slide-35
SLIDE 35

Potential Field Path Planning Strategies

  • Robot is treated as a point under the

influence of an artificial potential field.

  • Operates in the continuum
  • Generated robot movement is similar to a

ball rolling down the hill

  • Goal generates attractive force
  • Obstacle are repulsive forces

ShanghaiTech University - SIST - 23.05.2016

35

slide-36
SLIDE 36

Potential Field Path Planning:

  • Notes:
  • Local minima problem exists
  • problem is getting more complex if the robot is not considered as a point mass
  • If objects are non-convex there exists situations where several minimal distances exist →

can result in oscillations

ShanghaiTech University - SIST - 23.05.2016

36

slide-37
SLIDE 37

Graph Search

  • Overview
  • Solves a least cost problem between two states on a (directed) graph
  • Graph structure is a discrete representation
  • Limitations
  • State space is discretized à completeness is at stake
  • Feasibility of paths is often not inherently encoded
  • Algorithms
  • (Preprocessing steps)
  • Breath first
  • Depth first
  • Dijkstra
  • A* and variants
  • D* and variants

ShanghaiTech University - SIST - 23.05.2016

37

slide-38
SLIDE 38

Graph Construction: Visibility Graph

  • Particularly suitable for polygon-like obstacles
  • Shortest path length
  • Grow obstacles to avoid collisions

ShanghaiTech University - SIST - 23.05.2016

38

slide-39
SLIDE 39

Graph Construction: Visibility Graph

  • Pros
  • The found path is optimal because it is the shortest length path
  • Implementation simple when obstacles are polygons
  • Cons
  • The solution path found by the visibility graph tend to take the robot as close as possible to

the obstacles: the common solution is to grow obstacles by more than robot’s radius

  • Number of edges and nodes increases with the number of polygons
  • Thus it can be inefficient in densely populated environments

ShanghaiTech University - SIST - 23.05.2016

39

slide-40
SLIDE 40

Graph Construction: Voronoi Diagram

  • Tends to maximize the distance between robot and obstacles

ShanghaiTech University - SIST - 23.05.2016

40

slide-41
SLIDE 41

Graph Construction: Voronoi Diagram

  • Pros
  • Using range sensors like laser or sonar, a robot can navigate along the Voronoi diagram

using simple control rules

  • Cons
  • Because the Voronoi diagram tends to keep the robot as far as possible from obstacles, any

short range sensor will be in danger of failing

  • Voronoi diagram can change drastically in open areas

ShanghaiTech University - SIST - 23.05.2016

41

slide-42
SLIDE 42

Deterministic Graph Search

  • Methods
  • Breath First
  • Depth First
  • Dijkstra
  • A* and variants
  • D* and variants
  • ...

ShanghaiTech University - SIST - 23.05.2016

42

slide-43
SLIDE 43

DIJKSTRA‘S ALGORITHM

ShanghaiTech University - SIST - 23.05.2016

43

slide-44
SLIDE 44

1930 - 2002 "Computer Science is no more about computers than astronomy is about telescopes."

http://www.cs.utexas.edu/~EWD/

EDSGER WYBE DIJKSTRA

ShanghaiTech University - SIST - 23.05.2016

44

slide-45
SLIDE 45
  • Single-Source Shortest Path Problem - The problem of finding shortest

paths from a source vertex v to all other vertices in the graph.

  • Graph
  • Set of vertices and edges
  • Vertex:
  • Place in the graph; connected by:
  • Edge: connecting two vertices
  • Directed or undirected (undirected in Dijkstra’s Algorithm)
  • Edges can have weight/ distance assigned

SINGLE-SOURCE SHORTEST PATH PROBLEM

ShanghaiTech University - SIST - 23.05.2016

Dijkstra material from http://www.cs.utexas.edu/~tandy/barrera.ppt 45

slide-46
SLIDE 46

Diklstra’s Algorithm

  • Assign all vertices infinite distance to goal
  • Assign 0 to distance from start
  • Add all vertices to the queue
  • While the queue is not empty:
  • Select vertex with smallest distance and remove it from the queue
  • Visit all neighbor vertices of that vertex,
  • calculate their distance and
  • update their (the neighbors) distance if the new distance is smaller

ShanghaiTech University - SIST - 23.05.2016

46

slide-47
SLIDE 47

dist[s] ← 0 (distance to source vertex is zero) for all v ∈ V–{s} do dist[v] ← ∞ (set all other distances to infinity) S ← ∅ (S, the set of visited vertices is initially empty) Q← V (Q, the queue initially contains all vertices) while Q ≠∅ (while the queue is not empty) do u ← mindistance(Q, dist) (select the element of Q with the min. distance) S←S∪{u} (add u to list of visited vertices) for all v ∈ neighbors[u] do if dist[v] > dist[u] + w(u, v) (if new shortest path found) then d[v] ←d[u] + w(u, v) (set new value of shortest path) (if desired, add traceback code) return dist

Diklstra’s Algorithm - Pseudocode

ShanghaiTech University - SIST - 23.05.2016

47

slide-48
SLIDE 48

Dijkstra Example

ShanghaiTech University - SIST - 23.05.2016

48

slide-49
SLIDE 49

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

49

slide-50
SLIDE 50

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

50

slide-51
SLIDE 51

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

51

slide-52
SLIDE 52

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

52

slide-53
SLIDE 53

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

53

slide-54
SLIDE 54

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

54

slide-55
SLIDE 55

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

55

slide-56
SLIDE 56

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

56

slide-57
SLIDE 57

ShanghaiTech University - SIST - 23.05.2016

Dijkstra Example

57

slide-58
SLIDE 58
  • Navigation Systems
  • Internet Routing

APPLICATIONS OF DIJKSTRA'S ALGORITHM

ShanghaiTech University - SIST - 23.05.2016

58

slide-59
SLIDE 59

Dijkstra’s Algorithm for Path Planning: Topological Maps

  • Topological Map:
  • Places (vertices) in the environment

(red dots)

  • Paths (edges) between them

(blue lines)

  • Length of path = weight o edge
  • => Apply Dijkstra’s Algorithm to

find path from start vertex to goal vertex

ShanghaiTech University - SIST - 23.05.2016

59

slide-60
SLIDE 60

Dijkstra’s Algorithm for Path Planning: Grid Maps

  • Graph:
  • Neighboring free cells are connected:
  • 4-neighborhood: up/ down/ left right
  • 8-neighborhood: also diagonals
  • All edges have weight 1
  • Stop once goal vertex is reached
  • Per vertex: save edge over which

the shortest distance from start was reached => Path

ShanghaiTech University - SIST - 23.05.2016

60

slide-61
SLIDE 61

Graph Search Strategies: Breath-First Search

  • Corresponds to a wavefront expansion on a 2D grid
  • Breath-First: Dijkstra‘s search where all edges have weight 1

ShanghaiTech University - SIST - 23.05.2016

61

slide-62
SLIDE 62

Graph Search Strategies: Depth-First Search

B C D A E B C D A F E B C D A G H F E B C D A I D G H F E B C D A D A G H F E B C D A I I K D L A G H F E B C D A I D L A G H F E B C D A

First path found! NOT optimal

I K D L L A G H F E B C D A G I K D L L A G H F E B C D A F G I K D L L A G H I F E B C D A H F G I K C D L L A G H I F E B C D A H F G I K C D L L A A G H I F E B C D A H K F G I K C D L L A A G H I F E B C D A H K F G I K C D L L A A L G H I F E B C D A H K F G I K C D L L L A A L G H I F E B C D A

A=initial B C D F G H I K L=goal E

ShanghaiTech University - SIST - 23.05.2016

62

slide-63
SLIDE 63

Graph Search Strategies: A* Search

  • Similar to Dijkstra‘s algorithm, except that it uses a heuristic function h(n)
  • f(n) = g(n) + ε h(n)

ShanghaiTech University - SIST - 23.05.2016

63

slide-64
SLIDE 64

Graph Search Strategies: Randomized Search

  • Most popular version is the rapidly exploring random tree (RRT)
  • Well suited for high-dimensional search spaces
  • Often produces highly suboptimal solutions

ShanghaiTech University - SIST - 23.05.2016

64