Lecture 11:
Navigation
Dr. Giorgos A. Demetriou
Department of Computer Engineering and Computer Science
School of Engineering and Applied Sciences
[email protected]
http://staff.fit.ac.cy/com.dg
All lectures are based on the Lectures developed at ETH by Roland Siegwart, Margarita Chli and Martin Rufli
mailto:[email protected]
http://staff.fit.ac.cy/com.dg
Navigation is composed of localization, mapping and motion planning
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 2
Required Competences for Navigation
We have come a long way since Shakey!
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 3
Motion Planning in Action
Motion Planning
State-space and obstacle representation
• Work space
• Configuration space
Global motion planning
• Optimal control (not treated)
• Deterministic graph search
• Potential fields
• Probabilistic / random approaches
Local collision avoidance
BUG
VFH
DWA
...
Glimpses into state of the art methods
Dynamic environments
Interaction
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 4
Outline of this Lecture
The problem: find a path in the work space (physical space) from an initial
position to a goal position avoiding all collisions with obstacles
Assumption: there exists a good enough map of the environment for navigation.
Topological
Metric
Hybrid methods
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 5
The Planning Problem (1/2)
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)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 6
The Planning Problem (2/2)
State or configuration q can be described with k values qi
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 7
Work Space (Map) → Configuration Space
Mobile robots operating on a flat ground have 3 DoF: (x, y, θ)
For simplification, in path planning mobile roboticists often assume that the
robot is holonomic and that it is a point. In this way the configuration space is
reduced to 2D (x,y)
Because we have reduced each robot to a point, we have to inflate each obstacle
by the size of the robot radius to compensate.
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 8
Configuration Space for a Mobile Robot
Planning and Navigation I: Global Path Planning
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 9
1. Optimal Control
Solves for the truly optimal solution
Becomes intractable for even moderately
complex and/or nonconvex problems
2. Potential Field
Imposes a mathematical function over the
state/configuration space
Many physical metap ...
Mission Planning and Execution for the Unmanned Rotorcraft ARTISFlorian-Michael Adolf
Wrap-up slide deck on functions developed for the Unmanned Rotorcraft ARITS' Mission Planning and Execution Framework (MiPlEx) as well as a preliminary outlook into adaptations to (unmanned) fixed-wing aircraft kinematics.
[Paper research] GOSELO: for Robot navigation using Reactive neural networksJehong Lee
GOSELO: Goal-Direction Obstacle and Self-Location Map for Robot Navigation Using Reactive Neural Networks 라는 논문을 중심으로, mobile platform의 Path planning을 CNN으로 End-to-End 방식으로 수행하는 방법에 관하여 소개합니다.
광주과학기술원 인공지능 스터디 A-GIST 모임에서 발표했습니다.
발표영상(유튜브, 한국어): https://youtu.be/l-gKjzWKuHA
Optimising Autonomous Robot Swarm Parameters for Stable Formation DesignDaniel H. Stolfi
Autonomous robot swarm systems allow to address many inherent limitations of single robot systems, such as scalability and reliability. As a consequence, these have found their way into numerous applications including in the space and aerospace domains like swarm-based asteroid observation or counter-drone systems. However, achieving stable formations around a point of interest using different number of robots and diverse initial conditions can be challenging. In this article we propose a novel method for autonomous robots swarms self-organisation solely relying on their relative position (angle and distance). This work focuses on an evolutionary optimisation approach to calculate the parameters of the swarm, e.g. inter-robot distance, to achieve a reliable formation under different initial conditions. Experiments are conducted using realistic simulations and considering four case studies. The results observed after testing the optimal configurations on 72 unseen scenarios per case study showed the high robustness of our proposal since the desired formation was always achieved. The ability of self-organise around a point of interest maintaining a predefined fixed distance was also validated using real robots.
https://doi.org/10.1145/3512290.3528709
Path Planning for Mobile Robot Navigation Using Voronoi Diagram and Fast Marc...Waqas Tariq
For navigation in complex environments, a robot needs to reach a compromise between the need for having efficient and optimized trajectories and the need for reacting to unexpected events. This paper presents a new sensor-based Path Planner which results in a fast local or global motion planning able to incorporate the new obstacle information. In the first step the safest areas in the environment are extracted by means of a Voronoi Diagram. In the second step the Fast Marching Method is applied to the Voronoi extracted areas in order to obtain the path. The method combines map-based and sensor-based planning operations to provide a reliable motion plan, while it operates at the sensor frequency. The main characteristics are speed and reliability, since the map dimensions are reduced to an almost unidimensional map and this map represents the safest areas in the environment for moving the robot. In addition, the Voronoi Diagram can be calculated in open areas, and with all kind of shaped obstacles, which allows to apply the proposed planning method in complex environments where other methods of planning based on Voronoi do not work.
Mission Planning and Execution for the Unmanned Rotorcraft ARTISFlorian-Michael Adolf
Wrap-up slide deck on functions developed for the Unmanned Rotorcraft ARITS' Mission Planning and Execution Framework (MiPlEx) as well as a preliminary outlook into adaptations to (unmanned) fixed-wing aircraft kinematics.
[Paper research] GOSELO: for Robot navigation using Reactive neural networksJehong Lee
GOSELO: Goal-Direction Obstacle and Self-Location Map for Robot Navigation Using Reactive Neural Networks 라는 논문을 중심으로, mobile platform의 Path planning을 CNN으로 End-to-End 방식으로 수행하는 방법에 관하여 소개합니다.
광주과학기술원 인공지능 스터디 A-GIST 모임에서 발표했습니다.
발표영상(유튜브, 한국어): https://youtu.be/l-gKjzWKuHA
Optimising Autonomous Robot Swarm Parameters for Stable Formation DesignDaniel H. Stolfi
Autonomous robot swarm systems allow to address many inherent limitations of single robot systems, such as scalability and reliability. As a consequence, these have found their way into numerous applications including in the space and aerospace domains like swarm-based asteroid observation or counter-drone systems. However, achieving stable formations around a point of interest using different number of robots and diverse initial conditions can be challenging. In this article we propose a novel method for autonomous robots swarms self-organisation solely relying on their relative position (angle and distance). This work focuses on an evolutionary optimisation approach to calculate the parameters of the swarm, e.g. inter-robot distance, to achieve a reliable formation under different initial conditions. Experiments are conducted using realistic simulations and considering four case studies. The results observed after testing the optimal configurations on 72 unseen scenarios per case study showed the high robustness of our proposal since the desired formation was always achieved. The ability of self-organise around a point of interest maintaining a predefined fixed distance was also validated using real robots.
https://doi.org/10.1145/3512290.3528709
Path Planning for Mobile Robot Navigation Using Voronoi Diagram and Fast Marc...Waqas Tariq
For navigation in complex environments, a robot needs to reach a compromise between the need for having efficient and optimized trajectories and the need for reacting to unexpected events. This paper presents a new sensor-based Path Planner which results in a fast local or global motion planning able to incorporate the new obstacle information. In the first step the safest areas in the environment are extracted by means of a Voronoi Diagram. In the second step the Fast Marching Method is applied to the Voronoi extracted areas in order to obtain the path. The method combines map-based and sensor-based planning operations to provide a reliable motion plan, while it operates at the sensor frequency. The main characteristics are speed and reliability, since the map dimensions are reduced to an almost unidimensional map and this map represents the safest areas in the environment for moving the robot. In addition, the Voronoi Diagram can be calculated in open areas, and with all kind of shaped obstacles, which allows to apply the proposed planning method in complex environments where other methods of planning based on Voronoi do not work.
AUTO LANDING PROCESS FOR AUTONOMOUS FLYING ROBOT BY USING IMAGE PROCESSING BA...csandit
In today’s technological life, everyone is quite familiar with the importance of security
measures in our lives. So in this regard, many attempts have been made by researchers and one
of them is flying robots technology. One well-known usage of flying robot, perhaps, is its
capability in security and care measurements which made this device extremely practical, not
only for its unmanned movement, but also for the unique manoeuvre during flight over the
arbitrary areas. In this research, the automatic landing of a flying robot is discussed. The
system is based on the frequent interruptions that is sent from main microcontroller to camera
module in order to take images; these images have been distinguished by image processing
system based on edge detection, after analysing the image the system can tell whether or not to
land on the ground. This method shows better performance in terms of precision as well as
experimentally.
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The formalism of hybrid programs is a relatively recent development by Platzer et al. (CSD) that allows holistic reasoning about discrete and continuous behavior within the same model. This makes hybrid modeling and verification, supported by tools like KeYmaera, an attractive method for analyzing cyber-physical systems. However, hybrid programs do not operate architectural concepts, making it difficult to relate them between each other and other kinds of CPS models. My talk introduces architectural annotations for hybrid programs that allow engineers to express the otherwise implicit architectural knowledge. This presentation discusses annotation primitives and their interpretation.
UH Professor Arthur Weglein's M-OSRP Annual Report, 2013Arthur Weglein
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Waypoint Flight Parameter Comparison of an Autonomous Uavijaia
The present paper compares the effect of different waypoint parameters on the flight performance of a
special autonomous indoor UAV (unmanned aerial vehicle) fusing ultrasonic, inertial, pressure and optical
sensors for 3D positioning and controlling. The investigated parameters are the acceptance threshold for
reaching a waypoint as well as the maximal waypoint step size or block size. The effect of these parameters
on the flight time and accuracy of the flight path is investigated. Therefore the paper addresses how the
acceptance threshold and step size influence the speed and accuracy of the autonomous flight and thus
influence the performance of the presented autonomous quadrocopter under real indoor navigation
circumstances. Furthermore the paper demonstrates a drawback of the standard potential field method for
navigation of such autonomous quadrocopters and points to an improvement
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Robot navigation in unknown environment with obstacle recognition using laser...IJECEIAES
Robot navigation in unknown and dynamic environments may result in aimless wandering, corner traps and repetitive path loops. To address these issues, this paper presents the solution by comparing the standard deviation of the distance ranges of the obstacles appeared in the robot navigation path. For the similar obstacles, The standard deviations of distance range vectors, obtained from the laser range finder sensor of the robot at similar pose, are very close to each other. Therefore, the measurements of odometer sensor are also combined with the standard deviation to recognize the location of the obstacles. A novel algorithm, with obstacle detection feature, is presented for robot navigation in unknown and dynamic environments. The algorithm checks the similarity of the distance range vectors of the obstacles in the path and uses this information in combination with the odometer measurements to identify the obstacles and their locations. The experimental work is carried out using Gazebo simulator.
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How do courts determine if evidence is reliable and valid before allowing it into testimony?
What is the role of the Frye standard or Daubert standard in determining whether or not the courts will accept biometric evidence?
What rules does your state use in this regard?
How reliable is fingerprint evidence? Consider examples of its use in criminal courts.
How do other biometrics compare to the reliability and validity of fingerprint evidence?
What are some of the challenges associated with lower forms of biometrics, such as facial recognition, and acceptance as evidence in court?
What is the role of the expert witness related to biometric evidence in court?
Be sure to provide in-text citation and references
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special autonomous indoor UAV (unmanned aerial vehicle) fusing ultrasonic, inertial, pressure and optical
sensors for 3D positioning and controlling. The investigated parameters are the acceptance threshold for
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Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
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In 2003, China sent a person into space. China became just the third.docxjoyjonna282
In 2003, China sent a person into space. China became just the third country to do so. It sent a spaceship to go around Earth 14 times. It took less than a day. It was very important. China had never tried this before. Most countries do not send people into space. It costs a lot of money. China wanted to show the world that it could do it. China was proud to send people into space.
The trip to space was _________ for them.
.
In 250 words briefly describe the adverse effects caused by exposure.docxjoyjonna282
In 250 words briefly describe the adverse effects caused by exposure to radiation. Include some specific exposure levels associated with these significant health effects. Lastly, give some examples of measured radiation levels associated with the Three Mile Island incident in the U.S. and in the Chernobyl incident in the Soviet Union. Provide your reference source(s). (Wikipedia is not an accepted reference source.)
.
In 2.5 pages, compare and contrast health care reform in two differe.docxjoyjonna282
In 2.5 pages, compare and contrast health care reform in two different states. Your paper should include a minimum of three specific examples of similarities or differences in health care reform in the two states.
Example:
One possibility would be to compare Maine's health care reform in 2003 to Tennessee's 1994 health care reform known as "TennCare."
APA FORMAT
APA REFERENCES
.
In 2014 Virginia scientist Eric Betzig won a Nobel Prize for his res.docxjoyjonna282
In 2014 Virginia scientist Eric Betzig won a Nobel Prize for his research in microscope technology. Since receiving the award, Betzig has improved the technology so that cell functions, growth and even movements can now be seen in real time while minimizing the damage caused by prior methods. This allows the direct study of living nerve cells forming synapses in the brain, cells undergoing mitosis and internal cell functions like protein translation and mitochondrial movements.
Your assignment is to write a Python program that
graphically
simulates viewing cellular organisms, as they might be observed using Betzig’s technology. These simulated cells will be shown in a graphics window (representing the field of view through Betzig’s microscope) and must be animated, exhibiting behaviors based on the
“Project Specifications” below
. The simulation will terminate based on user input (a mouse click) and will include two (2) types of cells,
Crete
and
Laelaps
, (
pronounced
KREET
and
LEE
-
laps
).
Crete
cells should be represented in this simulation as three (3) small green circles with a radius of 8 pixels. These cells move nonlinearly in steps of 1-4 graphics window pixels. This makes their movement appear jerky and random.
Crete
cells cannot move outside the microscope slide, (the ‘
field
’), so they may bump along the borders or even wander out into the middle of the field at times. These cells have the ability to pass “through” each other.
A single red circle with a radius of 16 pixels will represent a
Laelaps
cell in this simulation.
Laelaps
cells move across the field straight lines, appearing to ‘bounce’ off the field boundaries.
Laelaps
sometimes appear to pass through other cells, however this is an optical illusion as they are very thin and tend to slide over or under the other cells in the field of view.
Project Specifications: ====================
Graphics Window
500 x 500 pixel window
White background
0,0 (x,y) coordinate should be set to the lower left-hand corner
Crete
Cells
Three (3) green filled circles with radius of 8 pixels
Move in random increments between -4 and 4 pixels per step
Movements are not in straight lines, but appear wander aimlessly
Laelaps
Cells
One (1) red filled circle with a radius of 16 pixels
Move more quickly than Crete cells and in straight lines
The Laelaps cell should advance in either -10 or 10 pixels per step
TODO #1: Initialize the simulation environment ========================================
Import any libraries needed for the simulation
Display a welcome message in the Python Shell. Describe the program’s functionality
Create the 500 x 500 graphics window named “
Field
”
Set the
Field
window parameters as specified
TODO #2: Create the
Crete
cells –
makeCrete()
========================================
Write a function that creates three green circle objects (radius 8) and stores them in a list
Each entry of the list represents one
Crete
cell
The.
In 200-300 words - How is predation different from parasitism What.docxjoyjonna282
In 200-300 words - How is predation different from parasitism? What structures and behavior aid the predaceous insect to be successful? Please give an example.
In 200-300 words-
Why is an understanding of metamorphosis crucial to identifying adult insects? Provide examples where knowing development patterns can prevent incorrect identification.
.
In 3 and half pages, including a title page and a reference page, di.docxjoyjonna282
In 3 and half pages, including a title page and a reference page, discuss various methods of establishing the identity of a murder victim.
In your discussion include an explanation of methods used to identify the dead when only teeth and bones of the victim are available for examination.
Use materials from the text and/or any outside resources to support your response.
.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Lecture 11 Navigation Dr. Giorgos A. Demetrio.docx
1. Lecture 11:
Navigation
Dr. Giorgos A. Demetriou
Department of Computer Engineering and Computer Science
School of Engineering and Applied Sciences
[email protected]
http://staff.fit.ac.cy/com.dg
All lectures are based on the Lectures developed at ETH by
Roland Siegwart, Margarita Chli and Martin Rufli
mailto:[email protected]
http://staff.fit.ac.cy/com.dg
planning
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 2
Required Competences for Navigation
2. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 3
Motion Planning in Action
-space and obstacle representation
• Work space
• Configuration space
• Optimal control (not treated)
• Deterministic graph search
• Potential fields
• Probabilistic / random approaches
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 4
3. Outline of this Lecture
from an initial
position to a goal position avoiding all collisions with obstacles
environment for navigation.
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 5
The Planning Problem (1/2)
planning
-dependent
a path on the transformed map
4. -dependent (e.g. Model based feed
forward, path following)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 6
The Planning Problem (2/2)
e or configuration q can be described with k values qi
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 7
Work Space (Map) → Configuration Space
θ)
mobile roboticists often
assume that the
robot is holonomic and that it is a point. In this way the
configuration space is
reduced to 2D (x,y)
inflate each obstacle
by the size of the robot radius to compensate.
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 8
5. Configuration Space for a Mobile Robot
Planning and Navigation I: Global Path Planning
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 9
1. Optimal Control
truly optimal solution
complex and/or nonconvex problems
2. Potential Field
state/configuration space
ue to its simplicity and
similarity to optimal control solutions
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 10
Path Planning: Overview of Algorithms
6. 3. Graph Search
nodes within the free space
-point boundary problem in the continuum
increases
Algorithms
-Jacobi-Bellman
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 11
Optimal Control based Path Planning Strategies
7. influence of an artificial potential field.
a ball rolling down the hill
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 12
Potential Field Path Planning Strategies
roportional to the force F(q)
generated by the field
-holonomics are
hard to deal with)
8. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 13
Potential Field Path Planning: Potential Field Generation
to the goal
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 14
Potential Field Path Planning: Attractive Potential Field
the object
to the object
9. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 15
Potential Field Path Planning: Repulsing Potential Field
m is getting more complex if the robot is not
considered as a point mass
-convex there exists situations where
several minimal distances exist
→ can result in oscillations
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 16
Potential Field Path Planning:
and a task potential field is introduced
orientation relative to the obstacles.
This is done using a gain factor that
reduces the repulsive force when
obstacles are parallel to robot’s
direction of travel
10. not influence the robots movements,
i.e. only the obstacles in the sector in
front of the robot are considered
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 17
Potential Field Path Planning: Extended Potential Field Method
stream
re no local minima
• Equipotential lines orthogonal on object boundaries (as in
image above!)
• Short but dangerous paths
• Equipotential lines parallel to object boundaries
• Long but safe paths
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 18
11. Potential Field Path Planning: Using Harmonic Potentials
graph
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 19
Graph Search
C wikipedia.org
12. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 20
Graph Construction (Preprocessing Step)
-like obstacles
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 21
Graph Construction: Visibility Graph (1/2)
ause it is the shortest length
path
the robot as close as
possible to the obstacles: the common solution is to grow
obstacles by more than
robot’s radius
polygons
13. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 22
Graph Construction: Visibility Graph (2/2)
Diagram tends to
maximize the distance between robot and obstacles
-building: Move on the Voronoi edges: 1D
Mapping
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 23
Graph Construction: Voronoi Diagram (1/2)
along the Voronoi
diagram using simple control rules
oi diagram tends to keep the robot as far as
possible from
obstacles, any short range sensor will be in danger of failing
14. straight and parabolic
segments
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 24
Graph Construction: Voronoi Diagram (2/2)
connectivity graph
d goal configuration (state)
lie and search for a
path in the connectivity graph to join them.
algorithm, compute
a path within each cell.
daries or by
sequence of wall following
movements.
• Fixed cell decomposition
15. • Adaptive cell decomposition
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 25
Graph Construction: Cell Decomposition (1/4)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 26
Graph Construction: Exact Cell Decomposition (2/4)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 27
Graph Construction: Approximate Cell Decomposition (3/4)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 28
Graph Construction: Adaptive Cell Decomposition (4/4)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 29
Graph Construction: State Lattice Design (1/2)
16. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 30
Graph Construction: State Lattice Design (2/2)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 31
Graph Search
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 32
Graph Search Strategies: Breadth-First Search
ds to a wavefront expansion on a 2D grid
17. -found solution is optimal if all edges have equal costs
-sorted” HEAP variation of
breadth first search
-found solution is guaranteed to be optimal no matter the
cell cost
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 33
Graph Search Strategies: Breadth-First Search
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 34
Graph Search Strategies: Depth-First Search
“f(n)-sorted”)
f(n) = g(n) + εh(n)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 35
Graph Search Strategies: A* Search
18. goal outward
f(n) = g(n) + εh(n)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 36
Graph Search Strategies: D* Search
(RRT)
-dimensional search spaces
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 37
Graph Search Strategies: Randomized Search
Planning and Navigation II: Obstacle Avoidance
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 38
is to avoid collisions with obstacles
19. independent task
should be optimal with respect to
cs of the
robot
-boards sensors
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 39
Obstacle Avoidance (Local Path Planning)
is once fully circled before it is
left at the point closest
to the goal
required
guaranteed
20. Solution
s are often
highly suboptimal
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 40
Obstacle Avoidance: Bug1
and goal is crossed
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 41
Obstacle Avoidance: Bug2
21. obstacle
• All openings for the robot to pass are found
• The one with lowest cost function G is selected
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 42
Obstacle Avoidance: Vector Field Histogram (VFH)
way for vehicle kinematics
ng on arcs or straight
lines
direction also blocks all the
trajectories (arcs) going through
22. this direction
kinematically blocked trajectories
are properly taken into account
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 43
Obstacle Avoidance: Vector Field Histogram+ (VFH+)
anteed
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 44
Obstacle Avoidance: Limitations of VFH
23. velocity space:
dynamic window approach
considers only circular
trajectories uniquely determined by pairs (v,ω) of translational
and rotational
velocities.
admissible, if the robot is able to
stop before it reaches the closest obstacle on the corresponding
curvature.
(b: breakage)
admissible velocities to those
that can be reached within a short time interval given the
limited accelerations of the
robot
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 45
24. Obstacle Avoidance: Dynamic Window Approach
areas, namely,
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 46
Obstacle Avoidance: Dynamic Window Approach
velocity, the maximum of the
objective function, G(v, ω), is computed over Vr.
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 47
Dynamic Window Approach
25. -free function (e.g. NF1
wave-propagation) to the
objective function O presented above.
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 48
Obstacle Avoidance: GlobalDynamic Window Approach
Planning and Navigation III: Architectures
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 49
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 50
Basic architectural example
26. -think-act)
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 51
Control decomposition
viors
-initiating the planner
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 52
27. General Tiered Architecture
-time capable
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 53
A Three-Tiered Episodic Planning Architecture
executive layer →
see case study
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 54
An integrated planning and execution architecture
28. Planning and Navigation IV: Case Studies
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 55
fusion
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 56
Localization –Position Estimation
traversability maps
Dr. Giorgos A. Demetriou ACSC 414 - Robotics 57
Planning in Mixed Environments
29. Dr. Giorgos A. Demetriou ACSC 414 - Robotics 58
Navigation in Dynamic Environments
-dimensional State Lattice