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EE-562:Robot Motion Planning Lecture 1 ۵۶۲ �ت ب رو�ِ ى ءء�Dr Abubakr Muhammad Assistant Professor Electrical Engineering, LUMS Director, CYPHYNETS Lab http://cyphynets.lums.edu.pk

EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

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Page 1: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

EE-562:Robot Motion PlanningLecture 1

 رو�با�ت ۵۶۲ ِ ءء    ��ى

Dr Abubakr MuhammadAssistant Professor

Electrical Engineering, LUMSDirector, CYPHYNETS Lab

http://cyphynets.lums.edu.pk

Page 2: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Resources

Course material from • CMPE-633x series (2010-13) at CYPHYNETShttp://cyphynets.lums.edu.pk/index.php/Teaching• CMU course RI 16-735 by Howie Choset.

Textbooks• Principles of Robot Motion by Choset et al. • Planning Algorithms by Steven Lavalle

Page 3: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a robot?

• Public perception• Pop culture images

Page 4: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a Robot?A mechanical system that has sensing, actuation

and computation capabilities. Other names (in other disciplines)• Autonomous system• Intelligent agent• Control system

Page 5: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a robot?

• Is a toaster a robot?

• Is a movie recommender system a robot?

• Is a thermostat a robot?

• Is a car cruise control system a robot?

• Is an aircraft auto-pilot a robot?

Page 6: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What are Robots?

• A robot is an intelligent connection of perception to action.

• A robot is an autonomous system which exists in the physical world, senses its environment and acts in it to achieve some goals.

Page 7: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Think again …• Is a toaster a robot?

• Is a movie recommender system a robot?

• Is a thermostat a robot?

• Is a car cruise control system a robot?

• Is an excavator a robot?

• Is an aircraft auto-pilot a robot?

A robot is an autonomous system which exists in the physical world, senses its environment and acts in it to achieve some goals.

Page 8: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What Makes a Robot?• A robot consists of:

– sensors– effectors/actuators– communication– controller

• A robot is a rational agent capable of– acting autonomously– achieving goals

• Robota means self labour, drudgery, hardwork in Czech

•  +�+آ� = رو�با� رو  (Urdu Wikipedia)

Page 9: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is Robotics?• The art and science of making robots

• Where are roboticists found – Electrical engineering (control systems) – Mechanical engineering (mechanisms) – Computer science (AI, learning) – Mechatronics– Bioengineering

• Increasingly important – Lawyers (legal issues, labor laws) – Philosophers (ethical issues) – Economists (disruptive technologies)– Social scientists (the social impacts of automation, aesthetics)

Page 10: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

When did the first robots appear?• Hero’s automatic devices (~50 AD Alexandria)• Su Song’s clock towers (~1000 AD China)• Al-Jazari’s hydraulic automatons (~1200 AD Arabia)• Leonardo de Vinci’s mechanical knights (~1500 AD)• Tea serving karakuri puppets (~1800 AD)

Page 11: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Modern RoboticsThree broad categories 1. Industrial robots: manipulators (1970’s)2. Mobile robots: platforms with autonomy (1980’s)3. Mobile manipulators = manipulator + mobility (2000’s)

Page 12: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Industrial Manipulators

Page 13: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones
Page 14: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Some Mobile Robots Terminology

• UAV: Unmanned Aerial Vehicle• UGV: Unmanned Ground Vehicle• UUV: Unmanned Undersea

(underwater) Vehicle• AUV: Autonomous Underwater

Vehicle

Page 15: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones
Page 16: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Bio-inspired / Walking Machines

Page 17: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Why do we create robots?

• A question for – the philosopher: rationalize the need? – the psychologist: man’s creative traits? – the theologist: man’s obsession with divinity?

• A personal view point– Bible: “God created man in His own image.” (Genesis 1:27)– Hadith: “Allah created Adam in His image.” (Bukhari,

Muslim) صورتهآدم على هللا خلق

Page 18: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Why Robots?• Natural continuation of the industrial & information

revolutions – automation

• Better at dull repetitive tasks• Increased productivity• Can perform risky/dangerous tasks• Can work round the clock• No labor unions!

• Fukushima Daichii nuclear reactor (2011 earthquake)– 1,973 TEPCO emergency workers affected by radiation

Page 19: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Robots and Future Economies• Why do Robots have a role to play?• Where will be the greatest impact?

– Driving, Mining, Agriculture, Healthcare, Humanitarian, Defense

• What are the challenges and problems? – Legal challenges– Ethical issues

• Robots and the developing world: What will be the social impact? – Automation and society – Social engineering – Conflicts and responsibility

Page 20: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Self-Driving Trucks for Mining

• 17 Self-driving trucks deployed for mining in australia

• Increased accuracy in operation as compared to humans

• Improved earth excavation

Page 21: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Autonomous Driving

• Market for advanced driver assistance systems to grow from $10 billion now to $130 billion in 2016

• Projected to reach $500 billion by 2020

Page 22: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Autonomous Driving

• Tesla—90% autonomous vehicle within 3 years

• EURO-NCAP automated emergency braking mandatory by 2014

• For 5-star safety rating, vehicle has to be ‘robotic’

Page 23: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Defense: Unmanned Aerial Vehicles• Drones—combat, surveillance• First appeared during the vietnam war• First recorded targeted killing– 2002

(afghanistan)• Global UAV market--$5.9 billion now to $8.35

billion in 2018

Page 24: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Defense: Unmanned Aerial Vehicles

• NYU/stanford report—2,562-3,325 fatalities in pakistan

• U.S pullout from Afghanistan-- integration of decommissioned UAVs

• Market ripe for drones for surveillance • Other uses: weather research, law

enforcement

Page 25: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Defense: Driverless Vehicles

• 1/3 of all U.S Military vehicles to be autonomous by 2015

• Terramax-- Oshkosh Trucking Corporation• Black Knight– Unmanned Tank

Page 26: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Unmanned Agricultural Machines

• Efficient utilization of resources• Uavs for spraying insecticides• Driverless tractors

Page 27: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Unmanned Agricultural Machines

• Possible Applications: Weeding, Harvesting, Pruning, Canal Cleaning (‘Bhal Safai’)

• Lettuce Bot (Blue River Technology)—Eliminates Leafy Buds 20x Faster

Page 28: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Humanitarian

• Landmine detection• Bomb disposal• Prosthetic limbs—full restoration of original

capabilities

Page 29: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Surgical Robots

• Surgical robotics-higher precision, repeatability, cost-effective

• Significantly lower blood loss• Minimally invasive surgery

Page 30: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Surgical Robots

• Flagship--da vinci surgical robot• Surgical robot market to reach significant

growth• Market size: $3.2 billion in 2012, anticipated

to reach $19.96 billion by 2019

Page 31: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Assistive Robots

• Robotic vacuum cleaners• Global market share of robotic vacuum

cleaners-- 12% of $680 million

Page 32: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Assistive Robotics

• Growing elderly population in developed countries

• Demographics to change by 2050 • Over 60 to form 22% of the world population

compared to the 11% today• Needs: visual assistance, emergency

assistance, mobility assistance

Page 33: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Factories of the Future• Declining costs

– Industrial grade manipulators ~ > $100,000– Baxter (rethink robotics) costs $22,000

• Small & Medium Enterprises (SME’s) entering the fray• Need consistent quality• Lean operation• Higher productivity• Higher accuracy in

safety critical applications

Page 34: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Baxter-Capabilities

VS

Page 35: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Case Study: China

• Low cost robots competing against the minimum wage rate

• Youth unwilling to perform manual labor• Delta electronics and foxconn looking to

develop a $10,000 robot

Page 36: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Case Study: India

• India--Market for Robots Will Increase From 1,547 to 3,500 Units By 2015

• SME’s entering into robotics • Labor is plenty but unskilled• Job hopping

Page 37: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Challenges: Demons of Automation• Unemployment ? – classical debate from

romantic era

• Worker lay-off

• Eventually little or no need for skilled labor

• Driving may look obsolete in 25 years– 4 million driving jobs will be lost

• Agricultural robotics—farming labor to lose jobs

Page 38: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Challenges: Legal and Ethical• Autonomous driving and legal aspects

– Who is driving the car? – Accident and insurance – Passenger safety

• Surgical robots – Similar issues– Patient care, liability

• Drones (e.g. unmanned aerial vehicles UAVs)– Who pulled the trigger? – Wars and international law

• Social Acceptance of Robots

Page 39: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is in store for developing countries?

• A storm is coming?

• Major challenges to the social fabric

• Raise ethical challenges

• From nuclear age to the robotic age

• A brave new world?

Page 40: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is in store for countries like Pakistan?• Why Automation in developing countries like Pakistan?

– Devolution of governance– Ensuring rights– Conflict resolution

• Bridging the gap of “expertise” – a different robotics paradigm

• Major challenges– Natural resources– Food and Agriculture Problems– Critical infra-structures– Security

• Robotics, AI and automation may be the answer to some of these!

Participation

Accountability

Entitlements

Page 41: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a Motion Planner?High Level Specifications

Low Level descriptions of how to move

Motion Planner

Page 42: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a Motion Planner?High Level Specifications

Low Level descriptions of how to move

Motion Planner

Page 43: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a Motion Planner?High Level Specifications

Low Level descriptions of how to move

Do this while 1. Avoiding obstacles2. Obey differential constraints3. Handle uncertainties4. Achieve optimality

Motion Planner

Page 44: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Other Perspectives• Control theory ~ feedback policies

– Tool: Differential equations on continuous spaces– Robustness, stability, optimality– Obstacle avoidance via explicit representations– Model constraints as holonomic / nonholonomic

Related Courses at LUMSCMPE-633B. Robot Dynamics and Control(Fall 2011)

CMPE-633C. Geometric Mechanics (Spring 2012)

Page 45: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Other ways of looking at it …• Control theory perspective ~ feedback policies• Artificial Intelligence

– Solving puzzles on a discrete space – Focus on algorithmic methods – Obstacle avoidance via explicit labeling

Page 46: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

A Merged Perspective

• Robot Motion Planning as a subject• Born in 1980’s• Matured in 2000’s

Page 47: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

A Merged Perspective

• Robot Motion Planning as a subject• Born in 1980’s• Matured in 2000’s

Related Courses at LUMSCMPE 633A. Robot Motion Planning (Fall 2010)

CASM Workshop at LUMSTopology of HyperplaneArrangements (Fall 2012)

HEC grant in MathematicsSelf Assembly of Hexagonal Structures (2013-14)

Page 48: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

A Merged Perspective

• Robot Motion Planning as a subject• Born in 1980’s• Matured in 2000’s

• In this course ….– We focus on algorithmic and computational issues

in motion planning.– We avoid talking about hardware

implementations, software architectures, formal algorithmic complexity analysis.

Page 49: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

A Merged Perspective

• Robot Motion Planning as a subject• Born in 1980’s• Matured in 2000’s

• Some capabilities of the robot are assumed• E.g. ability to sense, localize, map so that

real world = computer world

Page 50: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

A Merged Perspective

• Robot Motion Planning as a subject• Born in 1980’s• Matured in 2000’s

• Some capabilities of the robot are assumed• E.g. ability to sense, localize, map so that

real world = computer world Related Courses at LUMSEE 622. Applied State Estimation (Spring 2013)

ME 410. Probabilistic Robotics (Summer 2011)

Page 51: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

What is a Motion Planner?• Interaction between Robot and environment

• Where is the planner?

Page 52: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Classical Refinement Approach

Page 53: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Applications

• Parking a car / trailer

Page 54: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Applications

• Painting / sealing in automotive manufacturing

Page 55: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Applications

• Part assembly

Page 56: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Applications

• Humanoids / mobile manupilation

Page 57: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Applications

• Protein folding / docking• Drug discovery

Page 58: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Terminology• State / configuration

– E.g. position & velocity of a robot– Special states: initial state, final state

• Time – A sequence describing chronology of events – E.g. to describe initial, final, intermediate

• Actions – Manipulation of the state to get to another

state – Inputs or controls

• Plan– Strategy of actions acting on states. – E.g. When we are in Initial state move forward.

Page 59: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Challenges in Motion Planning• Notice that in practical problems

– Degrees of freedom are high– Structure of configuration / state space is complex– Difficulty in understanding CS topology– Uncertainty in representations (noise)

• General motion planning problem is PSPACE-hard [Reif 1979].• Complexity exponential in dimension of configuration space

[Canny 1998].

Page 60: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Where is the problem?

• Building a complete planner requires building the complete configuration space.

• Can we settle by trading completeness for some practical efficiency?

Page 61: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

Examples

Page 62: EE-562 Robot Motion Planning Lecture 1 ت اب ور ءءِى · Course material from • CMPE-633x series (2010-13) at CYPHYNETS ... decommissioned UAVs • Market ripe for drones

EE562 - Modules• Foundations

– Motivation & mathematical representation– Configuration spaces

• Analytical Motion Planning– No noise – Exact geometry available

• Probabilistic Motion Planning– No noise – Practical efficiency vs completeness

• Map building and localization – Uncertainties due to sensor and process noise– Real applications

• Running Theme– Open source hands-on tools (ROS, OMPL)