# Lecture 20 Motion Planning II - Publish.illinois.edu

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Lecture 20Motion Planning IIKatie DCModern Robotics Ch 10.2-10.5

Administrivia Upcoming homework due dates: HW6 due 11/14 at 8pm HW7 due 11/19 at 8pm HW8 (bonus) due 12/10 at 8pm Note that it will likely be a good review for the exam! Last few lectures: 11/16 will be a guest lecture – attendance is required! 11/18 will be a review session 11/30 and 12/2 will be project presentations Exam 2 is on 12/7 during lecture

all deadlines and submission instructions are on the website

Who is NancyAmato? Head of the CS department and expert in motion planning Her paper on probabilistic planning is one of the most importantpapers in PRM, the first to not use uniform sampling in theconfiguration space She and her team wrote a seminal paper that shows how robotplanning can be applied to protein motions (folding)à This line of work started a new research area in comp. biology

Motion Planning Overview

Graphs and Trees Motion planners often represent C-space as a graph A graph is a collection of nodes 𝒩 and edges ℰ, where edge 𝑒 connects two nodes A tree is a directed graph with no cycles and each node has at least one parent

Graphs and Trees

Grid-World Example

Graph Search MethodsA* search algorithm.Dijkstra’s algorithm.Credit: Subh83 on Wikipedia

A simple roadmap: visibility graph

A simple roadmap: visibility graph

Sampling Based Planners: Probabilistic Roadmaps

Reachability Tree for Dubin’s CarCredit: Steven LaValle, Planning Algorithms

Rapidly Exploring Random Trees (RRT)

Rapidly Exploring Random Trees (RRT)

RRT: Lunar LanderCheck out Steven Lavalle’s RRT Gallery: http://msl.cs.uiuc.edu/rrt/gallery.html

Summary Given an initial state and a desired final state, motion planning providesus with tools to find a time horizon and a sequence of actions to find atrajectory that reaches the goal without collisions A roadmap path planner uses a graph representation of free space,which can then provide a trajectory using search algorithms The basic RRT algorithm is a sampling-based method that grows a singlesearch tree from start to find a motion to goal Uses a local planner to find a motion from the nearest node to the sampled node

A few things that might be useful to know What are some key properties of planners? Think about what applications some properties or types of plannersmight be needed. If given a very simple graph, can you find the shortest path? Be somewhat familiar with the pros and cons of the planners we justdiscussed.

Course Recapsensethinkact1.2.3.4.5.6.7.8.9.Linear algebra and diff. eq. reviewDoF, configuration spaceRigid body motion & transformationsScrew theoryForward KinematicsVelocity KinematicsInverse KinematicsDynamicsMotion Planning

SensorsPerceptionDecision-MakingSimulation & ValidationTrajectory PlanningLow-level ControlEnvironment& Agent ModelsCompute Platform

If you liked Try this!Everything!ABE 424 Principles of Mobile RoboticsECE 484 Principles of Safe AutonomyLinear AlgebraMATH 415 Applied Linear AlgebraECE 515 / ME 540 Control System Theory and DesignSensing and State EstimationECE 310 / 417 Signal ProcessingECE 437 Sensors and InstrumentationABE 424 Principles of Mobile RoboticsRobot KinematicsECE 489 / ME 446 / SE 422 Robot Dynamics and ControlCS 498 Robot Manipulation and PlanningRigid Body MotionSE 598 Soft RoboticsECE 549 Computer VisionControlECE 486 Control Systems (or equivalent in your department)ECE 515 / ME 540 Control System Theory and DesignDecision-MakingECE 448 Introduction to AICS 446 Machine LearningPlanningCS 498 Robot Manipulation and PlanningLabsSE 423 Introduction to MechatronicsGraduate-Level Topics CoursesECE 598SG Learning-Based RoboticsECE 598HCR Human-Robot InteractionECE 598JK Humanoid RoboticsCS 598 Advanced Computational Robotics

If you liked Try this!Everything!ABE 424 Principles of Mobile RoboticsECE 484 Principles of Safe AutonomyLinear AlgebraMATH 415 Applied Linear AlgebraECE 515 / ME 540 Control System Theory and DesignSensing and State EstimationECE 310 / 417 Signal ProcessingECE 437 Sensors and InstrumentationABE 424 Principles of Mobile RoboticsRobot KinematicsECE 489 / ME 446 / SE 422 Robot Dynamics and ControlCS 498 Robot Manipulation and PlanningRigid Body MotionSE 598 Soft RoboticsECE 549 Computer VisionControlECE 486 Control Systems (or equivalent in your department)ECE 515 / ME 540 Control System Theory and DesignDecision-MakingECE 448 Introduction to AICS 446 Machine LearningPlanningCS 498 Robot Manipulation and PlanningLabsSE 423 Introduction to MechatronicsGraduate-Level Topics CoursesECE 598SG Learning-Based RoboticsECE 598HCR Human-Robot InteractionECE 598JK Humanoid RoboticsCS 598 Advanced Computational Robotics

Linear Algebra /DifferentialEquationsECE486(or equivalent)Control SystemsECE313(or equivalent)Intro to ProbabilityABE424Principles ofMobile RoboticsECE484Principles ofSafe AutonomyCS598AdvancedComp. RoboticsABE 524Autonomous Decisionmaking (Field Robotics)CS588Autonomous VehicleSystems EngineeringECE550Robot PlanningECE598Human-RobotInteractionIntroductionto RoboticsRobot Dynamics& ControlLegendManipulatorsGeneral RoboticsMobile Robotics AutonomyRobotSuggested PrereqsSE423Introductionto E598Humanoid RoboticsFor full list of recommendedand related courses, check outrobotics.Illinois.edu/educationCS 498Robot Manipulation& PlanningSE598Soft RoboticsECE598Learning-BasedRoboticsFamiliarity withML/AI/MDPsex: ECE448,CS446,ECE586

robotics.Illinois.edu/education ECE470/ME445/AE482 Introduction to Robotics ECE489/ME446/SE422 Robot Dynamics & Control ECE550 Robot Planning ABE424 Principles of Mobile Robotics CS 498 Robot Manipulation & Planning SE598 Soft Robotics ECE598 Humanoid Robotics ECE484 Principles of Safe Autonomy ECE313 (or equivalent) Intro to

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