CS 326A: Motion PlanningCS 326A: Motion Planningrobotics.stanford.edu/~latombe/cs326/2004/index.htm

Jean-Claude Latombe

Computer Science DepartmentStanford University

Goal of Motion PlanningGoal of Motion Planning

• Compute motion strategies, e.g.:– geometric paths – time-parameterized trajectories– sequence of sensor-based motion commands

• To achieve high-level goals, e.g.:– go to A without colliding with obstacles– assemble product P– build map of environment E– find object O

Fundamental QuestionFundamental QuestionAre two given points connected by a path?

Valid region

Forbidden region

Fundamental QuestionFundamental QuestionAre two given points connected by a path?

Valid region

Forbidden region

E.g.:▪Collision with obstacle▪Lack of visibility of an object▪Lack of stability

Basic ProblemBasic Problem

Statement: Compute a collision-free path for a rigid or articulated object (the robot) among static obstacles

Inputs:– Geometry of robot and obstacles– Kinematics of robot (degrees of freedom)– Initial and goal robot configurations (placements)

Output:– Continuous sequence of collision-free robot

configurations connecting the initial and goal configurations

Examples with Rigid ObjectExamples with Rigid Object

Ladder problem

Piano-mover problem

Is It Easy?Is It Easy?

Example with Articulated Example with Articulated ObjectObject

Tool: Configuration SpaceTool: Configuration Space

Compare!Compare!

Valid region

Forbidden region

Tool: Configuration SpaceTool: Configuration Space

Problems:• Geometric complexity• Space dimensionality

Some Extensions of Basic Some Extensions of Basic ProblemProblem

• Moving obstacles• Multiple robots• Movable objects• Assembly planning• Goal is to acquire

information by sensing– Model building– Object finding/tracking– Inspection

• Nonholonomic constraints

• Dynamic constraints• Stability constraints

• Optimal planning• Uncertainty in model,

control and sensing• Exploiting task

mechanics (sensorless motions, under-actualted systems)

• Physical models and deformable objects

• Integration of planning and control

• Integration with higher-level planning

Aerospace Robotics Lab Aerospace Robotics Lab RobotRobot

air bearing

gas tank

air thrusters

obstacles

robot

Total duration : 40 sec

Two concurrent planning goals:• Reach the goal• Reach a safe region

Autonomous HelicopterAutonomous Helicopter

[Feron] (MIT)

Assembly PlanningAssembly Planning

Map BuildingMap Building

Where to move next?

Target TrackingTarget Tracking

Planning for Nonholonomic Planning for Nonholonomic RobotsRobots

Under-Actuated SystemsUnder-Actuated Systems

video

[Lynch] (Northwestern)

Planning with Uncertainty in Planning with Uncertainty in Sensing and ControlSensing and Control

I

GWW11

WW22

Planning with Uncertainty in Planning with Uncertainty in Sensing and ControlSensing and Control

I

GWW11

WW22

Planning with Uncertainty in Planning with Uncertainty in Sensing and ControlSensing and Control

I

GWW11

WW22

Motion Planning for Motion Planning for Deformable ObjectsDeformable Objects

[Kavraki] (Rice)

Examples of ApplicationsExamples of Applications• Manufacturing:

– Robot programming– Robot placement– Design of part feeders

• Design for manufacturing and servicing

• Design of pipe layouts and cable harnesses

• Autonomous mobile robots planetary exploration, surveillance, military scouting

• Graphic animation of “digital actors” for video games, movies, and webpages

• Virtual walkthru• Medical surgery

planning• Generation of plausible

molecule motions, e.g., docking and folding motions

• Building code verification

Robot ProgrammingRobot Programming

Robot PlacementRobot Placement

Design for Design for Manufacturing/ServicingManufacturing/Servicing

General ElectricGeneral Electric

General MotorsGeneral MotorsGeneral MotorsGeneral Motors

Assembly Planning and Design Assembly Planning and Design of Manufacturing Systemsof Manufacturing Systems

Part FeedingPart Feeding

Part FeedingPart Feeding

Cable Harness/ Pipe designCable Harness/ Pipe design

Humanoid RobotHumanoid Robot

[Kuffner and Inoue, 2000] (U. Tokyo)

Modular Reconfigurable Modular Reconfigurable RobotsRobots

Xerox, ParcXerox, Parc

Casal and Yim, 1999

Military Scouting and Military Scouting and Planet ExplorationPlanet Exploration

[CMU, NASA]

Digital ActorsDigital Actors

A Bug’s Life (Pixar/Disney) Toy Story (Pixar/Disney)

Tomb Raider 3 (Eidos Interactive) Final Fantasy VIII (SquareOne)The Legend of Zelda (Nintendo)

Antz (Dreamworks)

Motion Planning for Digital Motion Planning for Digital ActorsActors

Manipulation

Sensory-based locomotion

Navigation Through Virtual Navigation Through Virtual EnvironmentsEnvironments

[Cheng-Chin U., UNC, Utrecht U.]

video

Building Code VerificationBuilding Code Verification

Radiosurgical PlanningRadiosurgical Planning

Cross-firing at a tumor while sparing healthy

critical tissue

Study of Study of the Motion of Bio-Moleculesthe Motion of Bio-Molecules

• Protein folding• Ligand binding

Goals of CS326AGoals of CS326A

Present a coherent framework for motion planning problems

Emphasis of “practical” algorithms with some guarantees of performance over “theoretical” or purely “heuristic” algorithms

FrameworkFramework

Continuous representation(configuration space and related spaces + constraints)

Discretization(random sampling, criticality-based decomposition)

Graph searching(blind, best-first, A*)

Practical Algorithms (1/2)Practical Algorithms (1/2)

A complete motion planner always returns a solution plan when one exists and indicates that no such plan exists otherwise.

Most motion planning problems are hard, meaning that complete planners take exponential time in # of degrees of freedom, objects, etc.

Practical Algorithms (2/2)Practical Algorithms (2/2)

Theoretical algorithms strive for completeness and minimal worst-case complexity. Difficult to implement and not robust.Heuristic algorithms strive for efficiency in commonly encountered situations. Usually no performance guarantee. Weaker completeness Simplifying assumptions Exponential algorithms that work in practice

Prerequisites for CS326APrerequisites for CS326A

Ability and willingness to complete a significant programming project with graphic interface.Basic knowledge and taste for geometry and algorithms.Interest in devoting reasonable time each week in reading papers.

CS326A is not a course in …CS326A is not a course in …

Differential Geometry and TopologyKinematics and DynamicsGeometric Modeling

… but it makes use of knowledge from all these areas

Work to DoWork to Do

A. Attend every classB. Prepare/give two presentations with

ppt slides (20 minutes each)C. For each class read the two papers

listed as “required reading” in advance

D. Complete the programming projectE. Complete two homework

assignments

Website and ScheduleWebsite and Schedulerobotics.stanford.edu/~latombe/cs326/2004/index.htm

January 6 1 Overview

January 8 2 Path planning for point robot

January 13 3 Configuration space of a robot

January 15 4 Collision detection 1/2: Hierarchical methods

January 20 5 Collision detection 2/2: Feature-tracking methods

January 22 6 Probabilistic roadmaps 1/3: Basic techniques

January 27 7 Probabilistic roadmaps 2/3: Sampling strategies

January 29 8 Probabilistic roadmaps 3/3: Sampling strategies

February 3 9Criticality-based motion planning: Assembly planning and target finding

February 5 10 Coordination of multiple robots

February 10 11 Kinodynamic planning

February 12 12 Humanoid and legged robots

February 17 13 Modular reconfigurable robots

February 19 14 Mapping and inspecting environments

February 24 15 Navigation in virtual environments

February 26 16 Target tracking and virtual camera

March 2 17 Motion of crowds and flocks

March 4 18 Motion of bio-molecules

March 9 19 Radiosurgical planning

Programming ProjectProgramming Project• Navigate in virtual environment

• Simulate legged robot

• Inspection of structures

• Search and escape