1. CS6370/ME6225 Geometric Computation for Motion Planning Instructor: David Johnson dejohnso@cs.utah.edu

2. Why This Course What do you want to get out of this?What do you want to get out of this?Students

3. Why This Course What do you want to get out of this?What do you want to get out of this? StudentsMe Understand common planning methods Appreciate underlying theory Better programmer and/or learn Matlab Use geometry to solve/simulate problems Practice reading and reporting scientific results Better applied mathematics Become part of your research endeavors Help form a chapter in your thesis Write a paper with you

4. Syllabus Check class web page for updatesCheck class web page for updateshttp://www.eng.utah.edu/~cs6370

5. Office 2875 WEB ph# 585-17262875 WEB ph# 585-1726 Bridge 2875 WEB Bioengineering front office

6. Course Topics Motion PlanningMotion Planning Geometric ComputationGeometric Computation

7. Course Structure Somewhat historical view of motion planningSomewhat historical view of motion planning –2D algorithms – geometry based –Sensor-based systems –Randomized algorithms Higher DOF systems –Probabilistic approaches Handle sensor noise –Geometric algorithms as needed

8. Geometric Computation Applies toApplies to –Robotics –VR –Haptics –Simulation –Animation

9. Goal of Motion Planning Compute motion strategies, e.g.:Compute motion strategies, e.g.: –geometric paths –time-parameterized trajectories –sequence of motion commands To achieve high-level goals, e.g.: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

10. Basic Problem Inputs:Inputs: –Geometry of robot and obstacles –Kinematics of robot (degrees of freedom) –Initial and goal robot configurations (placements) Output:Output: –Continuous sequence of collision-free robot configurations connecting the initial and goal configurations

11. Examples with Rigid Object Piano Mover’s ProblemPiano Mover’s Problem –3D environment Obstacles stationary and positions known –Piano can translate and rotate –Path planned in advance Perfectly followed

12. Example with Articulated Object Generalized Mover’s problem

13. Motion Planning vs Path Planning AERCam Sprint and miniAERCam Sprint and mini Need to plan for velocitiesNeed to plan for velocities –Limited forces Create a trajectoryCreate a trajectory –Path parameterized by time

14. Some Extensions of Basic Problem Moving obstaclesMoving obstacles Multiple robotsMultiple robots Movable objectsMovable objects Assembly planningAssembly planning Goal is to acquire information by sensingGoal 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 Physical models and deformable objects

15. Examples of Applications Application to many areasApplication to many areas Not just a mobile robot trying to reach some destinationNot just a mobile robot trying to reach some destination

16. Assembly Planning and Design of Manufacturing Systems

17. Inspection Places Humans cannot goPlaces Humans cannot go Tedious tasksTedious tasks http://www.youtube.com/watch?v=E0oN9yz5pTwhttp://www.youtube.com/watch?v=E0oN9yz5pTw

18. Navigation Through Virtual Environments [Cheng-Chin U., UNC, Utrecht U.]

19. Applications Building code simulationBuilding code simulation –Stadiums –Office buildings –http://www.youtube.com/watch?v=ixTiuLwlLSc&feature=related

20. Radiosurgical Planning Cross-firing at a tumor while sparing healthy critical tissue

21. Study of the Motion of Bio-Molecules Protein folding Ligand binding

22. Home Applications How to effectively clean?How to effectively clean? –coverage

23. Some Basic Planner Classifications TaskTask Robot PropertiesRobot Properties Algorithm PropertiesAlgorithm Properties

24. Task NavigationNavigation CoverageCoverage LocalizationLocalization MappingMapping

25. Robot Properties Degrees-of-freedomDegrees-of-freedom Velocity constraintsVelocity constraints –Nonholonomic robot Dynamic ConstraintsDynamic Constraints –Torque –Acceleration Robot GeometryRobot Geometry

26. Algorithm Properties OptimalityOptimality –Path length –Execution time –Energy Computational complexityComputational complexity –Memory, CPU resources CompletenessCompleteness –Always find a solution or prove impossible in finite time Offline or sensor-basedOffline or sensor-based

27. About Me! Ph.D from CS Department at UtahPh.D from CS Department at Utah InstructorInstructor –Motion Planning –Virtual Reality –Explorations in CS ResearcherResearcher OutreachOutreach –CS/Robotics summer camp –First Lego League in Utah

28. My Research Interests Geometric algorithms and their applicationsGeometric algorithms and their applications Dissertation on force-feedback interfacesDissertation on force-feedback interfaces Recent problem areas are symbolic solvers, path planning, optimization, CAD design, and algorithms for biology.Recent problem areas are symbolic solvers, path planning, optimization, CAD design, and algorithms for biology.

30. Motion Planning Deformable Robot Non-holonomic Motion

31. Questions?