cs 326a: motion planning robotics.stanford.edu/~latombe/cs326/2004/index.htm jean-claude latombe...
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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
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
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
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
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
Modular Reconfigurable Modular Reconfigurable RobotsRobots
Xerox, ParcXerox, Parc
Casal and Yim, 1999
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
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