CS 326 A: Motion Planning Instructor: Jean-Claude Latombe Teaching Assistant: Itay Lotan Computer Science Department Stanford University

Goal 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 Question Are two given points connected by a path?

Basic 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 Object  Ladder problem Piano-mover problem 

Is It Easy?

Example with Articulated Object

Tool: Configuration Space Problems: Geometric complexity Space dimensionality

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Aerospace Robotics Lab Robot air bearing gas tank air thrusters obstacles robot

Total duration : 40 sec Two concurrent planning goals: Reach the goal Reach a safe region

Autonomous Helicopter [Feron, 2000] (AA Dept., MIT)

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Dynamic Unpredictable Environment

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Assembly Planning

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Map Building Where to move next?

Target Finding

Target Tracking

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Planning for Nonholonomic Robots

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Planning with Uncertainty in Sensing and Control I G W1W1W1W1 W2W2W2W2

Some Extensions of Basic Problem Moving obstacles Multiple robots Movable objects Assembly planning Goal is to acquire information by sensing –Model building –Object finding/tracking Nonholonomic constraints Dynamic constraints Optimal planning Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Motion Planning for Deformable Objects [Kavraki, 1999]

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

Robot Programming

Robot Placement

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

Modular Reconfigurable Robots Xerox, Parc Casal and Yim, 1999

Video

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

Design for Manufacturing/Servicing General Electric General Motors

Assembly Planning and Design of Manufacturing Systems

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

Military Scouting and Planet Exploration

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

Digital 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 Actors Manipulation Sensory-based locomotion

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

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

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

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

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

Examples 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 Medical surgery planning Generation of plausible molecule motions, e.g., docking and folding motions Building code verification

Building Code Verification

Goals of CS326A  Present a coherent framework for motion planning problems: –configuration space and related spaces –random sampling and criticality-based decomposition algorithms  Emphasis of “practical” algorithms with some guarantees of performance over “theoretical” or purely “heuristic” algorithms

Framework Continuous representation (configuration space formulation) Discretization (random sampling, criticality-based decomposition) Graph searching (blind, best-first, A*)

Goals of CS326A  Present a coherent framework for motion planning problems: –configuration space and related spaces –random sampling and criticality-based decomposition algorithms  Emphasis of “practical” algorithms with some guarantees of performance over “theoretical” or purely “heuristic” algorithms

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) 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 CS326A Ability and willingness to complete a significant programming project with simple graphic interface. Basic knowledge and taste for geometry and algorithms. Interest in devoting reasonable time each week in reading four papers.

CS326A is not a course in … Differential Geometry and Topology Kinematics and Dynamics Basic Algorithms Geometrics Modeling … but it makes use of knowledge from all these areas

Work to Do A.Attend every class B.Prepare/give two presentations with ppt slides (30 min each) C.For each class read the two papers listed as “required reading” in advance D.Complete the programming project E.Complete two homework assignments

Website / Class Schedule robotics.stanford.edu/~latombe/cs326/2002

Programming Project Topic: Implement a Probabilistic Roadmap planner Assumptions: –The robot operates in a 2D workspace –It consists of one or several polygonal bodies moving independently or connected by joints (your software should allow various kinds of kinematics) –Obstacles are static polygons Goal: –Implement, test, and compare several algorithms for selecting samples (milestones), generating connections between them, and checking collision