CS 326A: Motion Planning robotics.stanford.edu/~latombe/cs326/2004/index.htm Jean-Claude Latombe 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? Valid region Forbidden region

Fundamental Question Are 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 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

Compare! Valid region Forbidden region

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 –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 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] (MIT)

Assembly Planning

Map Building Where to move next?

Target Finding

Target Tracking

Planning for Nonholonomic Robots

Under-Actuated Systems video [Lynch] (Northwestern)

Planning with Uncertainty in Sensing and Control I G W1W1W1W1 W2W2W2W2

I G W1W1W1W1 W2W2W2W2

I G W1W1W1W1 W2W2W2W2

Motion Planning for Deformable Objects [Kavraki] (Rice)

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

Robot Programming

Robot Placement

Design for Manufacturing/Servicing General Electric General Motors

Assembly Planning and Design of Manufacturing Systems

Part Feeding

Cable Harness/ Pipe design

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

Modular Reconfigurable Robots Xerox, Parc Casal and Yim, 1999

Military Scouting and Planet Exploration [CMU, NASA]

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

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

Building Code Verification

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

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

Goals 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

Framework Continuous representation (configuration space and related spaces + constraints) Discretization (random sampling, criticality-based decomposition) Graph searching (blind, best-first, A*)

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 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 … Differential Geometry and Topology Kinematics and Dynamics Geometric 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 (20 minutes 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 and Schedule robotics.stanford.edu/~latombe/cs326/2004/index.htm January 61Overview January 82Path planning for point robot January 133Configuration space of a robot January 154Collision detection 1/2: Hierarchical methods January 205Collision detection 2/2: Feature-tracking methods January 226Probabilistic roadmaps 1/3: Basic techniques January 277Probabilistic roadmaps 2/3: Sampling strategies January 298Probabilistic roadmaps 3/3: Sampling strategies February 39Criticality-based motion planning: Assembly planning and target finding February 510Coordination of multiple robots February 1011Kinodynamic planning February 1212Humanoid and legged robots February 1713Modular reconfigurable robots February 1914Mapping and inspecting environments February 2415Navigation in virtual environments February 2616Target tracking and virtual camera March 217Motion of crowds and flocks March 418Motion of bio-molecules March 919Radiosurgical planning

Programming Project Navigate in virtual environment Simulate legged robot Inspection of structures Search and escape