cs790e planning algorithms lecture 1: applications and basic ingredients of motion planning 19...

CS790E Planning Algorithms

Lecture 1:Applications

and Basic Ingredients ofMotion Planning

19 January 2010Instructor: Kostas Bekris

Computer Science & Engineering, University of Nevada, Reno

CS790E

“Planning” Algorithms?

The term “planning” corresponds to multiple research challenges:

•e.g., scheduling tasks, path planning, action selection, etc.

We will focus on planning in an algorithmic way motions and actions for

• “physical” systems, e.g., objects with geometry, mass and velocity, etc.

- This includes “real-world” systems such as:

✓3D rigid-bodies, robots and vehicles, machines in factory floors, molecules, etc.

- But also includes “virtual” agents such as:

✓animated characters, simulated environments, etc.

Many different fields are related to this challenge:

•Robotics

•Artificial Intelligence

•Control Theory

•Computer Graphics

•Computer Animation

•Scientific Simulation

•Computer Games

•Algorithms: Computational Geometry

•Computational Biology & Bioinformatics

•Virtual prototyping in manufacturing

•Architectural Design

•Aerospace Engineering

•Computational Geography

CS790E

Planning Challenges in Various Fields

Artificial Intelligence

•Originally:

- Search & Automated Planning: How to search for a sequence of operations that transform an initial problem state into a desired goal state

•Today:

- Decision-theory: How to make optimal decisions or sequence of decisions under the presence of uncertainty?

✓imperfect state information, markov-decision processes (MDPs), game-theory

- Reinforcement learning: Learn the right decisions or sequence of decisions that must be executed for every possible state from experience.

In general:

•Machine planning is the complement to machine learning

- Once learning is being successfully performed, planning deals with the decisions that have to be made

•AI focuses on discrete problems, we will mostly focus on continuous ones

CS790E

AI Examples

Discrete Puzzles, Operations and Scheduling

Mars Rovers - NASAMars Rovers - NASA

Kasparov vs. Deep Blue - IBMKasparov vs. Deep Blue - IBM

Earth Observing 1 - NASAEarth Observing 1 - NASA15-puzzle15-puzzleRubic’s CubeRubic’s CubeRubic’s CubeRubic’s Cube

CS790E


Robotics

•Originally:

- Motion Planning: How to move a rigid body without collisions (i.e., a piano from one room to another without collisions)

•Today, new complications are being considered:

- Trajectory Planning: How to compute feasible paths for robots/vehicles with constrains in velocity and acceleration (systems with dynamics)

- Planning under Uncertainty: How to plan the motion of a moving system if we are not absolutely certain about its location

- Motion Coordination: How to move in coordination with other robots or in the presence of other moving systems?

Many other problems are involved in building robots:

•state estimation, task allocation, mechanism design, dynamical system modeling, feedback control, sensor design, computer vision, inverse kinematics, humanoid robots, etc.

CS790E

Benchmarks

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Traditional Motion Planning

Alpha Puzzle - James Kuffner - Carnegie Mellon Univ.Alpha Puzzle - James Kuffner - Carnegie Mellon Univ.

Piano Mover’s Problem - Gamma GroupManocha & Lin - Univ. of N. Carolina, Chapel Hill

Piano Mover’s Problem - Gamma GroupManocha & Lin - Univ. of N. Carolina, Chapel Hill

Kostas Bekris - Rice UniversityKostas Bekris - Rice University

CS790E

Manipulators





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3 Manipulators moving a Piano - Juan 3 Manipulators moving a Piano - Juan Cortes & Tierry Simeon - LAAS-CNRS FranceCortes & Tierry Simeon - LAAS-CNRS France

3 Manipulators moving a Piano - Juan 3 Manipulators moving a Piano - Juan Cortes & Tierry Simeon - LAAS-CNRS FranceCortes & Tierry Simeon - LAAS-CNRS FranceLydia Kavraki - Rice UniversityLydia Kavraki - Rice University

Jean-Claude Latombe - Stanford UniversityJean-Claude Latombe - Stanford University

CS790E


Automotive Applications

Motion planning company:

•Kineo CAM

Customers:

•Renault

•Ford

•Airbus

•Optivus

Volvo cars plant

CS790E From Traditional Planning to Planning with Dynamics



CS790EMotion Planning with Dynamics & Under Uncertainty

Mobile Robots &

Vehicular ApplicationsCMU

DARPA Urban ChallengeCMU

DARPA Urban ChallengeStanford

DARPA Urban ChallengeStanford

DARPA Urban Challenge

A robot pulling a trailer A robot pulling a trailer Jean-Paul Laumond - LAAS - FranceJean-Paul Laumond - LAAS - France

A robot pulling a trailer A robot pulling a trailer Jean-Paul Laumond - LAAS - FranceJean-Paul Laumond - LAAS - France

Jean-Paul Laumond - LAAS - FranceJean-Paul Laumond - LAAS - France

PLEN Scating Robot - JapanPLEN Scating Robot - Japan

Honda - JapanHonda - JapanHonda - JapanHonda - Japan

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James Kuffner CMU

James Kuffner CMU

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CS790E


Control Theory

•Originally:

- Traditional Control: Optimal operation of continuous systems under differential constraints (constrains expressed through differential equations)

✓focusing on dynamics, stability, optimality, feedback (closed-loop control)

✓ignoring obstacles

•Today:

- Open-loop non-linear control: Feasible open-loop trajectories for non-linear syst.

In this course initially the focus will be on:- open-loop trajectories instead of closed-loop

- feasibility as opposed to optimality

- rigid bodies without dynamics

Eventually, we will include: closed-loop problems, optimality and dynamics

but from an algorithmic perspective instead of an analytical

CS790E


Algorithms

•Combinatorics and complexity theory are important for planning algorithms

•Important questions: are the algorithms complete?

•Most related sub-areas:

- Path finding in graphs

- Computational geometry

Computer Animation / Graphics / Simulation / Games

•Originally:

- Animated characters and agents moved in a cartoonish way

- As long as the agent reaches the goal that is enough

- Cool graphics more important than reasonable AI

•Today:

- Simulated Motion: It becomes increasingly important for simulated motion to be physically realistic

- Game AI: Becomes the most important selling point for new games

- Industrial Simulation: Physics-based simulation is increasingly used before real experiments are conducted - real products are produced - real factories are built

CS790E

Virtual Characters

James Kuffner - Carnegie Mellon UniversityJames Kuffner - Carnegie Mellon UniversityJames Kuffner - Carnegie Mellon UniversityJames Kuffner - Carnegie Mellon University Gamma Group Gamma Group University of North Carolina, Chapel HillUniversity of North Carolina, Chapel Hill

Gamma Group Gamma Group University of North Carolina, Chapel HillUniversity of North Carolina, Chapel Hill









CS790E

Types of Problems

Discrete

Continuous

3D

Freemoving

ConstrainedMotion

Differential Constraints &

Dynamics

2D

Other complications: • sensor-based problems (i.e., partial-observability)• uncertainty in sensing and acting • multi-agent systems• real-time requirements

CS790E

Class Overview

Plan for CS790E (check schedule online:

http://www.cse.unr.edu/robotics/bekris/cs790_s10/event):

1. Applications and Basic Ingredients of Motion Planning

2. 2D Planning: Combinatorial Algorithms and Potential Functions

3. 3D Planning: The Configuration Space Abstraction

4. Sampling-based Motion Planning for Free-Flying Rigid Bodies

- Extensions of Basic Motion Planning

- Presentations I: Literature Survey and Project Proposal

- Dynamics and Trajectory Planning

1. Planning for Cars and Trailers

2. Safety in Replanning with Dynamics

3. Feedback Planning & Planning for Hybrid Systems

4. Planning under Uncertainty

- Presentations II: Experimental Results and Conclusions

CS790E

Basic Ingredients of Planning

State

•Planning problems involve a state space: all possible situations that could arise

- e.g., position and orientation of a robot

- e.g., the locations of tiles in a puzzle

- e.g., the position, orientation, and velocity of a helicopter

•Typically, too large to represent and store explicitly

Time

•We have to make a sequence of decisions over a period of time

•Time can be modeled explicitly:

- e.g., driving a car as quickly as possible through an obstacle course (when velocity is important, time is important)

•Time may be modeled implicitly:

- e.g., in solving the Rubik’s cube, actions just have to be executed in succession

- e.g., the Piano Mover’s problem, the speed of the object is not important

CS790E


Actions

•A plan generates actions that manipulate/change the state.

- AI: actions and operators, Control theory and Robotics: inputs and controls

•How does the state change when actions are applied?

- Discrete time: State-valued function

- Continuous time: Ordinary differential equation

Initial and Goal States

•Start at an initial state and select actions so as to reach a goal state

Criterion

•Additional requirement the plan must satisfy:

- Feasibility: Find a plan that causes arrival at a goal state given the motion capabilities of a system, regardless of its efficiency (already hard)

- Optimality: Find a feasible plan that optimizes performance in some carefully specified manner, in addition to arriving in a goal state (even harder)

•Feasible solutions are preferable to having no solutions at all

CS790E


Plan

•A plan may be:

- simply a sequence of actions to be taken

- a time-sequence of controls

- (uncertainty in action) an assignment of actions to all states (AI: policy, Control theory: feedback control - feedback/reactive plan)

•Once a plan is available, there are three ways to use it:1.Execution

- Execute it either in simulation or on a physical device

- Refinement

- Hierarchical inclusion

CS790E “Simpler” Planning: Planning in Discrete Spaces

cs790e planning algorithms lecture 1: applications and basic ingredients of motion planning 19...

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