MEAM 620 Part II Introduction to Motion Planning. Peng Cheng. Levine 403,GRASP Lab

Transcription

1 MEAM 620 Part II Introduction to Motion Planning Peng Cheng Levine 403,GRASP Lab

2 Part II Objectives Overview of motion planning Introduction to some basic concepts and methods for motion planning problems Implementation of motion planning algorithms Some thoughts for the future research

3 Course Plan 7 lectures about basic motion planning by Peng Cheng 3 programming assignments Discrete planning (data structure + search) Collision checking between two polygons Planning algorithms for 2D problems Matlab, C++, java, 7 lectures in extensions of basic motion planning problems by Savvas Loizou 1 course project

4 References and Links [LaValle 05] Planning algorithms [Choset et. al. 05] Principles of robot motion [Latombe 91] Robot Motion Planning [Laumond 98] Robot motion planning and control Robotics VIP gallery 43/VipGallery/

5 This Class What is motion planning Basic motion planning problems General principles of motion planning algorithms

6 Robotic Systems (Mars Rover, NASA) (Roomba, irobot Co.) Autonomously complete assigned tasks: Security and surveillance Search and rescue Outer space exploration Home services

7 Humanoid Robot H6

8 A Recharging Task for a Robot

9 General Motion Planning An informal definition: A mapping from sensing information to action inputs to complete mechanical motion-required tasks z Non motion planning problems: Chemical reaction control Electronic motor control

10 Applications of Motion Planning Humanoid Manufacturing Autonomous systems Computer animation Rational drug design Virtual prototyping Many other cool things (Asimo, Honda)

11 Manufacturing

12 Autonomous Agile Systems Rapid taking-off and landing, OGI

13 Solar Sail Control of solar sail to reach escape velocity JPL, UIUC, Planetary.org

14 Computer Animation (Bird animation, U. of Washington)

15 Rational Drug Design (Rational drug design, Rice Univ.)

16 Virtual Prototyping Checking maintainability

17 Outline What is motion planning Basic motion planning problems General principles of motion planning algorithms

18 General Motion Planning A mapping from sensing information to action inputs to complete motion-required tasks z How to use a computer to solve this problem?

19 Building a Robot Model Motion model ( x, y) θ F 1 F 2 z Robot might not be able to Sensing model Robot might not where it is A mapping from sensing exactly. information z to state Action model A function from action input Robot umight to state not move z to where it wants. Geometry model ψ Configuration, dq Velocity, q& = dt dq& Acceleration, q&& = dt State, z = ( q, q& ) X Input, u = ( F, F Motion equation, 1 q 2 = ( x, y, θ, ψ ) C move in any direction, velocity, and acceleration. ) U z& = f ( z, u) z

20 The First Hierarchical Simplification Get recharged 1. Move to the door of the basement F High Level Planning 2. Move to the bottom of the stair Basic Motion Planning F 3. Move to the recharging location F ' F Handle sensing uncertainty 4. Reach the power plug Handle geometry complexity and motion constraints 5. Move the plug to the power plug ' F t t t t t Lower Level Planning F F F ' F Handle action uncertainties ' F t t t t t

21 Basic Motion Planning Problem Perfect sensing and action model Given : A robotic system, work environment, initial state, and goal state. τ Solution : a control, u ~ : [0,t f ] U, and its trajectory, τ : [0,t f ] X.

22 A Control and Its Trajectory u U u ~ 0 t 1 t f control u ~ t x i X τ 0 f Trajectory τ of x f control u~ from state x t i t Given a control u~ :[0, t f ] U and state x a trajectory τ :[0, t f ] X is obtained by integrating motion equation x& = f ( x, u~ ( t)) from state x. i, i

23 Search Core Challenges for control, u~, and its trajectory, τ, which satisfy : Configuration Constraints { ge( q) = 0; gi ( q) > 0} Collision avoidance Complicated geometry High Dimension Differential Constraints { h ( q, q& ) = 0; h ( q, q& e i ) > 0} { k ( q, q&, q&& ) = 0; k ( q, q&, q&& e i ) > 0} Restricted velocities and accelerations Nonlinear constraints

24 The Second Hierarchical Simplification Path planning With only configuration constraints { g ( q) = 0; g ( q) > Nonholonomic planning With first order differential constraints Kinodynamic planning e 0} { h ( q,q & ) = 0;h ( q,q& ) > e With second order differential constraints i i 0} { k ( q,q,q & && ) = 0;k ( q,q,q & & ) > e i 0}

25 Path Planning Problem (Piano Movers Problem) Given: Geometry and configuration constraints ge( q) 0; gi ( Objective: A collision-free path connecting the initial and goal configurations { = q) > 0}

26 Paths from Path Planning Could Be Infeasible (Parallel Parking) Infeasible because the robot cannot follow it.

27 Nonholonomic planning Problem (called steering problem when no obstacles exist) Given: A system under nonholonomic constraints{ h ( q,q & ) = 0;h ( q,q& e i ) > 0} Objective: A open loop control to move from the initial configuration to the goal configuration

28 Paths Could Be Inefficient 8 min. 3 min. But I can move faster on this purple path. I have to move slowly around sharp corners in the path from the planner. Inefficient in time, energy

29 Kinodynamic Planning Problem Given: A system under dynamics constraints k ( q, q&, q&& ) = 0, k ( q, q&, q& e i ) > 0 Objective: A open loop control to move from the initial state to goal state

30 Extensions of Basic Motion Planning Problems

31 Planning with Sensing Uncertainties Perfect action model Part orienting (Akella, Mason, 99)

32 Coverage Planning Given: Robotic systems A closed area A footprint function Objective: Find controls for the systems to cover the given area.

33 Ω X

34

35 Folding A folding sequence for a carton (Lu, Akella, 00)

36 Outline What is motion planning Different motion planning problems General principles of motion planning algorithms

37 Path Planning Problem (Piano Movers Problem) Given: Geometry and configuration constraints ge( q) Objective: A collision-free path connecting the initial and goal configurations { = 0; g ( q) > i 0}

38 Path Planning Algorithms Configuration Space Geometry Model Abstract Path Planning Problem: Collision-free Configuration Space An initial and goal configuration Continuous mathematical representation Exact and finite Complete Methods Discrete representation Search Methods Approximate Practical Methods Discrete computer representation

39 Representations Continuous mathematical representation Mathematical formulation of the problem Topology of the configuration space Parameterization of configuration space Computation of collision-free configuration space Abstract path planning problems Discrete computational representations Required for computer algorithms Exact and finite representations of the set of collisionfree configurations Approximate representations

40 Search Methods Discrete search methods Search with finite states and actions Deterministic complete search Best-first, A*, Dijstra, Sampling-based algorithms PRM(Probabilistic Road Map)-based methods RRT (Rapidly Exploring Random Tree)-based methods Heuristic design

41 Reading [LaValle 05], II-Overview [LaValle 05], II-3.1 [LaValle 05], II-4.1,4.2,4.3