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9780262033275

Principles of Robot Motion Theory, Algorithms, and Implementations

by ; ; ; ;
  • ISBN13:

    9780262033275

  • ISBN10:

    0262033275

  • Format: Hardcover
  • Copyright: 2005-05-20
  • Publisher: MIT PRESS

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Summary

Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts.

Author Biography

Howie Choset is Associate Professor in the Robotics Institute at Carnegie Mellon University.

Kevin M. Lynch is Associate Professor in the Mechanical Engineering Department, Northwestern University.

Seth Hutchinson is Professor in the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign.

George Kantor is Project Scientist in the Center for the Foundations of Robotics, Robotics Institute, Carnegie Mellon University.

Wolfram Burgard is Professor of Computer Science and Head of the research lab for Autonomous Intelligent Systems at the University of Freiburg.

Lydia E. Kavraki is Professor of Computer Science and Bioengineering, Rice University.

Sebastian Thrun is Associate Professor in the Computer Science Department at Stanford University and Director of the Stanford AI Lab.

Table of Contents

Foreword xv
Preface xvii
Acknowledgments xxi
Introduction
1(16)
Overview of Concepts in Motion Planning
9(3)
Overview of the Book
12(1)
Mathematical Style
13(4)
Bug Algorithms
17(22)
Bug1and Bug2
17(6)
Tangent Bug
23(7)
Implementation
30(9)
What Information: The Tangent Line
31(1)
How to Infer Information with Sensors: Distance and Gradient
32(3)
How to Process Sensor Information: Continuation Methods
35(4)
Configuration Space
39(38)
Specifying a Robot's Configuration
40(3)
Obstacles and the Configuration Space
43(4)
Circular Mobile Robot
43(2)
Two-Joint Planar Arm
45(2)
The Dimension of the Configuration Space
47(3)
The Topology of the Configuration Space
50(9)
Homeomorphisms and Diffeomorphisms
51(4)
Differentiable Manifolds
55(3)
Connectedness and Compactness
58(1)
Not All Configuration Spaces Are Manifolds
59(1)
Embeddings of Manifolds in Rn
59(7)
Matrix Representations of Rigid-Body Configuration
60(6)
Parameterizations of SO(3)
66(2)
Example Configuration Spaces
68(1)
Transforming Configuration and Velocity Representations
69(8)
Potential Functions
77(30)
Additive Attractive/Repulsive Potential
80(4)
Gradient Descent
84(1)
Computing Distance for Implementation in the Plane
85(4)
Mobile Robot Implementation
86(1)
Brushfire Algorithm: A Method to Compute Distance on a Grid
86(3)
Local Minima Problem
89(1)
Wave-Front Planner
90(3)
Navigation Potential Functions
93(6)
Sphere-Space
93(3)
Star-Space
96(3)
Potential Functions in Non-Euclidean Spaces
99(8)
Relationship between Forces in the Workspace and Configuration Space
100(1)
Potential Functions for Rigid-Body Robots
101(3)
Path Planning for Articulated Bodies
104(3)
Roadmaps
107(54)
Visibility Maps: The Visibility Graph
110(7)
Visibility Graph Definition
110(3)
Visibility Graph Construction
113(4)
Deformation Retracts: Generalized Voronoi Diagram
117(12)
GVD Definition
118(1)
GVD Roadmap Properties
119(2)
Deformation Retract Definition
121(2)
GVD Dimension: The Preimage Theorem and Critical Points
123(3)
Construction of the GVD
126(3)
Retract-like Structures: The Generalized Voronoi Graph
129(9)
GVG Dimension: Transversality
130(3)
Retract-like Structure Connectivity
133(3)
Lyapunov Control: Sensor-Based Construction of the HGVG
136(2)
Piecewise Retracts: The Rod-Hierarchical Generalized Voronoi Graph
138(3)
Silhouette Methods
141(20)
Canny's Roadmap Algorithm
142(9)
Opportunistic Path Planner
151(10)
Cell Decompositions
161(36)
Trapezoidal Decomposition
162(6)
Morse Cell Decompositions
168(19)
Boustrophedon Decomposition
169(1)
Morse Decomposition Definition
170(2)
Examples of Morse Decomposition: Variable Slice
172(6)
Sensor-Based Coverage
178(4)
Complexity of Coverage
182(5)
Visibility-Based Decompositions for Pursuit/Evasion
187(10)
Sampling-Based Algorithms
197(72)
Probabilistic Roadmaps
202(25)
Basic PRM
203(5)
A Practical Implementation of Basic PRM
208(8)
PRM Sampling Strategies
216(9)
PRM Connection Strategies
225(2)
Single-Query Sampling-Based Planners
227(11)
Expansive-Spaces Trees
230(3)
Rapidly-Exploring Random Trees
233(5)
Connection Strategies and the SBL Planner
238(1)
Integration of Planners: Sampling-Based Roadmap of Trees
238(4)
Analysis of PRM
242(11)
PRM Operating in Rd
243(3)
(ε, α, β)-Expansiveness
246(4)
Abstract Path Tiling
250(3)
Beyond Basic Path Planning
253(16)
Control-Based Planning
253(1)
Multiple Robots
254(3)
Manipulation Planning
257(2)
Assembly Planning
259(1)
Flexible Objects
260(2)
Biological Applications
262(7)
Kalman Filtering
269(32)
Probabilistic Estimation
270(2)
Linear Kalman Filtering
272(17)
Overview
273(1)
A Simple Observer
274(3)
Observing with Probability Distributions
277(5)
The Kalman Filter
282(2)
Kalman Filter Summary
284(1)
Example: Kalman Filter for Dead Reckoning
285(2)
Observability in Linear Systems
287(2)
Extended Kalman Filter
289(5)
EKF for Range and Bearing Localization
290(2)
Data Association
292(2)
EKF for Range-Only Localization
294(1)
Kalman Filter for SLAM
294(7)
Simple SLAM
294(2)
Range and Bearing SLAM
296(5)
Bayesian Methods
301(48)
Localization
301(27)
The Basic Idea of Probabilistic Localization
302(2)
Probabilistic Localization as Recursive Bayesian Filtering
304(4)
Derivation of Probabilistic Localization
308(2)
Representations of the Posterior
310(12)
Sensor Models
322(6)
Mapping
328(21)
Mapping with Known Locations of the Robot
328(9)
Bayesian Simultaneous Localization and Mapping
337(12)
Robot Dynamics
349(24)
Lagrangian Dynamics
349(4)
Standard Forms for Dynamics
353(4)
Velocity Constraints
357(4)
Dynamics of a Rigid Body
361(12)
Planar Rotation
362(1)
Spatial Rotation
363(10)
Trajectory Planning
373(28)
Preliminaries
374(1)
Decoupled Trajectory Planning
374(10)
Zero Inertia Points
378(6)
Global Time-Optimal Trajectory Planning
384(1)
Direct Trajectory Planning
384(17)
Optimal Control
385(4)
Nonlinear Optimization
389(3)
Grid-Based Search
392(9)
Nonholonomic and Underactuated Systems
401(72)
Preliminaries
402(12)
Tangent Spaces and Vector Fields
405(2)
Distributions and Constraints
407(2)
Lie Brackets
409(5)
Control Systems
414(2)
Controllability
416(8)
Local Accessibility and Controllability
419(3)
Global Controllability
422(2)
Simple Mechanical Control Systems
424(16)
Simplified Controllability Tests
425(9)
Kinematic Reductions for Motion Planning
434(4)
Simple Mechanical Systems with Nonholonomic Constraints
438(2)
Motion Planning
440(33)
Optimal Control
440(4)
Steering Chained-Form Systems Using Sinusoids
444(1)
Nonlinear Optimization
445(1)
Gradient Methods for Driftless Systems
446(1)
Differentially Flat Systems
447(3)
Cars and Cars Pulling Trailers
450(12)
Kinematic Reductions of Mechanical Systems
462(3)
Other Approaches
465(8)
A Mathematical Notation
473(2)
B Basic Set Definitions
475(3)
C Topology and Metric Spaces
478(9)
C.1 Topology
478(1)
C.2 Metric Spaces
479(1)
C.3 Normed and Inner Product Spaces
480(1)
C.4 Continuous Functions
481(2)
C.5 Jacobians and Gradients
483(4)
D Curve Tracing
487(2)
D.1 Implicit Function Theorem
487(1)
D.2 Newton-Raphson Convergence Theorem
488(1)
E Representations of Orientation
489(10)
E.1 Euler Angles
489(2)
E.2 Roll, Pitch, and Yaw Angles
491(1)
E.3 Axis-Angle Parameterization
492(2)
E.4 Quaternions
494(5)
F Polyhedral Robots in Polyhedral Worlds
499(14)
F.1 Representing Polygons in Two Dimensions
499(3)
F.2 Intersection Tests for Polygons
502(5)
F.3 Configuration Space Obstacles in Q = R2: The Star Algorithm
507(1)
F.4 Configuration Space Obstacles in Q = SE(2)
508(1)
F.5 Computing Distances between Polytopes in R2 and R3
509(4)
G Analysis of Algorithms and Complexity Classes
513(8)
G.1 Running Time
513(2)
G.2 Complexity Theory
515(5)
G.3 Completeness
520(1)
H Graph Representation and Basic Search
521(26)
H.1 Graphs
521(6)
H.2 A* Algorithm
527(9)
H.2.1 Basic Notation and Assumptions
530(1)
H.2.2 Discussion: Completeness, Efficiency, and Optimality
531(1)
H.2.3 Greedy-Search and Dijkstra's Algorithm
532(1)
H.2.4 Example of A* on a Grid
533(2)
H.2.5 Nonoptimistic Example
535(1)
H.3 D* Algorithm
536(10)
H.4 Optimal Plans
546(1)
I Statistics Primer
547(5)
I.1 Distributions and Densities
548(2)
I.2 Expected Values and Covariances
550(1)
I.3 Multivariate Gaussian Distributions
551(1)
J Linear Systems and Control
552(13)
J.1 State Space Representation
552(2)
J.2 Stability
554(3)
J.3 LTI Control Systems
557(2)
J.4 Observing LTI Systems
559(3)
J.5 Discrete Time Systems
562(3)
J.5.1 Stability
562(1)
J.5.2 Controllability and Observability
563(2)
Bibliography 565(32)
Index 597

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