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Principles of Robot Motion Theory, Algorithms, and Implementation

ISBN-10: 0262033275
ISBN-13: 9780262033275
Edition: 2004
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Description: 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  More...

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Book details

Copyright year: 2004
Publisher: MIT Press
Publication date: 5/20/2005
Binding: Hardcover
Pages: 632
Size: 8.00" wide x 9.00" long x 1.50" tall
Weight: 3.234
Language: English

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.

Foreword
Preface
Acknowledgments
Introduction
Overview of Concepts in Motion Planning
Overview of the Book
Mathematical Style
Bug Algorithms
Bug1 and Bug2
Tangent Bug
Implementation
What Information: The Tangent Line
How to Infer Information with Sensors: Distance and Gradient
How to Process Sensor Information: Continuation Methods
Configuration Space
Specifying a Robot's Configuration
Obstacles and the Configuration Space
Circular Mobile Robot
Two-Joint Planar Arm
The Dimension of the Configuration Space
The Topology of the Configuration Space
Homeomorphisms and Diffeomorphisms
Differentiable Manifolds
Connectedness and Compactness
Not All Configuration Spaces Are Manifolds
Embeddings of Manifolds in R[superscript n]
Matrix Representations of Rigid-Body Configuration
Parameterizations of SO(3)
Example Configuration Spaces
Transforming Configuration and Velocity Representations
Potential Functions
Additive Attractive/Repulsive Potential
Gradient Descent
Computing Distance for Implementation in the Plane
Mobile Robot Implementation
Brushfire Algorithm: A Method to Compute Distance on a Grid
Local Minima Problem
Wave-Front Planner
Navigation Potential Functions
Sphere-Space
Star-Space
Potential Functions in Non-Euclidean Spaces
Relationship between Forces in the Workspace and Configuration Space
Potential Functions for Rigid-Body Robots
Path Planning for Articulated Bodies
Roadmaps
Visibility Maps: The Visibility Graph
Visibility Graph Definition
Visibility Graph Construction
Deformation Retracts: Generalized Voronoi Diagram
GVD Definition
GVD Roadmap Properties
Deformation Retract Definition
GVD Dimension: The Preimage Theorem and Critical Points
Construction of the GVD
Retract-like Structures: The Generalized Voronoi Graph
GVG Dimension: Transversality
Retract-like Structure Connectivity
Lyapunov Control: Sensor-Based Construction of the HGVG
Piecewise Retracts: The Rod-Hierarchical Generalized Voronoi Graph
Silhouette Methods
Canny's Roadmap Algorithm
Opportunistic Path Planner
Cell Decompositions
Trapezoidal Decomposition
Morse Cell Decompositions
Boustrophedon Decomposition
Morse Decomposition Definition
Examples of Morse Decomposition: Variable Slice
Sensor-Based Coverage
Complexity of Coverage
Visibility-Based Decompositions for Pursuit/Evasion
Sampling-Based Algorithms
Probabilistic Roadmaps
Basic PRM
A Practical Implementation of Basic PRM
PRM Sampling Strategies
PRM Connection Strategies
Single-Query Sampling-Based Planners
Expansive-Spaces Trees
Rapidly-Exploring Random Trees
Connection Strategies and the SBL Planner
Integration of Planners: Sampling-Based Roadmap of Trees
Analysis of PRM
PRM Operating in R[superscript d]
([epsilon, alpha, beta])-Expansiveness
Abstract Path Tiling
Beyond Basic Path Planning
Control-Based Planning
Multiple Robots
Manipulation Planning
Assembly Planning
Flexible Objects
Biological Applications
Kalman Filtering
Probabilistic Estimation
Linear Kalman Filtering
Overview
A Simple Observer
Observing with Probability Distributions
The Kalman Filter
Kalman Filter Summary
Example: Kalman Filter for Dead Reckoning
Observability in Linear Systems
Extended Kalman Filter
EKF for Range and Bearing Localization
Data Association
EKF for Range-Only Localization
Kalman Filter for SLAM
Simple SLAM
Range and Bearing SLAM
Bayesian Methods
Localization
The Basic Idea of Probabilistic Localization
Probabilistic Localization as Recursive Bayesian Filtering
Derivation of Probabilistic Localization
Representations of the Posterior
Sensor Models
Mapping
Mapping with Known Locations of the Robot
Bayesian Simultaneous Localization and Mapping
Robot Dynamics
Lagrangian Dynamics
Standard Forms for Dynamics
Velocity Constraints
Dynamics of a Rigid Body
Planar Rotation
Spatial Rotation
Trajectory Planning
Preliminaries
Decoupled Trajectory Planning
Zero Inertia Points
Global Time-Optimal Trajectory Planning
Direct Trajectory Planning
Optimal Control
Nonlinear Optimization
Grid-Based Search
Nonholonomic and Underactuated Systems
Preliminaries
Tangent Spaces and Vector Fields
Distributions and Constraints
Lie Brackets
Control Systems
Controllability
Local Accessibility and Controllability
Global Controllability
Simple Mechanical Control Systems
Simplified Controllability Tests
Kinematic Reductions for Motion Planning
Simple Mechanical Systems with Nonholonomic Constraints
Motion Planning
Optimal Control
Steering Chained-Form Systems Using Sinusoids
Nonlinear Optimization
Gradient Methods for Driftless Systems
Differentially Flat Systems
Cars and Cars Pulling Trailers
Kinematic Reductions of Mechanical Systems
Other Approaches
Mathematical Notation
Basic Set Definitions
Topology and Metric Spaces
Topology
Metric Spaces
Normed and Inner Product Spaces
Continuous Functions
Jacobians and Gradients
Curve Tracing
Implicit Function Theorem
Newton-Raphson Convergence Theorem
Representations of Orientation
Euler Angles
Roll, Pitch, and Yaw Angles
Axis-Angle Parameterization
Quaternions
Polyhedral Robots in Polyhedral Worlds
Representing Polygons in Two Dimensions
Intersection Tests for Polygons
Configuration Space Obstacles in Q = R[superscript 2]: The Star Algorithm
Configuration Space Obstacles in Q = SE(2)
Computing Distances between Polytopes in R[superscript 2] and R[superscript 3]
Analysis of Algorithms and Complexity Classes
Running Time
Complexity Theory
Completeness
Graph Representation and Basic Search
Graphs
A* Algorithm
Basic Notation and Assumptions
Discussion: Completeness, Efficiency, and Optimality
Greedy-Search and Dijkstra's Algorithm
Example of A* on a Grid
Nonoptimistic Example
D* Algorithm
Optimal Plans
Statistics Primer
Distributions and Densities
Expected Values and Covariances
Multivariate Gaussian Distributions
Linear Systems and Control
State Space Representation
Stability
LTI Control Systems
Observing LTI Systems
Discrete Time Systems
Stability
Controllability and Observability
Bibliography
Index

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