Mobile Robot Motion Planning Outline
Last modified:
Thu, January 23, 2003
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references start
I. Intro
(last updated 01/23/2003, Copyright Howie Choset, 2001-2003)
II. Bug Algorithms
last updated 1/23/2003, Copyright
Howie Choset, 2001-3)
- A. Bug2
- B. TanBug (Rimon)
- C. Brief Mention of other bugs
III. Obstacle Avoidance
(Text: pdf, last updated 1/23/2003,
Copyright Howie Choset, 2001-3)
- A. Distance and Sensor Based Distance
- B. Grid Distance
- C. Collision Detection
IV. Potential Functions
(Text: pdf, last updated 1/12/2003,
Copyright Howie Choset, 2001-3)
- A. Attractive/Repulsive Functions
- B. Local Minimum Problem -- trapped
- C. Navigation Functions (Rimon
& Kodicheck)
- D. Principle of Optimality
- E. Randomized Potentials??? (Here or probabilistic
techniques chap) (Barraquand,
Langlois & Latombe)
V. Configuration Space (Text:
pdf, last updated 01/12/2003, Copyright
Howie Choset, 2003)
- A. Two Two-dimensional Configuration Spaces
- B. Introduction to Manifolds
- C. Configuration Space Definition (Lozano-Perez)
- D. Construction of Planar Configuration Spaces (De
Berg etc. Chapter 13)
- E. Non-Planar Configuration Space
VI. Roadmaps (Text: pdf/ps,
last updated 10/10/2001, Copyright Howie Choset, 2001)
- A. Visibility Graph
- B. Canny's Roadmap (Canny)
- C. OPP
- D. GVG
- E. Place Maps
VII. Probabilistic Motion Planning
Techniques 
- A. Introduction
- B. Multiple-Query Methods
- C. Single-Query Methods
- D. Beyond Basic Path Planning
VIII. Bayesian Methods
- A.
- B. Localization with known Maps
- C. SLAM
IX. Kalman Approaches 
- A. Kalman Primer - ps/pdf
(under serious construction)
- B. Localization
- C. SLAM
X. Cellular Decompositions (Text:
pdf/ps,
(last updated 09/17/2002, Copyright Howie Choset, 2001-2002)
- A. Trapezoid (Chazzelle or basic thing)
- B. Morse Decomposition and Sensor-Based Coverage
- C. Approximate Cell Decomposition and Coverage
- D. Visibility-based Decomposition and Coverage
- E. Cellular Decompomposition (Collins
- (no papers))
XI. Visual Exploration

- Arras - (laser and
visual homing)
XII. Trajectory Planning
(Text: pdf/ps,
(last updated 12/09/2002, Copyright 2002)
- path + time-scaling = trajectory
- robot dynamics
- fully actuated vs. underactuated (more on underactuated next chapter)
- kinodynamic (Canny, Donald, Reif, Xavier...)
- RRT (LaValle and Kuffner)
- decoupled approach: path planning followed by time-scaling (Bobrow et
al., Shin and McKay, Shiller, Hollerbach, ...)
- optimization approaches (Tan and Potts, Vukobratovic, many using SQP
like Bobrow)
XIII. Nonholonomic Motion Planning
(Text: pdf/ps,
(last updated 12/09/2002, Copyright 2002)
- (restrict to R^n, leave out Lie groups, coordinate-free formalisms,
appendix?)
- tangent vector, tangent space, tangent bundle
- vector fields, integral curves, Lie bracket
- distributions, involutivity, integral manifold, Frobenius
- dynamical polysystem, control affine systems, drift and drift-free
- controllability definitions
- Lie algebra of vector fields, LARC
- STLC
- nonholonomic constraints: (Pfaffian) rolling, conservation of momentum
- positive formulation: vector fields; negative: constraints
- underactuated robots (2nd order constraints)
- - motion planning for cars, cars and trailers (Latombe, Laumond, Lumelsky
IROS 2000, lots...)
- - holonomic planning followed by transform for STLC systems
- - optimization approaches, nonsingular loops (Wen, Sontag, Sussmann,
Fernandes, others)
- - geometric phase, iterative closed loops
- - RRT
- - differentially flat systems (Murray, Fliess, Martin, others)
- - chained form systems (many)
- - kinematically controllable systems (Bullo and Lynch)
- - averaging/oscillatory approaches
- (- mixed kinematic and dynamic)
- - fictitious inputs, Lafferiere's method
- some other references: Latombe book, Canny and Li book, Murray book,
Mason book, Wen article, my ME 495 lectures
XIV. Miscellaneous 
A.I Appendix (Text:pdf/ps,
last updated 08/19/2002, Copyright Howie Choset, 2001-2002)
- Mathematical Notation
- Closure and Interior Relationships
- Basic Definitions
- Graph Representation and Basic Search
- Statistics Primer
- Bayesian Primer (Howie ps/pdf
(under serious construction))
A.II Non-Appendix 