Index

base point of a path

basis

of open sets: Some

Basu-Pollack-Roy roadmap algorithm

Battle of the Sexes

9.4.1.1 to 9.4.1.1

Battleship game

11.7.2 to 11.7.2

Bayes' rule

Conditional | Marginalization | A | 11.2.3 | Discrete

Bayesian classifier

A | A to A

naive: A

behavioral strategies

best-first search

Best | Best to Best

bidirectional search

Bidirectional to Bidirectional | Further | Expansive-space | Exercises | The | 14.2.1.3 | 14.3.4 | 14.3.4 | 14.3.4 | Backward | Backward | Tree-based

balanced: Balanced, to Balanced,
for sampling-based planning: 5.4.1

bijective sensor

11.1.1 | 11.1.1 to 11.1.1

bilinear programming

9.4.1.2

binding constraints

2.5.1

bitangent line

6.2.4

bitangent ray

bitmap

Bitmaps to Bitmaps

black-box simulators

Black-box to Black-box

Blum and Furst

2.5.2

Blum and Kozen

Algorithms | Algorithms

body density

13.3.3

body frame

bond angle

bond length

Borel sets

5.1.3 | 5.1.3

boundary grid point

Discretization

boundary of a set

boundary point

boundary representation

3.1

boundary sensors

Boundary to Boundary

bounded set

bounded-acceleration model

8.4.4.2

bounded-velocity model

8.4.4.2

Boustrophedon decomposition

Boustrophedon to Spanning

Brachistochrone curve

bracket

15.4.3.1

breadth-first search

Breadth

bridge-test sampling

Bridge-test to Bridge-test

broad-phase collision detection

Two-phase

Brockett

13.2.3 | 15.5.2 | 15.5.2.2

Brockett's condition

Time-varying

bug algorithms

12.3.3 | 12.3.3 to Competitive

bug trap

5.4.1

Bug1 strategy

The | The to The

Bug2 strategy

The | The to The

caffeine

calculus of variations

9.1.1.1 | 13.4.1.1 | 13.4.1.1 to 13.4.1.4 | Variational to Variational

Campbell-Baker-Hausdorff-Dynkin formula

candidate Lyapunov function

Candorcet paradox

9.5.1.2

Canny

Canny's roadmap algorithm

6.4.3 to 6.4.3 | Further | Combinatorial | Fixed-path | Combinatorial

car pulling trailers

Parking | 13.1.2.4 to 13.1.2.4

Caratheodory, solution sense of

card-counting strategies

Exercises

Carnot-Caratheodory metric

Cartesian product

Cartesian

carton folding

Carton to Carton

causal links

2.5.1

CBHD formula

cell decomposition

6.2 | 6.3 | 6.3.1 | Simplicial to Complexity | 12.2.2 | 12.4.3

under differential constraints: Decomposing to Decomposing

center of mass

13.3.3

Central Limit Theorem

Generating

chain of integrators

13.2.1.3 | 13.2.1.3 to 13.2.1.3

chained-form system

15.4.3.2 | 15.5.2.3 | 15.5.2.3 to 15.5.2.3

change of coordinates

Coordinates | Coordinates to Coordinates

chasing a gap

Chazelle

Warning:

Chen-Fliess series

The | The to The | Returning to Returning

Chen-Fliess-Sussman equation

The to The

chi-square test

Testing

Chow-Rashevskii theorem

15.4.3.4

Christoffel symbol

13.4.2 | 13.4.2

Church-Turing thesis

1.4.1

classification rule

9.2.4.1

classifier

9.2.4.1 | 9.2.4.1 to A

cleared region

closed kinematic chains

What | 4.4 to 4.4.3

motion planning for: 7.4 to Computing

closed set

Closed

closed system (in mechanics)

Closed to Closed

closed-loop

control law: Open-loop
plan: 8.1

closure of a set

Special | Denseness

closure space

Closure

codistribution

coherent models

5.3.3

collision detection

5.3 to 5.3.4

broad-phase: Two-phase
checking a path segment: 5.3.4 to 5.3.4
hierarchical methods: 5.3.2 to 5.3.2
incremental methods: 5.3.3 to 5.3.3
narrow-phase: Two-phase
two-phase: Two-phase to Two-phase

collision pairs

Obstacle

collision-detection

14.3.1.3 to 14.3.1.3

collocation

combinatorial motion planning

6. to Specialized

cell decompositions: 6.3 to Complexity
introductory concepts: 6.1 to Roadmaps
polygonal case: 6.2 to 6.2.4

combinatorial roadmaps

5.6

commutative group

Groups | 15.4.2.3

commutative ring

Polynomials

commutator

15.4.2.3

commutator motion

15.4.2.3 to 15.4.2.3 | 15.5.1

compass

Simple | 12.2.2

compatible coordinate neighborhoods

competitive ratio

Landmark | Competitive | Competitive to Competitive

complementary pair

2.4.1

complete exclusion axiom

completely integrable

13.1.3.4 | 15.4.2.1 | 15.4.2.1 to 15.4.2.1

completeness

overview: Notions to Notions

complex

6.3.1 | 6.3.1 | 6.3.1 to Singular

complexity class

complexity of motion planning

6.5 to Specialized

lower bounds: 6.5.1 to Lower
upper bounds: 6.5.3 to Specialized

compliant motions

12.5.1 | Compliant | Compliant to Compliant | Backprojections

composition of funnels

8.5.1 to Termination | Squeezing | Domains

compressed mode

computational algebraic geometry

6.4 to 6.4.3

Conchoid of Nicomedes

Critical | Exercises

conditional Bayes' risk

Optimal

conditional Bayes' rule

conditional expectation

Expectation

conditional independence

conditional probability

Conditional | Conditional to Conditional

configuration space

4. | 4. | 4.2 to 4.4.3

of 2D rigid bodies: 4.2.1 to Interpreting
of 3D rigid bodies: 4.2.2 to Special
of chains of bodies: 4.2.3 to 4.2.3
of trees of bodies: 4.2.3 to 4.2.3
velocity constraints on: 13.1 to 13.1.3.4

conformations

The | Drug

connected space

Connected

connectivity-preserving roadmap

Roadmaps

connector in a roadmap

conservative approximations

11.4.3.2 | Conservative to Conservative

conservative system

constant vector field

constant-sum game

Exercises

contaminated region

continuous Dijkstra paradigm

Euclidean

continuous function

Continuous

continuous-steering car

13.2.4.2 | 13.2.4.2 to 13.2.4.2

contractible space

control system

13. | Open-loop

control-affine system

13.2.3 | 15.4.1 to 15.4.1

controllability matrix

Classical

controllability of a system

15.1.3 to STLC:

linear case: Classical to Classical

controlled Markov process

10.1.1

convex hull

5.3.2 | 5.3.2 | Piecewise-smooth

convex polygon

Convex to Convex

convex set

Convex

convolution

4.3.2

cooperative game theory

coordinate neighborhood

coordinates

coordination space

Fixed-path | Fixed-path

Coriolis matrix

13.4.2

cost functional

2.3 | General | 7.7.2 | 10.1.1 | Discounted | 11.7.2 | 14.5.2

approximating: Approximating
quadratic: 15.2.2

cost-to-come

Dijkstra's | 2.3.1.2 | 2.3.1.2 to 2.3.1.2 | 14.2.1.2

cost-to-go

A-star | 2.3.1.1 to 2.3.1.1 | General | Feasibility | Navigation | Navigation | Computing | Wavefront | Dial's | 8.4.1.2 | 8.4.3 | 8.4.3 | 8.4.3 | 8.4.3 | 8.4.3 | 8.5.1 | 8.5.2.1 | 8.5.2.1 | Continuous | 8.5.2.2 | Obtaining | Handling | Using | 8.5.2.3 | 8.5.2.3 | 8.5.2.3 | 8.5.2.3 | 8.5.2.3 | 10.6.1 | The | The | Distance | Distance | 14.5.2 | 14.5.2 | 14.5.2 | 14.5.2 | 14.5.2 | 14.5.2 | 14.6.3.4 | 14.6.3.4

Coulomb friction

Compliant

counting measure

5.1.3 | 5.1.3 to 5.1.3

covariance matrix

Moment-based

cover of a set

8.5.1.1

approximate: 8.5.1.1

coverage planning

7.6 | 7.6 to Spanning

Coxeter-Freudenthal-Kuhn triangulation

critical curves

critical gap events

Critical to Critical

critical point of a function

6.4.3 | 8.4.4.3

cube complex

Cube | Cube | Cube to Planning

cubical partition

Decomposing

CW-complex

6.3.1

cycloid function

cylinder over a cell

Cylindrical | Critical | The

cylindrical algebraic decomposition

6.4.2 to Solving | Combinatorial | Fixed-path

for motion planning: Solving to Solving

cylindrical decomposition

Cylindrical | Cylindrical to Cylindrical

D'Alembert

13.4.3.1

Davenport-Schinzel sequence

6.5.2 | 6.5.2 to 6.5.2

Davis-Putnam procedure

dead states

2.2.1 | 2.2.1 | Dijkstra's | Dijkstra's | 8.5.2.3

decision maker

1.1 | 9.

decision problem

The | The to The

decision theory

decision vertex (in a game tree)

10.5.1

decoupled planning

Reasons | 14.6 to 14.6.3.5

decoupling vector fields

14.6.3.2 | Decoupling | Decoupling to Decoupling

deformation retract

6.2.3

degrees of freedom

Translation

delayed-observation sensor

11.1.1 | 11.1.1 to 11.1.1

Denavit-Hartenberg parameters

3.3.2 | 3.3.2 to Two | The | The | 4.2.2 | 4.2.3 | Chains | 4.4.3

dense sequence

Denseness | 14.2

dense set

Denseness | Denseness | Denseness

dependent events

depth-first search

Depth | Depth to Depth

depth-mapping sensors

Depth-mapping to Depth-mapping

derivation (on a manifold)

Tangent

derived information space

11.2 | 11.2.1 to Sensor | 11.4.3 to 11.4.3.3

for continuous time: 11.4.3.3 to 11.4.3.3

derived information transition equation

Constructing

determining the environment

12.3.1 to 12.3.1 | 12.3.1 | Algorithms to Algorithms

deterministic finite automaton

2.1.2 | 11.3.2

language: 2.1.2

deterministic plan

10.5.1 | Defining | 11.7.1

Dial's algorithm

Dial's to Dial's | Other

diameter function

Squeezing

dielectric constant

diffeomorphic spaces

Smoothness

diffeomorphism

Smoothness

differential drive

15.4.3.4

model: 13.1.2.2 to 13.1.2.2
second-order: 13.2.4.3
showing it is nonholonomic: 15.4.2.4 to 15.4.2.4

differential game

13.5.2 | 13.5.2 | 13.5.2 to 13.5.2

against nature: 13.5.1
pursuit-evasion: 13.5.2

differential inclusion

Piecewise-smooth | 13.5.1

differential models

13. to 13.5.2

conversion from implicit to parametric: 13.1.1.3 to 13.1.1.3
implicit representation: 13.1.1.1 to General
parametric representation: 13.1.1.2 to 13.1.1.2

differential rotations

Differential to Differential

differentially flat systems

Differentially to Differentially

digital actor

Virtual | Virtual | Virtual

Dijkstra's algorithm

2. | Dijkstra's to Dijkstra's | 2.3.3 to 2.3.3 | Computing | Computing | Wavefront | Wavefront | Wavefront | Dial's | 8.4.2 | 8.4.3 | 8.4.3 | 8.5.2.3 | 8.5.2.3 | 8.5.2.3 | 8.5.2.3 | 10.6.1 | 12.3.2 | 12.3.2 | 12.3.2 | 14.4.1.1 | 14.5.2 | 14.5.2 | 14.6.3.4

extension of to continuous spaces: 8.5.2.3 to 8.5.2.3
with nondeterministic uncertainty: Nondeterministic to Nondeterministic
with probabilistic uncertainty: Probabilistic to Probabilistic

dimension

of a manifold: Manifold
of a vector space: Vector

directed roadmap

Sampling-based

Dirichlet boundary condition

8.4.4.4

disconnection proof

discount factor

Discounted

discounted cost model

10.3 | Discounted | Discounted to Discounted

discrepancy

5.2.4 to Low-discrepancy | 14.3.1.2 to 14.3.1.2

range space: 5.2.4
relation to dispersion: Relating

discrete feasible planning

2.1.1

discrete-time model

14.2.2 | 14.2.2 to 14.2.2.3

dispersion

5.2.3 | Dispersion to Dispersion | 8.5.2.1 | 14.3.1.2 to 14.3.1.2

relation to discrepancy: Relating

distance between sets

Distance to Distance

distance function

Distance

distribution (of vector fields)

15.4.2.2 to 15.4.2.2

regular: 15.4.2.2
singular: 15.4.2.2 to 15.4.2.2 | 15.4.2.2

disturbed odd/even sensor

11.1.1

disturbed sign sensor

domain of attraction

Domains | Domains to Domains

dominated action

9.1.1.2

dominated plan

7.7.2

Donald

Further | Backprojections

double integrator

13.2.1.1 | 13.2.1.1 to 13.2.1.1 | 13.2.4.3 | 13.3.2.1 | The | 14.1.1 | Kinodynamic | 14.1.3.2

lattice: 14.4.1 to Underactuated
optimal planning for: 15.2.3 to 15.2.3

doubly connected edge list

drift

13.2.1.3 | 13.2.3 | Drift | 15.4.1

driftless

13.2.3 | Drift

driftless system

13.2.1.3 | 15.4.1

controllability: 15.4.3.4 to 15.4.3.4

drug design

Designing | Drug to Drug

Dubins car

13.1.2.1 | 13.5.2 | Symmetric | 14.1.3.2 | 14.2.1.2 | 14.2.1.2 | 14.2.1.2 | 14.2.1.2 | 14.2.2.1 | 14.2.2.1 | 14.2.2.3 | The | 14.3.3 | 14.4.2 | Searching | Searching | Resolution | Resolution | Resolution | Distance | 14.5.1 | 14.6.1 | 14.6.2 | 14.6.2 | 14.6.2 | 14.6.3.2

plan-and-transform approach: 14.6.2 to 14.6.2
reachability tree of: 14.2.2.1 to 14.2.2.1

Dubins curves

15.3.1 | 15.3.1 to 15.3.1

Dubins metric

15.3.1

dynamic constraints

15.4.1

dynamic programming

applied to steering: Dynamic to Dynamic
continuous-time: 15.2 to Time

dynamics

of a particle: 13.3.2 to 13.3.2.1
of a rigid body: 13.3.3 to A
of a set of particles: 13.3.2.2 to 13.3.2.2
of a two-link manipulator: 13.4.2.1 to 13.4.2.1
of chains of bodies: 13.4.2 to 13.4.2.1
of constrained bodies: 13.4.3.1 to 13.4.3.1
with nonconservative forces: 13.4.3.2 to 13.4.3.2

efficient algorithm

Languages | Lower | General

elongated mode

EM algorithm

The to The

embedding of a manifold

Manifold

energy function

7.5 | Simplifying | Drug

equilibrium point of a vector field

Equilibrium

Erdmann

Backprojections | Backprojections | Backprojections

error detection and recovery (EDR)

Backprojections

Euclidean metric

Euclidean motion model

Euclidean norm

Euclidean shortest paths

Euclidean to Euclidean

Euler angles

Euler approximation

Obtaining

Euler-Lagrange equation

13.4.1.1 | 13.4.1.1 | 13.4.1.2 | 13.4.1.2 | 13.4.1.2 | 13.4.1.3 | 13.4.1.4 | 13.4.1.4 | 13.4.2 | 13.4.2 | 15.2.3 | 15.4.1 | 15.5.2.1 | Pontryagin's | Pontryagin's | Pontryagin's

with conservative forces: 13.4.3.2

event space

Probability

exit face

8.4.2

expansive-space planner

Expansive-space to Expansive-space

expectation of a random variable

Expectation to Expectation

expected-case analysis

9.2.2 | The | The

exploration vs. exploitation

exponential map

The to The

exponentially stable system

Asymptotic

EXPTIME

extended Kalman filter

11.6.1 | Continuous

extended system

15.5.1

exterior point

extremal function

falling particle

13.4.1.2 to 13.4.1.2

fast Fourier transforms

Handling

Faure sequence

feasible planning

discrete: 2.1.1
with feedback: Feasibility to Feasibility

feasible space (for closure constraints)

Closure

feature space

9.2.4.1

feature vector

9.2.4.1 | A | A | A

feedback motion planning

complete, optimal: 8.4.3 to 8.4.3
complete, some dynamics: 8.4.4 to 8.4.4.4
definitions: 8.4.1 to 8.4.1.2
motivation: 8.1 to 8.1
sampling-based: 8.5 to 8.5.2.3
under differential constraints: 14.5 to 14.5.2

feedback plan

8.2.1 | 8.2.1 to 8.2.1 | Defining | Defining to The

cost of: The to The
graph representation of: Graph to Graph
information feedback: 11.1.3 to 11.1.3
over a cover: 8.5.1.2 to 8.5.1.2
sensor feedback: Sensor

feedback planning

discrete: 8.2 to Other

feedback stabilization

15.1.1

fiber over a base

fictitious action variable

15.5.1

field

Fields | Fields | Fields to Fields

algebraically closed: Real

Filipov, solution sense of

Piecewise-smooth | Vector

finite state machine

2.1.2

firetruck

13.1.2.4

first-order controllable systems

15.5.2.2 | 15.5.2.2 to 15.5.2.2

first-order theory of the reals

fixed point of a vector field

Equilibrium

fixed-path coordination

Fixed-path to Fixed-path

fixed-roadmap coordination

Fixed-roadmap to Planning

flashlight example

2.4.1 to 2.4.1

Boolean expression for: 2.5.3
planning graph of: Mutex

flashlight sensor

12.4.3

flat cylinder

flat outputs

Differentially | Differentially

flat torus

flexible materials

Flexible

flying an airplane

13.1.3.2 to 13.1.3.2

folding problems

7.5 to Protein

foliation

14.2.1.1 | 15.4.2.1

force

Newton's | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.2 | 13.3.3 | 13.3.3 | 13.3.3 | The | The | A | 13.4.1.2 | 13.4.1.2

resultant: 13.3.2.1 | 13.3.2.2

force sensor

Boundary

formal Lie algebra

Formal to The

forward projection

10.1.2 | 14.2.1.2

differential: 13.5.1 to 13.5.1
nondeterministic: Nondeterministic to Nondeterministic
probabilistic: Probabilistic to Probabilistic
under a fixed plan: Forward to Forward

forward search

2.2.1 to Iterative

A algorithm: A-star
A algorithm: to A-star
best first: Best to Best
breadth-first: Breadth to Breadth
depth-first: Depth to Depth
Dijkstra's algorithm: Dijkstra's to Dijkstra's
general, discrete: 2.2.1 to 2.2.1
iterative deepening: Iterative to Iterative

forward value iteration

2.3.1.2 to 2.3.1.2

four-bar mechanism

Three

frame axiom

Fraunhofer Chalmers Centre

Sealing | Sealing

Frazzoli

14.2.3 | 14.2.3

free space

Obstacle

free variables

frequentist

9.5.2.1 to 9.5.2.1

frequentist risk

9.5.2.1

friction cone

Compliant

Frobenius theorem

15.4.2.4 to 15.4.2.4

frontier set

8.5.2.3 | Nondeterministic | 14.5.2

fully actuated system

Underactuation

function space

Vector | 11.4.1 | 13.4.1.1

functional

13.4.1.1 | 13.4.1.1

shortest-path: 13.4.1.1

fundamental group

The | The to The

higher order: The
of a simply connected space: The to The
of ${\mathbb{S}}^1$: The
of ${\mathbb{S}}^1$: to The
of ${\mathbb{T}}^n$: The
of ${\mathbb{T}}^n$: to The
of ${\mathbb{RP}}^2$: The
of ${\mathbb{RP}}^2$: to The

Fundamental Lemma of the Calculus of Variations

Gabriely and Rimon

Spanning

gain constant

8.4.4.1

game

alternating-play model: 10.5.1 | 11.7.1
extensive form: 10.5.1
ladder-nested: 11.7.1
normal form: 10.5.1
open-loop model: 10.5.1 | 11.7.1
stage-by-stage model: 10.5.1 | 11.7.1
unusual information model: 11.7.1 to 11.7.1

game against nature

9.2 to 9.2.4.2

sequential: 10.1 to The | 10.6.1 to 10.6.2

game graph

10.5.2

game theory

9. | 9. | 9.3 | 9.3 to 9.4.2 | 9.5.4 to 9.5.4 | 10.5 to Introducing | 11.7 to 11.7.2

information spaces in: 11.7 to 11.7.2

game tree

10.5.1 | 10.5.1 | 10.5.1 to 10.5.1.3

information space over: 11.7.1 to 11.7.1

gap navigation tree

12.3.4 to I-space

gap sensor

Depth-mapping

gap theorems

Real

garage configuration

Fixed-roadmap

Gaussian sampling

Gaussian to Gaussian

Geiger counter sensor

general linear group

general position

General | General to General | Critical

generalized coordinates

generalized cylinder

Generalized

generalized damper model

Compliant

generalized forces

13.4.1.3 | 13.4.1.4 | 13.4.1.4 | 13.4.3.1

generalized momentum

13.4.4

generator of a lattice

Making

geodesics

13.4.1.2 | Riemannian

geometric modeling

3.1 to Generalized

Gilbert-Johnson-Keerthi algorithm

gingerbread face

3.1.2 | Semi-algebraic | The

globally asymptotically stable

Domains

globally positive definite

globally randomized plan

goal recognizability

11.3.1 to 11.3.1 | Backprojections

goal sensor

12.3.3

Goldberg and Mason

Squeezing

golden ratio

Goursat normal form

15.5.2.3

Grübler's formula

4.4.3

gradient descent

Navigation | 8.4.1.2 | 8.4.4.3

graph search

on an information space: Graph-search to The

grasped configurations

gray-scale map

Bitmaps | 12.3.2

great circle

5.1.2

grid

7.1.3

2D planning on: 2.1.2
feedback plan on: Feasibility to Feasibility
infinite sequence: Infinite to Infinite
multi-resolution: Infinite
navigation function on: Navigation to Navigation | 8.2.3 to Other
neighborhoods: Neighborhoods to Neighborhoods
partial: Infinite
resolution issues: Grid to Grid
set of environments: 12.3.1 to Algorithms

grid point

Discretization

grid resolution

5.2.3

group

Groups

group axioms

Groups | Groups to Groups

guaranteed reachable

Convergence

guard in a roadmap

gyroscope

Haar measure

5.1.4 | 5.1.4 to 5.1.4

hairy ball theorem

8.4.1.1

half-edge

Polyhedral | 6.2.1

half-plane

Convex

half-space

Polyhedral

Halton sequence

Low-discrepancy | Low-discrepancy to Low-discrepancy

Hamilton's equations

13.4.4 | 15.2.3 | 15.4.1 | Pontryagin's | Pontryagin's

Hamilton's principle of least action

13.4.1.2 | 13.4.1.2 to 13.4.1.2

Hamilton-Jacobi-Bellman equation

10.2.2 | 15.2.1 | 15.2.1.2 to 15.2.1.3

Hamilton-Jacobi-Isaacs equation

15.2.1.3

Hamiltonian function

13.4.4 | 13.4.4 | 15.2.3 | 15.2.3

Hammersley point set

Low-discrepancy | Low-discrepancy to Low-discrepancy

harmonic potential function

8.4.4.4 to 8.4.4.4

Hausdorff axiom

Hausdorff space

helicopter flight

14.2.3

Hessian

8.4.4.3

hide and seek

Playing

hierarchical inclusion of a plan

Hierarchical | 12.5.1

hierarchical planning

Hierarchical | Manipulation

higher order controllability

15.5.2.3

Hilbert space

hill function

history

History | History to History

history information space

11.1.2 | The to The | 11.4.2 to 11.4.2

at stage: The
at time: 11.4.2

history information state

History | History to History

history-based sensor mapping

11.4.1 | 11.4.2

hitch length

13.1.2.4

holonomic

13.1.3.4 | 15.4.2.1

homeomorphic spaces

homeomorphism

Homeomorphism: | Homeomorphism: to Homeomorphism: | Smoothness | Coordinates

homicidal chauffeur

13.5.2 | 13.5.2 to 13.5.2

homing sensor

homogeneous transformation matrix

Combining | Combining | no title | Homogeneous | Homogeneous | 3.3.2 | Two | no title | The | The | The | The | The | Linear | Exercises | 4.2.1 | 4.3.3 | 4.3.3 | Chains

homology

homotopic paths

humanoid

hybrid state space

7.3.1 | 7.3.1

hybrid system

7.3 | 7.3.1 to 7.3.1 | Piecewise-smooth | Piecewise-smooth

motion planning: 7.3.1
with nature: 10.6.2 to 10.6.2

ibuprofen

ideal distance function

The to The

identification of points

Identifications

identity sensor

11.1.1 | Linear

implicit function theorem

13.1.1.3

implicit velocity constraints

improper prior

9.5.2.2

incomparable actions

9.1.1.2

incremental distance computation

5.3.3

incremental sampling and searching

adapting search algorithms: 5.4.2 to Grid
general framework: 5.4.1 to 5.4.1
under differential constraints: 14.4 to Sampling-based

independent events

independent-joint motion model

inertia matrix

Inertia | Inertia | Inertia to Simplifying | 13.4.1.2

inertial coordinate frame

Inertial | Inertial to Inertial | Newton's | Important | The | The | The | The | 13.4 | 13.4.1.2

infimum

9.1.1.1

infinite reflection (in a game)

9.5.4

infinite-horizon problem

10.3 | 10.3 to Solutions

inflection ray

information mapping

11.2.1 | 11.2.1 to Constructing

sufficient: Constructing to Constructing

information space

11. to 11.7.2

continuous examples: 11.5 to 11.5.4
continuous time: 11.4.2 to 11.4.2
conversion to a state space: The to The | 12.1.1 to 12.1.1
discrete examples: 11.3 to 11.3.3
for game theory: 11.7 to 11.7.2
in continuous state spaces: 11.4 to 11.5.4
limited memory: 11.2.4 to Sensor
sensor feedback: Sensor to Sensor

information state

11. | 11.

information transition equation

The to The

derived: Constructing to Constructing

information transition function

information-conservative property

information-feedback plan

11.1.3

initial condition space

The | The to The | 11.4.1 to 11.4.1

input string

11.3.2

integrable system

13.1.3.4

integral curve

An | An to An

integral manifold

15.4.2.1

interior of a set

interior point

interpolation neighbors

interpolation region (for value iteration)

8.5.2.1 | 10.6.1

interval homeomorphisms

Homeomorphism: to Homeomorphism:

intractable problem

inverse Ackerman function

6.5.2

inverse control problem

Reverse-time

inverse kinematics problem

What

involutive distribution

15.4.2.4

Isaacs

13.5.2 | 13.5.2

isomorphic graphs

isomorphic groups

isomorphism

iterative deepening

Iterative | Iterative to Iterative

Jacobi identity

15.4.3.1 | 15.4.3.3 | 15.4.3.3 | 15.5.2.2

Jacobian

jerk (third time derivative)

13.2.1.3 | 14.6.3.4

joint encoder

junction of links

Junctions

Kagami

Virtual | Virtual

Kalman filter

11.6.1 to 11.6.1

Kalman rank condition

Classical

Kd-tree

Approximate | Approximate to Approximate | Defining | Maintaining

Khalil-Kleinfinger parameterization

Junctions

Khatib

8.4.1.2

kidnapped-robot problem

12.2

kinematic chain

3.3

kinematic constraints

Nonholonomic | 15.4.1

kinematic singularities

Computing

kinematically controllable

Decoupling

kinematics for wheeled systems

13.1.2 to 13.1.2.4

Kineo CAM

An | An | An | Parking | Parking

kinetic energy

13.3.2.1 | 13.3.2.1 | Completing | 13.4.1.2 | 13.4.1.2 | 13.4.1.2 | 13.4.1.2 | 13.4.1.4 | 13.4.1.4 | 13.4.2 | 13.4.2.1 | 13.4.2.1 | 13.4.3.1

kinodynamic planning

Kinodynamic | Kinodynamic to Kinodynamic | 14.4.1 to Underactuated

Klein bottle

knot

knot simplification

Simplifying to Simplifying

knot vector

Nonuniform

Koditschek

Navigation | 8.4.4.3

Kolmogorov complexity

2.4.1 | Lower

Kuffner

A | A | 5.4.1

Kuhn

11.7.1 | Further

Kutzbach criterion

4.4.3

L-shaped corridor example

11.3.1 to 11.3.1

label-correcting algorithms

2.3.3 | 2.3.3 to 2.3.3

Lafferriere and Sussmann

15.5.1

Lagrange multiplier

13.4.3.1

Lagrangian function

13.4.1.2 | 13.4.1.4 | 13.4.2.1 | 13.4.3.1 | 13.4.4

Lagrangian mechanics

landmark region detector

landmark sensors

Landmark to Landmark

language

2.1.2 | 11.3.2

latitude in a grid

Algorithms

Latombe

lattice

Making | Making | Making | Low-discrepancy

for unconstrained mechanical systems: Unconstrained to Unconstrained

Laumond

Parking | Parking | Nonholonomic

lawn mowing

layered graph

Planning

layered plan

Plan

learning phase

leaves of a foliation

14.2.1.1 | 15.4.2.1

Lebesgue integral

Lebesgue measure

5.1.3 | 5.1.3 to 5.1.3

left translation

15.4.3.1

left-invariant vector field

15.4.3.1

left-turn predicate

6.2.4

Legendre transformation

13.4.4

Legendre-Clebsch condition

15.2.3

Leibniz rule

Tangent

Lennard-Jones radii

Lens spaces

level-set method

Lie

Lie algebra

15.4.3.1 | 15.4.3.1 | 15.4.3.1 to 15.4.3.2

cross product example: 15.4.3.1 to 15.4.3.1
of the system distribution: 15.4.3.2 to 15.4.3.2
on Lie groups: 15.4.3.1 to 15.4.3.1

Lie algebra rank condition

15.4.3.4

Lie bracket

15.4.2.3 | 15.4.2.3 to 15.4.2.3 | 15.4.3.1

Taylor series approximation of: 15.4.2.3 to 15.4.2.3

Lie derivative

Lie group

Matrix | 15.4.3.1 | 15.4.3.1

ligand

limit curve

14.6.3.5

limit cycle

Limit | Limit to Limit

limit point of a set

Lin-Canny

line-segment robot

6.3.4 to Complexity

linear combination

linear complementarity problem

9.4.1.2

linear differential game

13.5.2 | 13.5.2

linear interpolation

linear momentum

13.3.2.1

linear programming

9.1.1.1 | 9.3.3.2 | 14.7

linear sensing models

Linear | Linear to Linear

linear space

linear system

13.2.2 | 13.2.2 to 13.2.2

observability: 13.2.2
time-varying: 13.2.2

linear transformations

Linear

linear-Gaussian system

11.6.1 | 11.6.1 | Continuous

linear-quadratic problems

15.2.2 to 15.2.2

linear-quadratic-Gaussian (LQG) system

11.6.1 | 15.2.2

link

3.3

linkage

3.3

linkage graph

4.4.3

Lipschitz condition

5.3.4 | An | An to An | 14.2.2.3 | 14.2.2.3 | 14.2.2.3 | 14.3.4 | Resolution | 14.5.2 | 14.7

Lipschitz constant

5.3.4 | An

LMT framework

12.5.1

local operator

Navigation | Navigation | Navigation to Navigation | Computing | 8.2.3 | 8.4.1.2 to 8.4.1.2 | 8.4.2 | 8.4.4.3 | Using | 14.5.2

continuous space: 8.4.1.2

local planning method

5.4.1 | 5.4.1 | 5.4.1 | 5.4.1 | 5.4.1 | 5.4.3 | 5.4.3 | Ariadne's | Expansive-space | Random-walk | 5.5.1 | Generic | Some | Some | Some | Planning | 14.7 | 15. | STLC: | 15.3 | 15.3.1 | 15.3.1 | 15.3.2 | 15.3.3 | 15.4.3.4 | 15.5 | Decoupling

in plan-and-transform: 14.6.2 | 14.6.2 | 14.6.2 | 14.6.2 | 14.6.2 | 14.6.2 | 14.6.2 | 14.6.2
under differential constraints: 14.3.3 | 14.3.3 to 14.3.3 | 14.3.4 | 14.4.3 | 14.4.3 | 14.4.3 | Designing | Designing

local visibility sensor

12.3.3

localization

12.2 to The

active: 12.2 | Solving to Solving
combinatorial: 12.2.2 to 12.2.2
discrete: 12.2.1 to Other
passive: 12.2 | 12.2.1 | Solving to Solving
probabilistic: 12.2.3 to Continuous
symmetries: Solving to Solving

locally positive definite

locally randomized plan

Logabex LX4 robot

Computing | Computing

logic-based planning

2.4 to 2.5.3

as satisfiability: 2.5.3 to 2.5.3
converting to state space: 2.4.2 to 2.4.2
in plan space: 2.5.1 to 2.5.1
operator: 2.4.1
via a planning graph: 2.5.2 to Plan

loop path

lost-cow problem

Competitive | Exercises | Exercises

low-discrepancy sampling

5.2.4 to Low-discrepancy

low-dispersion sampling

5.2.3 to Dispersion

lower envelope

6.5.2 | 6.5.2 | 6.5.2 | 6.5.2 | 6.5.2 | 9.3.3.2

lower pairs

3.3.2 | 3.3.2

lower value of a game

9.3.2 | 10.5.1.1 | Saddle

Lozano-Pérez

Lozano-Pérez, Mason, and Taylor

12.5.1

lunar lander

13.3.2.1 to 13.3.2.1

Lyapunov function

8.5.1 | 15.1.2 | Determining to Lyapunov

in planning: Lyapunov to Lyapunov

Lyapunov stability

Equilibrium | Equilibrium to Equilibrium

uniform: Equilibrium

Lynch and Mason

13.1.3.1 | 13.1.3.1

Möbius band

2D | 2D | The | Exercises | Exercises

Mahalanobis metric

maneuver

14.2.3

maneuver automaton

14.2.3 | 14.2.3 | 14.2.3

Manhattan metric

Manhattan motion model

manifold

4.1.2 | Manifold | Manifold to Higher

embedding: Manifold
higher dimensional: Higher to Higher
one-dimensional: 1D to 1D
two-dimensional: 2D to 2D
with boundary: Manifold

manipulation graph

Manipulation to Manipulation

manipulation planning

7.3.2 to Multiple

under uncertainty: 12.5 to Squeezing

manipulator

The | What | Further | 7.3.2 to Multiple | 7.4 | 7.4 | 7.4 | Carton | 13.4.2.1 to 13.4.2.1 | 14.6.3 | 14.6.3.3

map building

12.3 | 12.3.1 to The

marginalization

Markov chain

10.1.1

Markov decision process

10.1.1

Markov game

Introducing

Markov process

10.1.1 | 10.1.1

mass matrix

matching pennies

9.1.3 to 9.1.3

Matlab

matrix game

9.3.1

matrix groups

Matrix to Special

matrix subgroup

maximal ball

Medial-axis

maximum-clearance navigation function

Maximum to Maximum

maximum-clearance roadmap

6.2.3 | 6.2.3 to 6.2.3

maze searching

Algorithms to Algorithms

Mealy/Moore machines

2.1.2

means-end analysis

measurable function

measurable sets

measure axioms

measure space

5.1

measure theory

5.1.3 to 5.1.4 | Defining to Defining

measure zero

mechanics

13.3 to 13.4.4

Hamiltonian: 13.4.4 to 13.4.4
Lagrangian: 13.4.1 to 13.4.3.2
Newton-Euler: 13.3 to A

medial-axis sampling

Medial-axis to Medial-axis

Mersenne twister

Pseudorandom

metric space

5.1 | 5.1.1 | 5.1.1 to Cartesian

Cartesian products of: Cartesian to Cartesian
definition: 5.1.1
for motion planning: 5.1.2 to Pseudometrics
from: 5.1.2
from: to 5.1.2
from: 5.1.2
from: to 5.1.2
from: 5.1.2
from: to 5.1.2
from: 5.1.2
from: to 5.1.2
from ${\mathbb{T}}^n$: 5.1.2 to 5.1.2
nonpositively curved: 14.7
Riemannian manifold: Riemannian to Riemannian
robot displacement metric: 5.1.2
subspaces of: Metric to Metric

metric tensor

Riemannian

metrizable

5.1.1

mine sweeping

minimalism

12.5.2

minimax

9.2.2

minimum turning radius

13.1.2.1

Minkowski difference

4.3.2 | 6.2.1 | 6.2.1 | Specialized | Specialized

Minkowski sum

4.3.2

mod sensor

mode space

7.3 | 7.3.1

mode transition function

mode-dependent dynamics

7.3

moment of a density

Moment-based

moment of force

13.3.2.2

moment of inertia

moment of momentum

13.3.2.1 | 13.3.2.1 | 13.3.2.2 | The | Differential | The

moment-based approximations

Moment-based to Moment-based

momentum

monomial

monotone polygon

morphing a path

Morse function

Morse theory

motion capture

motion command

Motion | Motion | Motion to Motion

motion planning

14.1.2.2

motion primitive

14.2.3 | 14.2.3 to 14.2.3 | Designing to Designing

multi-chained-form systems

15.5.2.3

multi-level approach

14.6.2

multi-linear interpolation

multi-resolution grid

Infinite

multiobjective optimization

9.1.1.2 to 9.1.1.2

multiple observations

Receiving to Receiving

multiple query

Notions | 5.6

multiple shooting

multiple-robot motion planning

7.2 to Planning

multiple-robot optimality

7.7.2 to Computing

multiply connected

Murphy's Law

9.2.2

Murray and Sastry

15.5.2

mutex condition

Mutex | Mutex to Mutex

mutex relation

Mutex

NAG Fortran Library

naive Bayes

Receiving

narrow-phase collision detection

Two-phase

NASA/Lockheed Martin X-33

14.1.3.1 | 14.1.3.1 | 14.1.3.1

Nash equilibrium

9.4 to 9.4 | 9.4.1 | 9.4.1 to Summary | 9.4.2 | 9.5.4 to 9.5.4 | 11.7 | 11.7.2

admissible: 9.4.1.1
in a sequential game: Nash to Nash
nonuniqueness: 9.4.1.1 to 9.4.1.1
randomized: 9.4.1.2 | 9.4.1.2 to 9.4.1.2 | 9.4.2 | 11.7.1

nature

9. | 9.2.1

nature action space

9.2.1

nature observation action

Nature | Nature

nature sensing action

11.1.1 | 11.1.1 | 11.4.1 | Linear to Linear | 11.5.3 to 11.5.3

nature sensing actions

11.1.1

navigation function

2.2.1 | 2.3.2 | Navigation to Other

continuous space: 8.4.1.2
in the sense of Rimon-Koditschek: 8.4.4.3 to 8.4.4.3
stochastic: 10.6.2 | 10.6.2

navigation problem

12.3.1 | Algorithms to Algorithms

negative literal

2.4.1 | 2.4.1

neighborhood function

neighborhood of a cover

8.5.1.1

Neumann boundary condition

8.4.4.4

Newton's laws

Newton's to Newton's | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.1 | 13.3.2.2 | The | The | Inertia | 13.4.1.2 | 13.4.1.2

next-best-view problem

12.3.5

NF2 (a navigation function)

Maximum

nicotine

nilpotent

nilpotent system

nilpotentizable

Nilsson

Nixederreiter-Xing sequence

nonconservative forces

13.4.3.2 to 13.4.3.2

nonconvex

polygon: Nonconvex to Nonconvex | Nonconvex
polyhedron: Nonconvex
set: Convex

noncooperative game

noncritical regions

nondeterministic finite automaton

11.3.2 | 11.3.2 to 11.3.2

nondeterministic information space

11.2.2 to 11.2.2

approximations: Conservative to Conservative
examples: 11.3.1 to 11.3.2
planning on: 12.1.2 to The

nondeterministic Turing machine

nondeterministic uncertainty

9.2.2 to 9.2.2

criticisms of: 9.5.3 to 9.5.3

nondirectional backprojections

Backprojections

nonholonomic

13.1.3.4 | Nonholonomic | Nonholonomic | 15.4 | 15.4.2.1

nonholonomic constraints

13.1.2

nonholonomic integrator

13.2.3 | 13.2.3 to 13.2.3 | 15.4.2.3 | 15.4.3.4 | 15.5.1 | The | The

showing it is nonholonomic: 15.4.2.4 to 15.4.2.4
steering: 15.5.2.1 to 15.5.2.1

nonholonomic metric

nonholonomic planning

Parking | Nonholonomic | Nonholonomic to Nonholonomic

nonholonomic system

Underactuated to Underactuated

nonholonomic system theory

15.4 to 15.4.3.5

noninformative prior

9.5.2.2 | 9.5.2.2 to 9.5.2.2

nonintegrable

15.4.2.1

nonlinear optimization

nonlinear programming

14.7 | 14.7 to 14.7

nonlinear system

13.2.3 to 13.2.3

affine in control: 15.4.1 to 15.4.1
affine-in-control: 13.2.3

nonparametric methods

9.5.2.3

nonpositively curved space

nonprehensile manipulation

12.5.2 | 12.5.2 to Squeezing

nonrigid transformations

3.5

nonzero-sum game

9.4 to 9.4.2

with more than two players: 9.4.2 to 9.4.2
with two players: 9.4.1 to Summary

NP (complexity class)

null sensor

11.1.1 | 11.1.1 to 11.1.1

numerical continuation

Stepping

numerical integration

Euler: Euler to Euler
multistep methods: Multistep | Multistep to Multistep
Runge-Kutta: Obtaining | Runge-Kutta to Runge-Kutta
single-step methods: Multistep

NURBS

Nonuniform to Nonuniform

OBB

5.3.2 | 5.3.2

observability

13.2.2

observation space

Formulating | 11.1.1 | 11.1.1

observations

9.2.3 to Receiving

obstacle region

3.2 | Obstacle

in the C-space

4.3 to Chains

1D case: to 4.3.2 | 4.3.2
general case: 4.3.3 to Chains
polygonal case: A to Computing
polyhedral case: A to A

in the state space

14.1.3 to 14.1.3.2

in the world

3.1 | 3.1 to Generalized

polygonal case

6.2 to 6.2.4

time-varying

7.1.1 | 7.1.3 to 7.1.3

obstacles

3.1

occupancy grid

Bitmaps | The

Ochiai unknot benchmark

Simplifying | Simplifying

octane transformations

The to The

odd/even sensor

odometric coordinates

Solving | Solving | Algorithms

odometry sensors

Odometry to Odometry

on-line algorithm

1.4.1 | Competitive to Competitive

open ball

open set

3.1.2 | 4.1.1

open-loop

control law: Open-loop
plan: 8.1

operator

2.4.1

optical character recognition

A to A

optimal motion planning

7.7 to Computing

optimal planning

discrete: 2.3 | 2.3.2 to 2.3.3
fixed-length plans: 2.3.1 to 2.3.1.2
unspecified length: 2.3.2 to 2.3.2

optimization

9.1.1 | 9.1.1.1 to 9.1.1.2

orientation sensor

oriented bounding box

5.3.2 | 5.3.2

orienteering problem

origami

7.5

orthogonal group

outdoor navigation

painting

parallel manipulator

7.4

parallel-jaw gripper

Squeezing

parameter estimation

9.2.4.2 | 9.2.4.2 to 9.2.4.2

parameterization

1D | Coordinates

Pareto optimal

7.7.2 | 7.7.2 | 7.7.2 to Computing | 9.1.1.2 to 9.1.1.2 | 9.4.1.1 | 9.4.1.1 | 9.4.2 | 9.5.2.1

parking a car

Parking | 13.1.2.1 | 13.2.4.3 | 14.2.1.2 | Exercises | Classical | 15.4.2.3

part configuration space

partial grid

partial plan

particle

dynamics: 13.3.2 to 13.3.2.1
falling: 13.4.1.2 to 13.4.1.2
on a sphere: 13.4.3.1 to 13.4.3.1

particle filtering

Particle | Particle to Particle | Continuous

path

Paths | Paths to Paths

path connected

Connected

path tuning

7.1.3 | 7.1.3

path-constrained phase space

14.6.3.3

path-directed subdivision tree

Other

pattern classification

9.2.4.1 | 9.2.4.1 to A

pebble

peg-in-hole problem

pendulum

13.3.2.1 to 13.3.2.1

double: Exercises

Pennsylvania Turnpike

9.1.1.2

perfect recall

permissible action trajectories

14.1.1

Pfaffian constraints

13.1.1.3 to 13.1.1.3 | 13.1.1.3 | 13.1.2.1 | 13.1.3.4 | 13.2.3 | 13.2.3 | 13.4.3.1 | 13.4.3.1 | 13.4.3.1 | 13.4.3.1 | 15.4.1 | 15.4.1 | 15.4.1 | 15.4.1 | 15.4.1 | 15.4.1 | 15.4.1 | 15.4.2.1 | 15.4.2.1 | 15.4.2.1 | 15.4.2.1 | 15.4.2.2 | 15.4.2.2 | 15.4.2.4 | 15.5.2.3

pharmacophore

phase constraints

14.1.3.1

phase space

13.2 | 13.2.1.1 to 13.2.4.3

obstacles: 14.1.3 to 14.1.3.2
path-constrained: 14.6.3.3 to 14.6.3.3

phase transition equation

13.2.1.1 | 13.2.1.2

phase vector

13.2.1.1

Philip Hall basis

15.4.3.3 | 15.4.3.3 | 15.4.3.3 to 15.4.3.3 | 15.5.1 to 15.5.1 | Formal | The | Returning | 15.5.2

Piano Mover's Problem

Definition to Definition | 14.1.1 | 14.1.1 | 14.3.3 | 14.3.4 | 14.4.3 | 14.4.3 | Handling | Distance | 14.5.1 | 14.6.1 | 14.7

piecewise-linear obstacle motion

7.1.1 to 7.1.1 | 7.1.3

pitch rotation

Yaw, | Yaw,

plan-and-transform method

14.6.2 to 14.6.2

plan-based state transition graph

Graph

plan-space planning

2.5.1 | 2.5.1

plane-sweep principle

Plane-sweep to Algorithm

radial sweep: 6.2.4 | 8.4.3

planetary navigation

planner

1.4.2 to 1.4.2

planning graph

2.5.2 | Planning to Plan

planning under sensing uncertainty

12. to Squeezing

general methods: 12.1 to The
manipulation: 12.5 to Squeezing

Poinsot

13.3.3 | Completing

point robot

6.2.1

point-location problem

8.5.2.1 | Maintaining

policy iteration

10.2.2 | 10.2.2 to 10.2.2

for reinforcement learning: Policy to Policy
on an information space: Policy to Policy
with average cost-per-stage: Solutions to Solutions
with discounted cost: Policy to Policy

polygonal model

3.1.1 to Nonconvex | 6.2 to 6.2.4

face: 6.2.1
half-edge: 6.2.1
representation: 6.2.1 to 6.2.1

polyhedral model

Polyhedral to Polyhedral

polynomial

Polynomials | Polynomials to Polynomials

coefficient: Polynomials
in formal Lie algebra: Formal
term: Polynomials
total degree: Polynomials

polynomial-time reducible

Hardness

POMDP

11.3.3 | 11.3.3 to 11.3.3 | 12.1.3 to The

Pontryagin's minimum principle

10.2.2 | 14.7 | 15.2.3 | 15.2.3 to Time | Pontryagin's | Pontryagin's to Pontryagin's

time-optimality case: Time to Time

portiernia

7.3.1 | 7.3.1 to 7.3.1

position sensor

positive definite function

positive literal

2.4.1 | 2.4.1

posterior

potential energy

13.4.1.2 | 13.4.1.2 | 13.4.1.2 | 13.4.1.2 | 13.4.1.4 | 13.4.2 | 13.4.2.1 | 13.4.2.1

potential function

Pseudometrics | 5.4.3 | 13.4.1.2

attractive term: 5.4.3
continuous state space: 8.4.1.2
discrete: Navigation
repulsive term: 5.4.3

PQP (Proximity Query Package)

predicate

2.4.1

for geometric models: Defining to Defining

preimage of a function

Continuous

preimage of a motion command

Preimages to Preimages

preimage of an observation

11.1.1

preimage planning

12.5.1 | 12.5.1 to Computing

Princess and the Monster

11.7.2 to 11.7.2

principle of virtual work

13.4.3.1

principle subresultant coefficients

prior distribution

Conditional | 9.5.2.2 to 9.5.2.2

prioritized planning

Prioritized to Prioritized

prismatic joint

Attaching | Attaching | Attaching | Homogeneous | The

Prisoner's Dilemma

9.4.1.1 to 9.4.1.1 | 9.5.4 | 9.5.4

probabilistic completeness

Notions

probabilistic information space

11.2.3 to Sensor

approximations: Moment-based to Moment-based
examples: 11.3.3 to 11.3.3
planning on: 12.1.3 to The

probabilistic information state

computation of: 11.6 to Particle

probabilistic uncertainty

9.2.2 to 9.2.2

criticisms of: 9.5.2 to 9.5.2.3

probability function

Probability

probability measure

5.1.3 to 5.1.3

probability space

Probability to Probability

probability theory

9.1.2 to Expectation

problem solving

2. | 2.

product of inertia

projection sensors

Simple to Simple | 11.5.2 to 11.5.2

projective geometry

Combining

projective space

Higher

protein cavity

8.1

protein folding

Designing | Protein to Protein

proximity sensor

Boundary

pseudometric

Pseudometrics to Pseudometrics | Sampling-based | Sampling-based

pseudorandom number generation

Pseudorandom to Pseudorandom

linear congruential: Pseudorandom

PSPACE

Puma 560 robot

pure strategy

9.1.3

pursuit-evasion game

11.7.2 | 13.5.2 | 13.5.2

pushing a box

13.1.3.1 to 13.1.3.1

Q-factor

10.4.3

Q-learning

10.4.3 to Policy

quadratic cost functional

15.2.2

quadratic potential function

8.4.1.2 to 8.4.1.2

quantified variables

quantifier

quantifier-elimination problem

Tarski | The

quantifier-free formula

quasi-static

13.1.3

quaternion

Quaternions to Finding

from a rotation matrix: Finding to Finding

quotient topology

Identifications

radar map

Radar | Radar to Radar

radial sweep

6.2.4 | 8.4.3

random loop generator

7.4.2 | Loop | Loop to Loop

random sampling

5.2.2 to Testing

of: Generating
of: to Generating
of directions: Generating to Generating
tests: Testing to Testing

random variable

Random | Random to Expectation

random-walk planner

Random-walk to Random-walk

randomized algorithm

randomized lower value

9.3.3.1 | 10.5.1.2 | Value

randomized plan

10.5.1 | 10.5.1 | Defining

randomized potential field

5.4.3 | 5.4.3 to 5.4.3 | 8.4.1.2

under differential constraints: Randomized to Randomized

randomized saddle point

9.3.3.1

randomized security plan

10.5.1.2

randomized strategy

9.1.3 | 9.1.3 to 9.1.3

randomized upper value

9.3.3.1

randomized value

9.3.3.1 | 10.5.1.2

range scanner

Depth-mapping

range space (for discrepancy)

5.2.4

rapidly exploring dense tree

exploration: 5.5 to 5.5.1
finding nearest points: 5.5.2 to Approximate
making planners: 5.5.3 to More
under differential constraints: 14.4.3 to Designing

Rapoport

9.5.4

rational decision maker

9.3.1 | 9.5.1.1 | 9.5.1.2

reachability graph

14.2.2.1 | 14.2.2.1 to 14.2.2.1

reachability tree

14.2.2.1 | 14.2.2.1 to 14.2.2.1

reachable set

14.2.1 | 14.2.1.1 to 14.2.1.3

backward: Domains
for simple car models: 14.2.1.2 to 14.2.1.2

real algebraic numbers

Real | Real to Real

reality television

9.5.1.1 to 9.5.1.1

reckless driving

``Wreckless''

recognizability

11.3.1 | Backprojections

reconfigurable robot

recontamination

Reeds-Shepp car

13.1.2.1 | Symmetric | 14.2.1.2 | 14.2.1.2 | 14.2.1.2 | 14.6.2

Reeds-Shepp curves

15.3.2 | 15.3.2 to 15.3.2

refinement of a plan

Refinement | 14.6.1

reflex vertex

6.2.4

region of inevitable collision

14.1.3.2 | 14.1.3.2 | 14.1.3.2 to 14.1.3.2

regret

Regret | Regret to Regret | Regret to Regret

regret matrix

Regret | Regret

reinforcement learning

10.4 | 10.4.1 | Terminology to Policy

evaluating a plan: 10.4.2 to Temporal
general framework: The to The
terminology: Terminology to Terminology

relative value iteration

repulsive vertex

reroute path

resolution

resolution completeness

under differential constraints: 14.2.2.2 to 14.2.2.3

resultant

force: 13.3.3
moment: 13.3.3

reverse-time system simulation

Reverse-time to Reverse-time

revolute joint

Attaching | Attaching | Attaching | Attaching | Attaching | Homogeneous | Homogeneous | 3.3.2 | 3.3.2 | 3.3.2 | 3.3.2 | The | The | The | The | 8.1 | Common | Flexible | Exercises

reward

Terminology

reward function

9.1.1.1

reward functional

Terminology

reward space

9.5.1.1

Riemannian manifold

Riemannian metric

Riemannian | Riemannian to Riemannian

Riemannian tensor

Riemannian

Rimon

Navigation | 8.4.4.3

risk

conditional Bayes': Optimal
frequentist: 9.5.2.1

roadmap

directed: Sampling-based
general requirements: Roadmaps to Roadmaps

robot displacement metric

5.1.2 to 5.1.2

robot-robot collisions

7.2.1

Rock-Paper-Scissors

9.5.4 | Exercises

roll rotation

Yaw, | Yaw,

rolling a ball

13.1.3.3 to 13.1.3.3

rotation

2D: Rotation to Combining
3D with quaternions: Quaternions to Quaternions
3D with yaw-pitch-roll: Yaw, to The

Rubik's cube

1.1 | Discrete | Discrete | Time | 2.1.2

Runge-Kutta

Obtaining

Russell and Norvig

sample point of a cell

Defining

sample sequence

5.2.1

sample set

5.2.1

sample space (of a probability space)

Probability

sampling-based neighborhood graph

8.5.1.3

sampling-based planning

for closed chains: Sampling-based to Computing
philosophy: 5. | 5. | 5. to 5.
time-varying: Sampling-based to Sampling-based
under differential constraints: 14.3 to Sampling-based
with feedback: 8.5 to 8.5.2.3 | 14.5 to 14.5.2

sampling-based roadmap

$\epsilon$ -goodness: Some
analysis: Some to Some
basic method: 5.6 to Some
boundary sampling: Sampling to Sampling
bridge-test sampling: Bridge-test to Bridge-test
Guassian sampling: Gaussian to Gaussian
medial-axis sampling: Medial-axis to Medial-axis
preprocessing phase: Generic to Selecting
query phase: Query to Query
vertex enhancement: Vertex to Vertex
visibility roadmap: 5.6.2 to 5.6.2

sampling-based roadmaps

5.6 | 5.6 to Medial-axis

under differential constraints: Sampling-based to Sampling-based

Sard's Theorem

8.4.4.3

scalarization

Scalarization to Scalarization

scaling an object

Linear

screw transformation

Two

sealing cracks

Sealing

search algorithms

7.1.3

adaptation to continuous spaces: 5.4.2 to Grid
under differential constraints: 14.3.4 to 14.3.4 | Searching to Searching
unified view: 2.2.4 to 2.2.4

search graph

2.2.4 | 5.4.1 | 14.3.4

searching an environment

12.3.1

second-order controllable systems

15.5.2.2

second-order differential drive

13.2.4.3

second-order unicycle

13.2.4.1

section (of a cylinder)

sector (of a cylinder)

security plan

10.5.1.1 | 10.5.1.1 to 10.5.1.1 | Value

security strategy

9.3.2

randomized: 9.3.3.1

selective sensor

semi-algebraic decomposition

semi-algebraic model

3.1.2 to 3.1.2

semi-algebraic set

3.1.2

sensing history

History

sensor feedback

Sensor

sensor mapping

11.1.1 | 11.1.1 | 11.1.1 to 11.1.1 | 11.4.2 to 11.4.2

sensor observation

11.

sensorless manipulation

12.5.2

sensorless planning

11.3.1 | 11.3.1 to 11.3.1 | 11.5.4 to 11.5.4

sensors

continuous: 11.5.1 to Odometry
discrete: 11.1.1 to 11.1.1

sequential game

10.5 | 10.5.1 to Introducing

information space of: 11.7.1 to 11.7.2
Markov assumption: 10.1.1 to 10.1.1
more than two players: Introducing to Introducing
on state spaces: 10.5.2 to Introducing
saddle point: 10.5.1.2 to 10.5.1.3 | Saddle to Saddle | 11.7 | 11.7.1 to 11.7.1 | 11.7.1 to 11.7.1 | 11.7.2 to 11.7.2
zero-sum with nature: Introducing to Introducing

shadow component

12.3.4

shadow region

12.3.4

shearing transformation

Linear

shooting methods

shortest-path functional

13.4.1.1 to 13.4.1.1

shortest-path roadmap

6.2.4 | 6.2.4 | 6.2.4 to 6.2.4 | Using

SICK LMS-200

Depth-mapping

sigma algebra

sign assignment

sign sensor

sign-invariant region

silhouette curves

6.4.3 | 6.4.3

simple polygon

Nonconvex

simple-car model

13.1.2.1 to 13.1.2.1

two-car game: 13.5.2 to 13.5.2
with nature: 13.5.1 to 13.5.1

simple-unicycle model

13.1.2.3 to 13.1.2.3

simplicial complex

simply connected space

Simpson paradox

9.5.1.2

simulation-based methods

Terminology

simultaneous localization and mapping

12.3.1

single query

Notions | 5.4.1

single shooting

singular 0-simplex

Singular

singular arcs

15.2.3

singular complex

6.3.1 | Singular | Singular | Singular

singular distribution

singular matrix

singular point of a distribution

singular simplex

Singular

singular value decomposition (SVD)

10.2.2

situation calculus

skew symmetry

15.4.3.1 | 15.4.3.3

SLAM

12.3 | 12.3.1 to The

probabilistic: 12.3.5 to The

sliding-mode control

Piecewise-smooth

sliding-tile puzzle

1.1 | Discrete | Discrete | 2.1.2

small-time local controllability

13.1.2 | 13.1.2.1 | 14.6.2 | STLC: to STLC: | 15.3.1 | 15.3.2 | 15.4 | 15.4.2 | 15.4.3 | 15.4.3.4 to 15.4.3.5 | 15.5 | 15.5.1 | Decoupling

smooth differential drive

13.2.4.3 to 13.2.4.3

smooth distribution

smooth function

Smoothness

smooth manifold

Manifold | 8.3.2 | Coordinates to Vector | 15.4.2.2

${\mathbb{R}}^n$: Coordinates
${\mathbb{R}}^n$: to Coordinates
${\mathbb{S}}^n$: Coordinates
${\mathbb{S}}^n$: to Coordinates
${\mathbb{RP}}^n$: Coordinates
${\mathbb{RP}}^n$: to Coordinates
Riemannian: Riemannian to Riemannian

smooth structure

smoothness of a function

Smoothness to Smoothness

Sobol sequence

Sod's Law

9.2.2

Sokoban

Lower

solid representation

3.1

solution in the sense of Filipov

Piecewise-smooth

solution trajectory

An | Vector

span of vector fields

spanning tree

Spanning

spanning-tree covering

Spanning to Spanning

spatial constraints

special Euclidean group

Special | Special to Special | Special to Special

special orthogonal group

speedometer

spherical coordinates

Tangent

spherical joint

The | 8.1

spherical linear interpolation

spine curve

spiral search

squeeze function

squeezing parts

Squeezing to Squeezing

stability of a system

15.1.1 to Determining

time-varying case: Time-varying to Time-varying
uniform: Equilibrium

stable configuration space

stage-dependent plan

Defining

standard grid

Making

star algorithm

A to A

star-shaped regions

8.4.4.3

state estimation

Making to Making

state history

8.4.1.1

state mapping

11.4.1

state space

2.1.1 | 2.1.1

state trajectory

8.2.1 | 8.4.1.1 | 14.1.1

state transition equation

2.1.1 | 2.1.1 | 13.2.1.1 | 13.2.1.2

state transition function

2.1.1 | 2.1.1

state transition graph

2.1.1

state transition matrix

Probabilistic

state-nature mapping

11.4.1 | 11.4.2

state-sensor mapping

11.4.2

state-space discretization

14.4.2 to Backward

stationary cost-to-go function

2.3.2 | Convergence | Convergence | Using

stationary differential equations

statistical decision theory

9.2.4

steering methods

14.3.3 | 15.5 to Dynamic

piecewise-constant actions: 15.5.1 to Using
sinusoidal action trajectories: 15.5.2 to 15.5.2.3

steering problem

14.1.2.2

Stentz's algorithm

General | 12.3.2 to Interpretation

stereographic projection

Solving | Coordinates

sticking

stochastic control theory

10.

stochastic differential equation

13.5.1

stochastic fractal

5.5.1

stochastic iterative algorithm

Temporal | Temporal

stochastic shortest-path problem

strange topology

strategy

Formulating

STRIPS

2. | 2.4.1 | 2.4.1 | 2.4.1 | 2.4.1 | 2.4.2 to 2.4.2 | 2.5

strong backprojection

Backprojections | Backprojections | Backprojections | Backprojections | Backprojections

structure problem

Protein

sub-Riemannian metric

subgroup

subjective probabilities

9.5.2.2

subspace topology

Some | Some to Some

sufficient information mapping

Constructing

sufficient statistic

Constructing

Sukharev grid

Making

superquadric

Superquadrics

supremum

Dispersion | 9.1.1.1

Sussmann and Tang

15.3.2 | 15.3.2

swath

5.5.1 | 5.5.1 | 5.5.1 | 14.2.2.1 | 14.2.2.1 | 14.2.2.1 | 14.2.3 | 14.3.4

swath-point selection method

5.5.1 | 14.3.4 | 14.3.4

Swiss cheese

switching boundary

Piecewise-smooth

switching time

15.2.3

symmetric systems

Symmetric to Symmetric

symmetric Turing machine

Lower

symmetry class

Solving

symplectic manifold

13.4.4

system

13. | Open-loop

determining whether controllable: 15.4.3 to 15.4.3.5
determining whether nonholonomic: 15.4.2 to 15.4.2.4
distribution: 15.4.2.2
simulator: 14.3.2 to Reverse-time

system vector fields

15.4.1

systematic search

2.2 to 2.2

tangent bundle

Vector | 13.2.1.2 | 15.4.2.2

tangent point

14.6.3.5

tangent space

Vector | Vector to Vector | 8.3.2 | 8.3.2 | 8.3.2 to 8.3.2 | Tangent

on a manifold: Tangent to Tangent

TangentBug

Tarski sentence

Tarski-Seidenberg Theorem

Taylor series

15.2.1.2 | 15.2.1.3 | 15.4.2.3 | 15.4.2.3 | 15.4.2.3 | 15.4.2.3

team theory

11.7.2

temporal difference

Temporal | Temporal to Temporal

temporal logic

termination action

2.3.2 | 11.1.3

THC

theory of computation

6.5.1

time scaling

7.1.3 | Trajectory

time-invariant

13.2.2

time-limited reachable set

14.2.1.2

time-monotonic path

time-optimal trajectory planning

14.6.3.5 to 14.6.3.5

time-varying motion planning

7.1 to 7.1.3

algebraic obstacle motion: Combinatorial
bounded speed: Bounded to Bounded
unbounded speed: 7.1.1 to Combinatorial

timing function

7.1.3

tire skidding

Tit-for-Tat

9.5.4

topological complexity

topological graph

Homeomorphism: | Homeomorphism: to Homeomorphism: | 14.2.2.1

topological property

14.6.2 | 15.4.3.4

topological space

4.1.1 | 4.1.1 to Homeomorphism:

connected: Connected | Connected
identification: Identifications to Identifications
metrizable: 5.1.1
path connected: Connected
simply connected: Simply | Simply

topologist's sine curve

Connected

torque

13.3.2.1 | 13.3.2.2 | 13.4.2.1

torus

2D | Higher | The | 4.4.2 | Two | A | Three

total differential

13.4.4 | 13.4.4 | 13.4.4 | 13.4.4

tower exponentiation

6.5.2

Towers of Hanoi

Exercises

trailers

13.1.2.4 to 13.1.2.4

trajectory

trajectory optimization

14.7 | 14.7 to 14.7

trajectory planning

Trajectory | Trajectory to Trajectory

path-constrained: 14.6.3 to 14.6.3.5

transcription

transfer mode

transfer path

transformations

2D chain: 3.3.1 to Homogeneous
2D rigid body: 3.2.2 to Combining
3D chain: 3.3.2 to The
3D rigid body: 3.2.3 to The
general concepts: 3.2.1 to Defining
kinematic tree: 3.4 to What
nonrigid: 3.5 to Flexible

transit path

transition configurations (mode change)

translating a disc

Translation

trapped on a surface

13.1.3.4 to 13.1.3.4

Traveling Salesman Problem

tray tilting

11.5.4 to 11.5.4 | 12.5.2

triangle fan

triangle inequality

5.1.1

triangle model

3D to 3D

triangle strip

triangular enumeration

14.2.2.3

triangulation

tricycle

trim trajectory

trivial operator

trivial topology

Turing machine

1.4.1 | 6.5.1

two-point boundary value problem

14.1.1 | 14.1.2.2 | 14.2.1 | 14.2.2.1 | 14.3 | Reverse-time | 14.3.3 | 14.3.3 | 14.3.3 | 14.3.3 | 14.3.3 | 14.3.3 | 14.3.3 | 14.3.3 | 14.3.4 | 14.3.4 | 14.3.4 | 14.3.4 | 14.3.4 | 14.3.4 | 14.3.4 | 14.3.4 | 14.4.1.1 | Searching | Backward | Backward | 14.4.3 | Tree-based | Tree-based | Tree-based | Tree-based | Sampling-based | 14.7 | 14.7 | 14.7 | 14.7 | 15. | 15. | Classical | 15.5

Type EE contact

A | 3D

Type EV contact

Computing | Computing | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | Exercises

Type FV contact

A | 3D

Type VE contact

Computing | Computing | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | 4.3.3 | Exercises | Exercises

Type VF contact

A | 3D

Udupa

uncertainty

brief overview: Overview to Uncertainty
due to partial predictability: Planning | 10.1 to Policy
due to sensing: Planning | 11. to 11.7.2 | 12. to Squeezing

underactuated system

13.1.2 | Underactuation | 14.2.2.1 | Underactuated to Underactuated

unicycle

13.1.2.3 to 13.1.2.3 | 13.2.4.1 to 13.2.4.3

uniform random

5.2.2

union-find algorithm

Grid | Generic

unique point

Algorithms

unit complex number

unit quaternions

Quaternions

unknot

unsupervised classification

9.2.4.1

unvisited states

2.2.1

upper envelope

9.3.3.2

upper value of a game

9.3.2 | 10.5.1.1 | Saddle

utility function

9.5.1.3 to 9.5.1.3

utility of money

9.5.1.3 to 9.5.1.3

utility theory

9.5.1 | 9.5.1.1 to 9.5.1.3

vacuum cleaning

value iteration

2.3.1 | 2.3.1

backward: 2.3.1.1 to 2.3.1.1
convergence issues: Convergence to Convergence
forward: 2.3.1.2 to 2.3.1.2
relative: Solutions
with interpolation: 8.5.2 to Continuous

van der Corput sequence

variation of a function

variety

4.4 | Varieties | Varieties to Varieties

for 2D chains: 4.4.2 to Three
for general linkages: 4.4.3 to 4.4.3

vector field

8.3.1 | Vector to Piecewise-smooth | Vector | Vector to Vector | 13.1.1.2

equilibrium point: Equilibrium
normalized: 8.4.1.1
over a cell complex: 8.4.2 to 8.4.2
piecewise-smooth: Piecewise-smooth to Piecewise-smooth

vector space

Vector | Vector | Vector to Vector

${\mathbb{R}}^n$ over ${\mathbb{R}}$: Vector
${\mathbb{R}}^n$ over ${\mathbb{R}}$: to Vector
of functions: Vector to Vector

velocity field

Vector | Vector to Vector

velocity-tuning method

7.1.3 to 7.1.3

vertex selection method

5.4.1 | 5.4.1 | 5.4.1 | 5.4.1 | 5.4.3 | Ariadne's | Expansive-space | Expansive-space | Random-walk | 5.5.1 | 5.5.1

vertical decomposition

6.2.2 to Algorithm | Singular to Singular | 7.1.3 | 7.1.3

3D: 6.3.3 to 6.3.3

violation-free state

14.1.3.1

virtual human

Virtual

VisBug

visibility polygon

12.2.2

visibility region

12.3.4

visibility roadmap

visibility sensor

Depth-mapping | 12.2.2

visibility skeleton

12.2.2

visibility-based pursuit-evasion

12.4 | 12.4.1 to 12.4.3

a sequence of hard problems: 12.4.1
complete algorithm: 12.4.2 to 12.4.2
problem formulation: 12.4.1 to 12.4.1
variations: 12.4.3 to 12.4.3

Voronoi diagram

Testing

Voronoi region

Testing | Low-discrepancy | Low-discrepancy | 5.3.3 | 5.3.3 | 5.3.3 | 5.3.3 | 5.3.3 | A

Voronoi vertex

wall clock

wall following

warping a path

wavefront

wavefront propagation

Wavefront to Wavefront | 8.5.2.3

wavelet

Euclidean

way point

8.4.3

weak backprojection

Backprojections | Backprojections | 10.6.1 | Backprojections | Backprojections

weighted-region problem