Index

for reinforcement learning: Value to Value
for sequential games: Value to Value
on a nondeterministic I-space: Value to Value
on a probabilistic I-space: Approximate to Exact
path-constrained: 14.6.3.4 to 14.6.3.4
running time: 2.3.1.1
under differential constraints: 14.5.2 to 14.5.2
with average cost-per-stage: Solutions to Solutions
with discounted cost: Value to Value
with nature and continuous spaces: 10.6.1 to 10.6.1
with nondeterministic uncertainty: Nondeterministic to Nondeterministic | Convergence to Using
with probabilistic uncertainty: Probabilistic to Using

bad bracket

15.4.3.5

Balkcom-Mason curves

15.3.3 | 15.3.3 to 15.3.3

Balkcom-Mason drive

15.3.3

Balkcom-Mason metric

15.3.3

bang-bang approach

14.6.3.5 | 14.6.3.5 to 14.6.3.5

Barraquand-Latombe nonholonomic planner

14.4.2 to Backward

base point (on a manifold)

15.4.2.2

base point of a path

The

basis

Vector

of open sets: Some

Basu-Pollack-Roy roadmap algorithm

6.4.3

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

11.7.1

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

Critical

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

The

bond length

The

Borel sets

5.1.3 | 5.1.3

boundary grid point

Discretization

boundary of a set

Special

boundary point

Special

boundary representation

3.1

boundary sensors

Boundary to Boundary

bounded set

Homeomorphism:

bounded-acceleration model

8.4.4.2

bounded-velocity model

8.4.4.2

Boustrophedon decomposition

Boustrophedon to Spanning

Brachistochrone curve

13.4.1.1

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

Designing | Designing

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

The

candidate Lyapunov function

Determining

Candorcet paradox

9.5.1.2

Canny

6.4.3

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

The

Cartesian product

Cartesian

carton folding

Carton to Carton

causal links

2.5.1

CBHD formula

The

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

Critical

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

12.4.2

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

15.4.2.2

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

14.7

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

Coordinates

competitive ratio

Landmark | Competitive | Competitive to Competitive

complementary pair

2.4.1

complete exclusion axiom

2.5.3

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

Languages

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

7.3.1

computational algebraic geometry

6.4 to 6.4.3

Conchoid of Nicomedes

Critical | Exercises

conditional Bayes' risk

Optimal

conditional Bayes' rule

Conditional

conditional expectation

Expectation

conditional independence

Conditional

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

5.6.2

conservative approximations

11.4.3.2 | Conservative to Conservative

conservative system

13.4.1.2

constant vector field

Vector

constant-sum game

Exercises

contaminated region

12.4.2

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

The

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

Further

coordinate neighborhood

Coordinates

coordinates

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

8.5.2.1

critical curves

Critical

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

13.4.1.1

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

2.5.3

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

Conditional

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

Drug

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

Further

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

11.1.1 to 11.1.1

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

7.3.1

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

General to General

Euclidean norm

Euclidean shortest paths

Euclidean to Euclidean

Euler angles

Further

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

The

exponential map

The to The

exponentially stable system

Asymptotic

EXPTIME

Languages

extended Kalman filter

11.6.1 | Continuous

extended system

15.5.1

exterior point

Special

extremal function

13.4.1.1

falling particle

13.4.1.2 to 13.4.1.2

fast Fourier transforms

Handling

Faure sequence

Low-discrepancy

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

15.4.2.2

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

The

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

2.5.3

Fraunhofer Chalmers Centre

Sealing | Sealing

Frazzoli

14.2.3 | 14.2.3

free space

Obstacle

free variables

Tarski

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

13.4.1.1

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

Landmark

general linear group

Matrix

general position

General | General to General | Critical

generalized coordinates

13.4.1.2

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