## Archives: Book Pages

This is the book page

#### Introduction Autoplay

Autoplay of the YouTube playlist for all videos in this chapter.  This description box will not be updated with information about each video as the videos advance.

#### Introduction to the Lightboard

This video introduces the Lightboard, a convenient tool that was used to generate the videos for “Modern Robotics.”

#### Acknowledgments

Thanks to the people who helped make the “Modern Robotics” videos possible, particularly my wife Yuko and my kids Erin and Patrick for putting up with some late nights.

#### Chapter 2 Autoplay

Autoplay of the YouTube playlist for all videos in this chapter.  This description box will not be updated with information about each video as the videos advance.

#### Foundations of Robot Motion

This video introduces chapters 2 and 3 on configuration space, degrees of freedom, and rigid-body motions.

#### 2.1. Degrees of Freedom of a Rigid Body

This video introduces the concepts of configuration, configuration space (C-space), and degrees of freedom, and describes a method for counting the degrees of freedom of a rigid-body in n dimensions.

#### 2.2. Degrees of Freedom of a Robot

This video describes common robot joints and derives Grubler’s formula for calculating the degrees of freedom of a mechanism.

#### 2.3.1. Configuration Space Topology

This video introduces basic concepts in topology as applied to configuration spaces.

#### 2.3.2. Configuration Space Representation

This video introduces representations of manifolds using minimum-coordinate explicit parametrizations and implicit representations, where the manifold is viewed as a surface embedded in a higher-dimensional space.

#### 2.4. Configuration and Velocity Constraints

This video introduces holonomic configuration constraints, nonholonomic velocity constraints, and Pfaffian constraints.

#### 2.5. Task Space and Workspace

This video introduces the task space, the space in which the robot’s task can most naturally be expressed, and the workspace, a characterization of the reachable configurations of the end-effector.

#### Chapter 3 Autoplay

Autoplay of the YouTube playlist for all videos in this chapter.  This description box will not be updated with information about each video as the videos advance.

#### Introduction to Rigid-Body Motions

This video introduces rotation about an axis by the right-hand rule and right-handed frames, including the body frame and the space frame.

#### 3.2.1. Rotation Matrices (Part 1 of 2)

This video introduces the space of rotation matrices SO(3), a Lie group, and properties of rotation matrices.

#### 3.2.1. Rotation Matrices (Part 2 of 2)

This video introduces three common uses of rotation matrices: representing an orientation, changing the frame of reference of a vector or a frame, and rotating a vector or a frame.

#### 3.2.2. Angular Velocities

This video introduces 3-vector angular velocities and the space of 3×3 skew-symmetric matrices called so(3), the Lie algebra of the Lie group SO(3). Any 3-vector angular velocity has a corresponding so(3) representation.

#### 3.2.3. Exponential Coordinates of Rotation (Part 1 of 2)

This video introduces the 3-vector exponential coordinates of rotation and the matrix exponential using the so(3) representation of exponential coordinates.

#### 3.2.3. Exponential Coordinates of Rotation (Part 2 of 2)

This video describes how the solution of a vector linear differential equation calculates the rotation achieved after rotating a given time at a constant angular velocity. The matrix exponential maps the so(3) matrix representation of the 3-vector of exponential coordinates of rotation to a rotation matrix in SO(3), and the matrix logarithm maps a rotation

#### 3.3.1. Homogeneous Transformation Matrices

This video introduces the 4×4 homogeneous transformation matrix representation of a rigid-body configuration and the special Euclidean group SE(3), the space of all transformation matrices. It also introduces three common uses of transformation matrices: representing a rigid-body configuration, changing the frame of reference of a frame or a vector, and displacing a frame or a

#### 3.3.2. Twists (Part 1 of 2)

This video introduces the 6-vector twist, a representation of the linear and angular velocity of a rigid body. A twist can be represented as a normalized screw axis, a representation of the direction of the motion, multiplied by a scalar speed along the screw axis. A screw axis or twist can be represented in any