## Book Chapter: Chapter 13

Wheeled Mobile Robots

#### Chapter 13 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.

#### 13.1. Wheeled Mobile Robots

This video introduces Chapter 13 of “Modern Robotics” on wheeled mobile robots. This chapter covers kinematic modeling of omnidirectional and nonholonomic wheeled robots, motion planning for nonholonomic robots, feedback control, odometry, and mobile manipulation: feedback control of the end-effector of a mobile robot equipped with a robot arm.

#### 13.2. Omnidirectional Wheeled Mobile Robots (Part 1 of 2)

This video derives the kinematics, relating the chassis velocity to wheel speeds, for omnidirectional wheeled mobile robots employing mecanum or omniwheels.

#### 13.2. Omnidirectional Wheeled Mobile Robots (Part 2 of 2)

This video introduces feedback control for an omnidirectional wheeled mobile robot, as well as the constraints on the chassis twist resulting from limits on the wheels’ speeds.

#### 13.3.1. Modeling of Nonholonomic Wheeled Mobile Robots

This video introduces kinematic modeling of nonholonomic wheeled mobile robots and a single canonical model for car-like, diff-drive, and unicycle robots.

#### 13.3.2. Controllability of Wheeled Mobile Robots (Part 1 of 4)

This video introduces the concept of linear controllability for a control system. The canonical nonholonomic wheeled mobile robot does not satisfy linear controllability, which motivates concepts in nonlinear controllability in the next video.

#### 13.3.2. Controllability of Wheeled Mobile Robots (Part 2 of 4)

This video introduces the nonlinear controllability concepts of small-time local accessibility and small-time local controllability, which are used to describe nonholonomic mobile robots.

#### 13.3.2. Controllability of Wheeled Mobile Robots (Part 3 of 4)

This video introduces the Lie bracket describing the noncommutativity of two vector fields. The Lie bracket plays a key role in the controllability analysis of nonlinear systems.

#### 13.3.2. Controllability of Wheeled Mobile Robots (Part 4 of 4)

This video introduces the Lie Algebra Rank Condition, a test of the iterated Lie brackets of the control vector fields of a nonlinear control system, and its use in establishing small-time local accessibility and small-time local controllability. The LARC is applied to example nonholonomic mobile robots.

#### 13.3.3. Motion Planning for Nonholonomic Mobile Robots

This video introduces shortest paths for forward-only cars (“Dubins curves”) and for cars with a reverse gear (“Reeds-Shepp curves”). It also shows how Reeds-Shepp curves can be used for motion planning among obstacles.

#### 13.3.4. Feedback Control for Nonholonomic Mobile Robots

This video introduces feedback stabilization of a planned trajectory for a nonholonomic wheeled mobile robot.

#### 13.4. Odometry

This video introduces odometry for omnidirectional and nonholonomic wheeled mobile robots: estimating the motion of the robot’s chassis from the wheel motions.

#### 13.5. Mobile Manipulation

This video describes mobile manipulation: feedback control of the end-effector of a mobile robot equipped with a robot arm.