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.

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

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.

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.

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.

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.

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.

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

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

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