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.

## Book Chapter: Chapter 12

Grasping and Manipulation

This video introduces Chapter 12 of “Modern Robotics” on grasping and other types of manipulation. Examples of non-grasping (nonprehensile) manipulation include pushing, carrying a tray of glasses, vibratory transport, and the meter-stick trick. Such manipulation tasks are analyzed based on contact kinematics, contact forces, and rigid-body dynamics. This video also introduces the definitions of the

This video introduces contact kinematics, the study of the feasible motions of bodies in contact. The analysis is first-order, meaning it considers the contact locations and the contact normal directions, but not the local contact curvature.

This video introduces contact labels for first-order contact kinematics, which indicate whether a particular contact is sliding, rolling (sticking), or breaking free given the relative twist between the two bodies.

This video introduces the contact mode for a given relative twist between two bodies in contact. The contact mode specifies the contact label at each of the contacts as sliding (S), rolling (R), or breaking free (B).

This video demonstrates how a polyhedral convex cone of planar twists (velocities of a rigid body restricted to the plane) can be represented as a set of centers of rotation (CoRs).

This video describes how to represent the feasible twist cone of a planar rigid body subject to stationary contacts as a set of centers of rotation (CoRs). It also describes how to associate a contact mode (describing whether the individual contacts are sliding, rolling, or breaking free) with each CoR.

This video introduces the conditions for form closure, which occurs when a set of stationary contacts completely kinematically constrains a rigid body. Specifically, this video focuses on first-order form closure, which can be established based only on the contact locations and the contact normals, without considering the contact curvature. The conditions are expressed as a

This video introduces dry Coulomb friction, where the friction force resisting sliding motion at a contact is proportional to the normal force. The constant of proportionality is the friction coefficient. The set of forces that can be applied through a frictional contact can be interpreted as a friction cone, which can also be represented as

This video shows how the positive span of a set of planar wrenches (a wrench cone) can be represented graphically by labeling all points in the plane according to their moment labels: +, -, +/-, or no label. The label + indicates that the wrenches cannot make negative moment about the point, the label –

This video introduces the conditions for force closure (or a force closure grasp), which occurs when a set of frictional contacts on a rigid body can generate an arbitrary wrench to counteract a disturbance wrench. The conditions are expressed as a linear program for the general case as well as graphically for the planar case.

This video describes the duality of force and motion freedoms in rigid-body contact with friction. A contact with a rigid body provides the same total number of equality constraints on force and motion regardless of the contact label (sliding, rolling, or breaking contact). Rolling contacts provide the most motion equality constraints and fewest force equality

This video describes the analysis of manipulation tasks as finding contact modes and velocities or accelerations consistent with the contact kinematics, Coulomb friction model, and rigid-body dynamics. For quasistatic tasks, the contact forces balance external forces, such as gravity. The approach is demonstrated using the meter-stick trick.

This video shows how to test whether a given assembly of rigid bodies in frictional contact can stay assembled in the presence of gravity and inertial forces.