Most of the book so far has been concerned with kinematics, dynamics, motion planning, and control of the robot itself. Only in Chapter 11, on the topics of force control and impedance control, did the robot finally begin interacting with an environment other than free space. Now the robot really becomes valuable – when it can perform useful work on objects in the environment.

In this chapter our focus moves outward from the robot itself to the interaction between the robot and its environment. The desired behavior of the robot hand or end-effector, whether motion control, force control, hybrid motion–force control, or impedance control, is assumed to be achieved perfectly using the methods discussed so far. Our focus now is on the contact interface between the robot and objects as well as on contacts among objects and between objects and constraints in the environment. In short, our focus is on manipulation rather than the manipulator. Examples of manipulation include grasping, pushing, rolling, throwing, catching, tapping, etc. To limit our scope, we will assume that the manipulator, objects, and obstacles in the environment are rigid.

To simulate, plan, and control robotic manipulation tasks, we need an understanding of (at least) three elements: contact kinematics; forces applied through contacts; and the dynamics of rigid bodies. In contact kinematics we study how rigid bodies can move relative to each other without penetration and classify these feasible motions according to whether the contacts are rolling, sliding, or separating. Contact force models address the normal and frictional forces that can be transmitted through rolling and sliding contacts. Finally, the actual motions of the bodies are those that simultaneously satisfy the kinematic constraints, contact force model, and rigid-body dynamics.

This chapter introduces contact kinematics (Section 12.1) and contact force modeling (Section 12.2) and applies these models to problems in robot grasping and other types of manipulation.

The following definitions from linear algebra will be useful in this chapter.