Robotic manipulators use contact forces to grasp and manipulate objects in their environments. Fixtures rely on contacts to immobilize workpieces. Mobile robots and humanoids use wheels or feet to generate the contact forces that allow them to locomote. Modeling of the contact interface, therefore, is fundamental to analysis, design, planning, and control of many robotic tasks.

This chapter presents an overview of the modeling of contact interfaces, with a particular focus on their use in manipulation tasks, including graspless or nonprehensile manipulation modes such as pushing. Analysis and design of grasps and fixtures also depends on contact modeling, and these are discussed in more detail in Chap. 38. Sections 37.2–37.5 focus on rigid-body models of contact. Section 37.2 describes the kinematic constraints caused by contact, and Sect. 37.3 describes the contact forces that may arise with Coulomb friction. Section 37.4 provides examples of analysis of multicontact manipulation tasks with rigid bodies and Coulomb friction. Section 37.5 extends the analysis to manipulation by pushing. Section 37.6 introduces modeling of contact interfaces, kinematic duality, and pressure distribution and soft contact interface. Section 37.7 describes the concept of the friction limit surface and illustrates it with an example demonstrating the construction of a limit surface for a soft contact. Finally, Sect. 37.8 discusses how these more accurate models can be used in fixture analysis and design.