Contact Modes and Complementary Cones

In this paper, we use a linear complementarity problem (LCP) formulation of rigid body dynamics with unilateral contacts to obtain definitions for contact modes. We show how the complementary cones of the LCP correspond to each of the intuitive contact modes: slide right, slide left, roll and separate. These complementary cones allow us to make rigorous definitions for contact modes in three-dimensional systems, where our intuitive understanding fails.

Authors

• Stephen Berard
• Kevin Egan
• Jeffrey C. Trinkle

Keywords

• Jacobian matrices
• Computer science
• Acceleration
• Robots
• Mathematical model
• Differential equations
• Kinematics
• Rigid Body
• Linear Problem
• Three-dimensional System
• Rigid Body Dynamics
• Electrostatic Interactions
• Dynamic Model
• Rolling
• Model Formulation
• Friction Coefficient
• Structural Inequalities
• Friction Force
• Jacobian Matrix
• Contact Force
• Normal Component
• Linear Inequalities
• Slack Variables
• Complementary Pairing
• Model Instances
• Static Friction
• Friction Model
• Feasible Modality
• Convex Cone
• Degenerate Case
• Static Friction Coefficient
• Polytope
• Tangential Components
• Static Objects