Multirate Haptic Rendering Using Local Stiffness Matrix for Stable and Transparent Simulation Involving Interaction with Deformable Objects

Abstract

Simulation involving interaction with deformable objects often causes stability problems because a slowly updated force generates additional energy to the human user. This paper proposes a stable and transparent haptic rendering for simulation involving interaction between a rigid tool and deformable objects. This method computes visual and haptic feedback in the simulation and haptic feedback loops, respectively. A local stiffness matrix consisting of points around contact points is constructed based on collision detection between a virtual tool and a deformable object in the simulation loop. The haptic feedback is then computed at a higher update rate in the haptic feedback loop using the local stiffness matrix. Equivalent springs computed by using the equivalent stiffness energy are added to the boundary of the local stiffness matrix to minimize errors in the rendered force. The proposed method is compared with the virtual coupling widely used in simulation involving interaction with deformable objects. The proposed method reduces the x-, y-, and z-axis maximum force errors by up to 52%, 80%, and 70%, respectively, compared to the virtual coupling in the simulation involving interaction with the Stanford bunny object consisting of 2087 points and 9997 tetrahedrons.