Transparent Rendering of Tool Contact with Compliant Environments

Transparent haptic rendering of the contact between a tool and its environment requires very frequent update of the contact forces acting on the tool. Given a rigid tool and a deformable environment, we define contact constraints by solving a constrained dynamic simulation problem, typically at a low update rate. A generalized contact Jacobian defines velocities at the constraints given the velocity of the rigid tool. We define an inverse of the contact Jacobian that is dynamically consistent with the constraints and, once we know other forces acting on the rigid tool, it allows a fast update of the accumulated contact forces, and thereby highly transparent rendering