Haptic rendering and interactive simulation using passive midpoint integration

Abstract

We propose a novel framework of haptic rendering and interactive simulation, which, by exploiting midpoint time integration, that is known for its superior energy-conserving property but has not yet been adopted for haptics and interactive simulation, can enforce discrete-time passivity of the simulation effectively in practice, while retaining real-time interactivity due to its being non-iterative. We derive this passive midpoint integration (PMI) simulation for mechanical systems both in maximal coordinates (i.e. in SE(3)) and in generalized coordinates (i.e. in[Formula: see text] ), with some potential actions as well to implement joint articulation, constraints, compliance, and so on. We also fully incorporate multi-point Coulomb frictional contact into them via the PMI-LCP (linear complementarity problem) formulation. The proposed PMI-based simulation framework is applied to some illustrative examples to demonstrate its advantages: (1) haptic rendering of a peg-in-hole task, where very light/stiff articulated objects can be simulated with multi-point contact; (2) haptic interaction with a flexible beam, where marginally stable/lossless behavior (i.e. vibration) can be stably emulated; and (3) under-actuated tendon-driven hand grasping, where mixed maximal-generalized coordinates are used with very light/stiff fingers.