Accelerating optimization-based haptic rendering by parallel quadratic programming method

It is a challenging problem to achieve fast and realistic six degree-of-freedom (DOF) haptic simulation of scenarios involving large number of multi-region contacts. In this paper, we propose an optimization-based constrained method enhanced by parallel quadratic programming to solve the rendering problem. Hierarchical sphere-tree models are used to represent the moving haptic tool and its surrounding static objects. Given a moving graphic tool as the avatar of the haptic tool in the virtual environment, we compute its quasi-static motion by solving a configuration-based optimization. Instead of using traditional active-set method, we transform the original optimization problem into its dual problem and solve the optimum about the graphic tool using a parallel quadratic programming method. Our algorithm has been implemented with a 6-DoF Phantom Premium 3.0. We validate the proposed algorithm in several benchmarks involving complex, large-region contacts. The results demonstrate that the proposed method can achieve a two to three times speed improvement than the active-set method. A further speed-up for haptic rendering may be achieved by the parallel implementation on parallel processor such as graphic processing units.