Configuration-based optimization for six degree-of-freedom haptic rendering for fine manipulation

Six-degree-of-freedom (6-DOF) haptic rendering for fine manipulation in narrow space is a challenging topic because of frequent constraint changes caused by small tool movement and the requirement to preserve the feel of fine-features of objects. In this paper, we introduce a configuration-based constrained optimization method for solving this rendering problem. We represent an object using a hierarchy of spheres, i.e., a sphere tree, which allows faster detection of multiple contacts/collisions among objects than polygonal mesh and facilitates contact constraint formulation. 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. The constraints in the 6D configuration space of the graphic tool is obtained and updated through online mapping of the nonpenetration constraint between the spheres of the graphic tool and those of the other objects in the three-dimensional physical space, based on the result of collision detection. This problem is further modeled as a quadratic programming optimization and solved by the classic active-set methods. Our algorithm has been implemented and interfaced with a 6-DOF Phantom Premium 3.0. We demonstrate its performance in several benchmarks involving complex, multiregion contacts. The experimental results show both the high efficiency and stability of haptic rendering by our method for complex scenarios. Nonpenetration between the graphic tool and the object is maintained under frequent contact switches. Update rate of the simulation loop including optimization and constraint identification is maintained at about 1 kHz.