A hybrid constraint-penalty proxy method for six degree-of-freedom haptic display of deforming objects

There are many applications and tasks in which the precise, high-fidelity haptic display of deforming objects is required. A crucial element in haptic rendering is the definition of a proxy pose that follows the motion of the user, while respecting the geometry of the object being displayed. Conventional methods for computing the dynamics of a proxy interacting with a deforming object suffer from several issues relating to numerical instabilities when the proxy becomes over-constrained and high computational demands. This paper presents a novel hybrid proxy that combines modified versions of constraint-based and penalty-based proxies together to give high fidelity rendering with reduced computational requirements and enhanced robustness to situations where the proxy becomes enclosed. Experimental analysis of the proposed method shows that it can efficiently compute proxy dynamics that faithfully render the required object. This research forms a basis for further development of novel hybrid dynamic proxies for haptics and allows for increasingly complex deforming geometries to be rendered.