Haptic Assembly Using Skeletal Densities and Fourier Transforms

TL;DR

This paper introduces a novel Fourier transform-based method to efficiently compute geometric constraints for haptic virtual assembly, enabling real-time interaction with complex shapes.

Contribution

It presents a new approach using skeletal densities and Fourier transforms to automatically generate energy fields for geometric guidance in haptic assembly.

Findings

Efficient computation of constraint forces using FFT on GPU.

Effective handling of complex, arbitrary-shaped objects in virtual assembly.

Improved real-time performance for haptic feedback at 1 kHz rate.

Abstract

Haptic-assisted virtual assembly and prototyping has seen significant attention over the past two decades. However, in spite of the appealing prospects, its adoption has been slower than expected. We identify the main roadblocks as the inherent geometric complexities faced when assembling objects of arbitrary shape, and the computation time limitation imposed by the notorious 1 kHz haptic refresh rate. We addressed the first problem in a recent work by introducing a generic energy model for geometric guidance and constraints between features of arbitrary shape. In the present work, we address the second challenge by leveraging Fourier transforms to compute the constraint forces and torques. Our new concept of 'geometric energy' field is computed automatically from a cross-correlation of 'skeletal densities' in the frequency domain, and serves as a generalization of the manually specified virtual fixtures or heuristically identified mating constraints proposed in the literature. The formulation of the energy field as a convolution enables efficient computation using fast Fourier transforms (FFT) on the graphics processing unit (GPU). We show that our method is effective for low-clearance assembly of objects of arbitrary geometric and syntactic complexity.