A Parallel Computing Platform for Real-Time Haptic Interaction with Deformable Bodies

Abstract

Real-time simulation of haptic interaction with deformable objects is computationally demanding. In particular in finite-element (FE) based analysis of such interactions, a large system of equations must be solved at an update rate of 100-1,000 Hz for simulation fidelity and stability. A new hardware-based parallel implementation of a Preconditioned Conjugate Gradient (PCG) algorithm is proposed for solving the linear systems of equations arising from FE-based deformation models. Concurrent utilization of a large number of fixed-point computing units on a Field-Programmable Gate Array (FPGA) device yields a very fast solution to these equations. Quantization and overflow errors in the fixed-point implementation of the iterative solver are minimized through dynamic scaling and preconditioning. Numerical accuracy of the solution, the architecture design, and issues pertaining to the degree of parallelism and scalability of the architecture are discussed in detail. The implementation of the solver on an Altera EP3SE110 FPGA device has enabled real-time simulation of three-dimensional linear elastic deformation models with 1,500 nodes at an update rate of up to 2,500 Hz.

A Multiple-FPGA parallel computing architecture for real-time simulation of soft-object deformation

“…This quad-FPGA system has enabled real-time simulation of haptic interaction with a 3D FE model of 6000 nodes (∼21000 elements) at update rate of 400Hz. Using the same FPGAs, the quad-FPGA architecture in this article results in an 8.4 fold increase in the number of arithmetic operations per second compared to the single-FPGA design in Mafi et al [2009], and a 2.6-fold increase compared to the earlier quad-FPGA design in Mahdavikhah et al [2010].…”

“…Iterative methods are also more suitable for hardware-based parallelization [Karniadakis and Kirby 2003]. It should be noted that in deformation analysis even with linear elastic models the matrix K would change depending on the contact node, that is, the node at which the object is subject to external forces [Mafi et al 2009]. Moreover, nonlinear FE modeling of deformation can lead to a matrix K which would be dependent on the deformation u.…”

“…The computing architecture presented in this article improves on our earlier design in Mafi et al [2009] by allowing for multiple FPGAs to concurrently solve the system of equations in FE-based deformation models. To this end, the design attempts to balance the load among the FPGAs and maximize parallelism by minimizing communication, computation, and data overhead.…”

“…That design can process larger FE meshes compared with the one in Mafi et al [2009] but its resource requirements per FPGA grow linearly by the number of the FPGAs. In this article we propose a new vector storage format that will substantially reduce memory usage in the multiple FPGA architecture.…”

Haptic Simulation of Organ Deformation and Hybrid Contacts in Dental Operations

“…S IX-DOF haptic rendering for deformable objects is an important topic that has many potential applications such as in virtual prototyping, surgical simulator for virtual training, and games [1], [2], [3], [4], [5], [6]. For example, as shown in Fig.…”