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首页> 外文会议>Haptics Symposium, 2010 >A higher order polynomial reproducing radial basis function neural network (HOPR-RBFN) for real-time interactive simulations of nonlinear deformable bodies with haptic feedback
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A higher order polynomial reproducing radial basis function neural network (HOPR-RBFN) for real-time interactive simulations of nonlinear deformable bodies with haptic feedback

机译：高阶多项式再现径向基函数神经网络（HOPR-RBFN），用于带触觉反馈的非线性可变形体的实时交互式仿真

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摘要

Interactive simulation of nonlinear deformable bodies with haptic feedback is particularly challenging as the corresponding coupled nonlinear equations must be solved at a high rate of 1 kHz. With increasing demand on the complexity of the models and scenarios that must be simulated to develop interactive applications such as surgical simulators, and given the current state of hardware, a nai¿ve solution strategy based on iterative finite element algorithms is not feasible. However, much advantage may be gained if the deformation response of the computational models may be characterized a priori and a radial basis function neural network (RBFN) is trained based upon this data. Once trained, the RBFN may be used during real time computations to calculate deformation fields and reaction forces with minimal computational cost. However, traditional RBFNs have zeroth order polynomial accuracy, implying that they cannot recreate polynomial fields. Since the error in the RBFN approximation is governed by the highest order of the polynomial that the approximant can reproduce, we have developed and successfully tested a higher order polynomial reproducing RBFN (HOPR-RBFN) which, compared to traditional RBFN, reduces the approximation error significantly and allows much fewer neurons to be used for comparable accuracy. Results are provided for realistic surgical scenarios with hyperelastic (neo-Hookean) material models within a fully nonlinear large deformation simulation framework.
机译：具有触觉反馈的非线性可变形体的交互式仿真特别具有挑战性，因为必须以1 kHz的高速率求解相应的耦合非线性方程。随着对模型和方案的复杂性的需求日益增加，必须开发模型和方案以开发交互式应用程序（例如手术模拟器），并且鉴于硬件的当前状态，基于迭代有限元算法的简单解决方案是不可行的。但是，如果可以先验地表征计算模型的变形响应，并基于此数据训练径向基函数神经网络（RBFN），则可以获得很多优势。一旦经过训练，RBFN可以在实时计算过程中用于以最小的计算成本来计算变形场和反作用力。但是，传统的RBFN具有零阶多项式精度，这意味着它们无法重新创建多项式字段。由于RBFN近似中的误差由近似值可以重现的多项式的最高阶决定，因此我们开发并成功测试了高阶多项式重现RBFN（HOPR-RBFN），与传统的RBFN相比，RBFN降低了近似误差显着提高了效率，并允许使用更少的神经元以达到可比的准确性。在完全非线性的大变形模拟框架内，使用超弹性（新胡克）材料模型为现实的手术场景提供了结果。

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