中文摘要：

目的 在进行虚拟乐器交互演奏时,需要模拟触力觉-视觉-听觉多通道同步反馈,其中触力觉反馈的难点在于模拟人手操作乐器的六自由度（6-DoF）力觉交互过程.方法 提出一种基于混合模型和单边约束优化的六自由度力觉合成方法,实现了虚拟人手和琴弦的多点多区域接触力觉模拟.虚拟人手采用层次化球树模型表达,古琴采用混合模型表达,其中琴体和琴弦分别采用层次化球树模型和直线解析模型.提出了基于混合模型的离散碰撞检测算法,实时检测虚拟手和琴弦是否产生碰撞;基于发生碰撞的几何元素对建立单边不可穿透约束方程,通过ActiveSet方法求解约束优化后方程,获得6维位姿变量保证图形显示场景中的虚拟手不会和琴弦产生穿透.为模拟琴弦变形,提出变直径的圆柱体模型来模拟琴弦在不同振动幅度下的动力学响应;提出交互状态敏感的力计算模型以刻画人手在弹奏不同状态琴弦（静态、振动态）的力觉感受差异.结果 基于力觉交互设备Phantom Premium3.0建立了实验平台,实验结果表明,本文算法可以模拟单点、多点等不同接触状态,并能模拟6维力和力矩,操作者可以感受到琴弦振动时的细腻力感觉,力觉交互过程稳定,算法计算效率在1 kHz以上.结论 算法可模拟针对琴弦一类的超薄形状物体的多点接触力觉交互过程,算法计算效率高,包含碰撞检测、约束优化、琴弦变形仿真等计算回路的更新频率也能达到要求,该混合模型能为后续复杂形状物体的碰撞响应研究提供思路.

英文摘要：

Objective Synchronous haptic-visual-audio multi-sensory feedback should be rendered to realize an interactive simulation of music instrument playing. Method For the haptic feedback, a 6-DoF haptic rendering of multi-region contacts between a rigid hand and the surface of the instrument is a fundamental requirement. In this study, we proposed a hybrid model to simulate the various parts of the instrument through collision response, i. e. , analytic model for the thin-sized components （i. e. , a line segment） and a sphere-tree for the other parts. We proposed a discrete collision detection method to detect the collision pairs between the sphere-tree of the virtual hand and the analytic model of the strings. A model based on constraint optimization is solved by using an active set method to obtain the non-penetrated configuration of the held hand. To simulate string deformation, a cylindrical volume with variable diameters is defined with the response to the realtime interaction force applied by the hand. Different force feelings can be rendered to reflect hand collision with a static or vibrating string. Result Experimental results based on Phantom Premium 3.0 illustrated that the proposed method could simulate single-and multi-region contacts between the virtual hand and the strings. Six-dimensional force and torque can be stably simulated. Users can sense the subtle feeling of coming in contact with a vibrating string. Conclusion This study performs several multi-region contact instances with the use of a discrete collision detection method. No penetration occurs in these instances, and the stacked frequency is above 1 kHz in the loop circuit of collision detection, constraint optimiza- tion, and deformation simulation. The penalty-method may cause a distinct torque jump because of the transformation of contact position and normal, thus causing a discrepancy between force feeling and visual feeling. The proposed constraint optimization-based method can improve computational precision.