Haptic rendering often deals with interactions between stiff objects. A traditional way of force computing models the interaction using a spring-damper system, which suffers from stability issues when the desired stiffness is high. Instead of computing a force, this paper continues to explore shifting the focus to rendering an interaction with no penetration, which can be accomplished by using a position controller in the joint space using the encoders as feedback directly. In order to make this approach easily adaptable to any device, an alternative way to model the dynamics of the device is also presented, which is to linearize a detailed simulation model. As a family of linearized models is used to approximate the full dynamic model of the system, it is important to have a smooth transition between multiple sets of controller gains generated based on these models. Gain scheduling is introduced to improve the performance in certain areas and a comparison among three controllers is conducted in a simulation setup.

触觉渲染通常处理刚性对象之间的交互。传统的力计算方法使用弹簧-阻尼器系统对相互作用进行建模，当所需刚度很高时，该系统会出现稳定性问题。本文没有计算力，而是继续探索将焦点转移到渲染无穿透的交互，这可以通过在关节空间中使用位置控制器直接使用编码器作为反馈来实现。为了使这种方法易于适用于任何设备，还介绍了一种对设备动态进行建模的替代方法，即对详细的仿真模型进行线性化。由于使用一系列线性化模型来近似系统的完整动态模型，在基于这些模型生成的多组控制器增益之间进行平滑过渡非常重要。引入增益调度以提高某些领域的性能，并在模拟设置中对三个控制器进行比较。