# The Application of an Impedance-Passivity Controller in Haptic Stability Analysis
## 1 Introduction  
Haptic-based virtual reality (VR) [1] technology has become an active research area because of the realization of real interaction between humans and computers. The literature includes versatile haptic rendering systems and applications. Typically, new-generation haptic-based VR systems have more benefits than traditional training methods do; for example, they can provide vivid perceptual awareness and immersive experiences through methods that include real-time frameworks for haptic tracking [2, 3] and advanced haptic interfaces [4, 5, 6]. For real-time haptic VR applications, haptic rendering requires both fidelity and stability. Educational training is an area of particular interest in the development of virtual simulation systems such as stable robust haptic interaction [7, 8], haptic-based augmented reality (AR) systems [9, 10], haptic force feedback interfaces for needle insertion training systems [11], and teleoperated haptic robotic systems [12, 13, 14] because of their low costs and low risks. Haptic feedback interfaces connect the operator to the simulator and enable the operator to perform a designated interaction procedure between the virtual objects and tools composing the virtual environment.  
Tactile instability can be caused by several factors, such as quantization and delays [15]. A disturbance observer approach is typically used to improve the performance of haptic motions [16, 17]. Although many objects in real life have relatively high stiffness, they are limited in most haptic simulation environments, and their stiffness must be substantially reduced to ensure the haptic stability of haptic VR systems. Therefore, to solve the energy dissipation problem in haptic simulations, several control methods have been proposed. On the basis of passive analysis, virtual coupling can be applied to change the simulationenvironment to ensure system stability [18; 19; 20]. In addition, time-domain passivity control can be implemented by monitoring system energy to provide necessary compensation for ensuring system passivity [21; 22; 23]. In a haptic simulation system, the virtual environment (VE) module may engender active behavior with negative damping, which can cause unstable oscillations in the haptic device. Here, stability is defined as the ability of a haptic stylus to remain on a surface with convergent oscillation behavior during interaction with virtual objects.  
Accordingly, this paper proposes a stable haptic simulation development scheme for modules on the basis of deformable simulation technology, haptic feedback technology, and information technology. To alleviate the oscillation and divergence effects caused by negative damping coefficients and high spring constants, the stability of haptic feedback is considered. An impedance-passivity controller (IPC) is derived to improve haptic display performance. Compared with general time-domain passivity controllers, the control approach proposed here can provide improved stabilization performance in cases of negative damping coefficients and high stiffness constants. Finally, a haptic-based training platform is developed for economical and simple implementation using general-purpose personal computers. All proposed approaches are packaged, implemented, and tested here. At the end, a haptic paradigm-based simulation platform with haptic feedback was successfully developed and tested for passive impedance stability.  
The rest of this paper is organized as follows: Section 2 provides an overview of the system framework. The planning and design of the IPC are described in Section 3. Section 4 presents the experimental system and integration test of haptic stability. Section 5 presents the experimental results for stable haptic rendering. Finally, conclusions are drawn in Section 6.