## 2 Related Work
### Haptic and Vestibular Feedback Systems in VR for Wheelchair Users  
In the realm of VR for users with disabilities, particularly those who use wheelchairs, there have been significant strides. Early work in this field focused primarily on visual and auditory feedback. However, as the technology evolved, there has been a growing emphasis on incorporating haptic and vestibular feedback to enhance realism and effectiveness. Haptic feedback involves providing tactile sensations that mimic real-world interactions, while vestibular feedback simulates the physical sensations of movement, such as acceleration and turning.  
One notable example of a VR application for wheelchair users is the power wheelchair driving simulator developed by [PERSON] et al. [3]. This system integrates vestibular feedback to simulate the motion sensations experienced during wheelchair use. The inclusion of vestibular feedback significantly enhances the sense of presence and reduces cybersickness, a common issue in VR environments. The study by [PERSON] et al. demonstrated that users experienced improved quality of experience (QoE) when vestibular feedback was active, highlighting the importance of multisensory integration in VR systems for mobility-impaired users. This system has the advantage of transmitting vestibular feedback to the user but has several drawbacks. Firstly, it does not allow the user to use their wheelchair, as the simulator chair is motorized and is fixed and adapted (without wheels) for this use. This increases the user's dependence on other people to use the simulator. Secondly, and more importantly, it does not allow the use of a manual wheelchair. Finally, and linked to the above, the system does not transmit feedback in terms of slope force or ground friction index.  
Another significant contribution to the field is the work by [PERSON] et al. [4], who developed a haptic guidance system for assisted wheelchair navigation. This system provides real-time haptic feedback to users, simulating various terrain conditions and obstacles. The study showed that haptic feedback could help users navigate complex environments more safely and efficiently, making it a valuable tool for training and rehabilitation.  
Recent advancements in haptic interaction have explored the simulation of fluid dynamics and terrain-based interactions in virtual environments. For instance, the work of [PERSON], [PERSON] [5] introduces SPH-based haptic interaction to simulate multiple fluid behaviors in virtual reality, providing a realistic representation of fluid motion through advanced simulation techniques. Similarly, [PERSON] [6] developed GroundFlow, a liquid-based haptic system capable of simulating fluid interactions on the ground in virtual environments. While these studies focus on fluid-based interactions, our approach is specifically designed to simulate solid terrain properties, such as slopes, resistances, and uneven surfaces, to allow wheelchair users to navigate virtual environments in a manner identical to real-world conditions. By integrating haptic feedback into the user's natural wheelchair movements, we provide a unique interaction method that emphasizes realism for solid ground navigation.