With the proliferation of Virtual Reality (VR) markets, VR applications are rapidly expanding in scale and complexity, thereby driving an urgent need for assuring VR software quality. Different from traditional mobile applications and computer software, VR testing faces unique challenges due to diverse interactions with virtual objects, complex 3D virtual environments, and intricate sequences to complete tasks. All of these emerging challenges hinder existing VR testing tools from effectively and systematically testing VR applications. In this paper, we present VRExplorer, a novel model-based testing tool to effectively interact with diverse virtual objects and explore complex VR scenes. Particularly, we design the Entity, Action, and Task (EAT) framework for modeling diverse VR interactions in a generic way. Built upon the EAT framework, we then present the VRExplorer agent, which can achieve effective scene exploration by incorporating meticulously designed path-finding algorithms into Unity’s NavMesh. Moreover, the VRExplorer agent can also systematically execute interaction decisions on top of the Probabilistic Finite State Machine (PFSM). Experimental evaluation on 11 representative VR projects shows that VRExplorer consistently outperforms the state-of-the-art (SOTA) approach VRGuide by achieving significantly higher coverage and better efficiency. Specifically, VRExplorer yields up to 122.8% and 52.8% improvements over VRGuide in terms of executable lines of code (ELOC) coverage and method (function) coverage, respectively. Furthermore, ablation results also verify the essential contributions of each designed module. More importantly, our VRExplorer has successfully detected two functional bugs and one non-functional bug from real-world projects.

Current methods for achieving fixed-time convergence in continuous sliding mode control are extensively studied, whereas there are limited studies on fixed-step convergence in discrete sliding mode control. The control objective of this paper aims to develop control schemes assuring that the number of convergence steps of the tracking error remains within the desired range, even as the initial value increases, and this paper proposes a guaranteed fixed-step convergence approach to form the reaching law. An upper bound on convergent steps, independent of the initial value, is established, thereby having the fixed-step convergence property . The performance assessment, including attractiveness, invariance, and convergence steps, is provided to meet the required specifications. The steady-state band results offer guidance in selecting parameters to achieve the control objective. To achieve fixed-step convergence of the tracking error, one can develop a dead-beat terminal sliding mode control scheme, where the tracking error is governed by the prescribed error dynamics. To illustrate the approach more concretely, specific designs are proposed for both switching and non-switching reaching laws aimed at ensuring fixed-step convergence. The simulation and experiment results validate the performance evaluation and demonstrate effectiveness of the proposed control schemes.