A Two-Layer Task Model for Rendering Stable Cooperative Haptics in Multiuser Haptic-Enabled Robotic Systems

The multiuser haptic-enabled robotic system (M-Hers) facilitates shared control among human operators through task-dependent authority allocation, where interaction relationships are typically dictated by task requirements. However, some of these relationships can be nonpassive, generating excess energy that violates passivity constraints and compromises system stability. To address this, we first introduce the interaction architecture (IA) to formalize how operators influence task execution. Based on this framework, we propose a tank-based two-layer task model that ensures system passivity despite nonpassive IAs. This model comprises a virtual object (VO) layer for task rendering and a virtual system (VS) layer that passively executes nonpassive IA behaviors. The VS layer uses a global energy tank to compensate for IA-induced energy violations and modify the VO model when tank energy is depleted. This structure decouples task rendering from low-level robotic control, enabling seamless integration of an arbitrary number of robots with heterogeneous dynamics and control modes. Simulation and experimental results validate the proposed method’s scalability, flexibility, and effectiveness in preserving passivity while accurately realizing diverse IAs. This approach paves the way for scalable and easy-to-deploy control framework that supports multiuser haptic interaction.