Modelling and stabilization of coupled vibrating metamorphotic constraints: application in underground multirobot transportation planning

Multirobot transportation path planning is one of the most important issue on fully mechanized underground mining face. However, the problem is extremely complicated due to coupling yet variable configuration constraints caused by manipulating objects. Considering the physical similarity of complex internal coupling force between the metamorphotic constraint and vibrating string, the principle of coupled vibrating metamorphotic constraints (CVMC) based on PDE-based vibrating string model is proposed and expected to be applied in long-term full cycle prediction of the underground multirobot transportation system. Pose evolution of underground multirobot system under external metamorphotic constraints is described both in temporal scale and spatial scale through PDE equations. To eliminate unexpected vibrations of digital-twin simulation for the underground multirobot transportation system, both the dynamics and stability of CVMC are discussed by establishing PDE equations with anti-stable term compensation and active disturbance rejection. Finally, a digital-twin simulation framework is first proposed for the transportation planning based on CVMC modeling. Numerical simulations considering three different kind of disturbance are conducted in the prototype framework, and the results show that the proposed simulation approach is effective for multirobot manipulation planning. The hardware in loop demonstration also shows the feasibility of potential application ability for underground multirobot transportation.