Nested Constraint Dynamic Modeling and Cooperative Control of Reconfigurable Micro Modular Robotic Vehicle Swarms

Reconfigurable miniature modular robotic swarms realize flexible payload transportation by the serial assembly of micro vehicle modules. Strong dynamic coupling and unsynchronized motion among interconnected modules bring prominent challenges to the stable cooperative operation of micro-robotic transport systems. To tackle modeling and coordination control challenges of scalable micro modular robots with variable chassis structures, this paper develops a hierarchical nested constraint-following modeling and cooperative control framework based on UK analytical dynamics, with distinct mathematical and computational advances over conventional monolithic modeling approaches. Each miniature module is equipped with an integrated steering micro chassis and embedded controllers for real-time motion computation. First, an underactuated nonlinear dynamic model for each individual unit is built without redundant auxiliary variables. Based on this unit model, the proposed framework supports swarm system modeling for transportation swarms composed of an arbitrary number of modules. Second, inter-module geometric constraints are transformed into second-order acceleration equations. Moore–Penrose pseudoinverse analytically solves constraint forces, enabling recursive nested full-system modeling for n connected modules. From a computational perspective, the recursive nested architecture eliminates the need to reconstruct global mass and constraint matrices from scratch when the swarm configuration changes, which significantly reduces modeling complexity and enables scalable dynamic computation. Third, global trajectory tracking missions are recursively decomposed into independent constraint-following subtasks for each module, with a damping correction term embedded to eliminate initial tracking errors. Numerical simulations with four serially connected miniature modular robot units demonstrate that trajectory tracking errors converge to near zero within 0.5s. Compared with the LQR baseline controller, the proposed approach achieves a lower peak deviation and a substantially reduced cumulative tracking error. When subject to external torque disturbance, the system maintains satisfactory heading synchronization and rapidly recovers steady-state control outputs, verifying favorable disturbance-rejection performance. This work offers a unified modeling and coordination-control solution for reconfigurable micro robotic transport platforms, supporting micro-robotics haulage research.