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This paper introduces a novel approach to the kinodynamic motion planning problem for multi-robot systems with task constraints and obstacle avoidance. The proposed method, designed for robots with uncertain linear dynamics, maintains the optimality close to that of centralized systems while preserving the scalability and structural flexibility of decentralized systems. The approach involves a two-step process: task assignment based on approximations of distances and energy consumption, and the creation of a future map to define obstacle-free regions. At every time step, the method solves a mixed integer quadratic problem, applying an affine feedback law, thereby generating global paths dynamically. This kinodynamic aspect allows the system to adapt to changes in the environment and robot states with kinematic constraints. The proposed method is validated through experiments using omnidirectional robots, with results compared to both decentralized and centralized systems.
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