Space-Constrained Multi-Robot Formation Control via an Enhanced Discrete-Time Control Lyapunov and Barrier Function Approach

This paper focuses on the design of controller for trajectory tracking and obstacle avoidance in robot formations operating within confined spaces. Specifically, to achieve obstacle avoidance, we approximate obstacles and robots as convex polyhedra and utilize the Lagrangian dual function to design an enhanced discrete-time control barrier function (DCBF). Moreover, a discrete-time control Lyapunov function (DCLF) algorithm is employed to maintain the formation while tracking a predefined trajectory. This enables the natural unification of DCBFs with DCLFs within a quadratic program (QP) framework. The proposed method eliminates the nested optimization problem in the QP framework, and the solving time is significantly reduced. Theoretical analysis demonstrates the feasibility of the proposed method. Finally, simulations and hardware experiments are conducted to validate its effectiveness.