B-splines-based mechanism design in population games for distributed evolutionary dynamics formation control

• On-line formation design using population games with stability guarantees and experimental validation for multiple nanodrones. • Fitness function design based on B-spline properties, guaranteeing smooth transitions between formations while inherently enforcing constraints on drone motion. • Revision protocols evaluation in terms of implementation complexity, computational efficiency and formation convergence. This paper presents a novel formation control framework for autonomous multi-agent systems based on distributed evolutionary dynamics and time-varying population games. We design the fitness functions using B-spline parameterization, enabling smooth, constraint-aware trajectory generation that incorporates both equilibrium targets and transient behavior. The proposed method is integrated with multiple distributed dynamics, namely replicator, projection, and Smith dynamics, and ensures convergence under connectivity and stability assumptions. Compared to conventional static fitness designs, the B-spline-based approach provides enhanced performance in formation reconfiguration and motion planning. The effectiveness of the proposed strategy is validated through extensive simulations and real-world experiments with multiple aerial nanodrones.