To address the challenges regarding consensus control and parameter tuning in collaborative obstacle avoidance for heterogeneous multi-agent systems, a control strategy fusing the artificial potential field method and a genetic algorithm was proposed. First, the dynamics model of a leaderless heterogeneous multi-agent system was established. Second, a collaborative obstacle avoidance consensus controller based on Lyapunov functions was designed, and the system stability was theoretically proven under the conditions of a connected communication topology and positive definite control gains. To overcome the reliance of traditional methods on empirical parameter tuning, a genetic algorithm was introduced to globally optimize key controller parameters, thereby resolving issues related to local minima and oscillation. Finally, an “air-ground collaborative reconnaissance” simulation scenario involving multiple unmanned aerial vehicles and unmanned ground vehicles was constructed. Simulation results demonstrate that the proposed method effectively achieves collaborative obstacle avoidance in complex environments. Compared with unoptimized parameters, the system consensus error is reduced by approximately 70%. Furthermore, compared to model predictive control, the proposed method significantly reduces computational time while ensuring collision avoidance safety. The results indicate that the proposed method achieves a good balance among stability, effectiveness, and computational efficiency, and can provide theoretical support and methodological reference for real-time cooperative control of heterogeneous multi-agent systems.