Multi-robot swarms play an essential role in complex missions including battlefield reconnaissance, agricultural pest monitoring, as well as disaster search and rescue. Unfortunately, given the complexity of swarm algorithms, logical vulnerabilities are inevitable and often lead to severe safety and security consequences. Although various methods have been presented for detecting logical vulnerabilities through software testing, when they are used in swarm environments, these techniques face significant challenges: 1) Due to the swarm's vast composable parameter space, it is extremely difficult to generate failure-triggering scenarios, which is crucial to effectively expose logical vulnerabilities; 2) Because of the swarm's high flexibility and dynamism, it is challenging to model and evaluate the global swarm state, particularly in terms of cooperative behaviors, which makes it difficult to detect logical vulnerabilities. In this work, we propose RSFuzz, a robustness-guided swarm fuzzing framework designed to detect logical vulnerabilities in multi-robot systems. It leverages the robustness of behavioral constraints to quantitatively evaluate the swarm state and guide the generation of failure-triggering scenarios. In addition, RSFuzz identifies and targets key swarm nodes for perturbations, effectively reducing the input space. Upon the RSFuzz framework, we construct two swarm fuzzing schemes, Single Attacker Fuzzing (SA-Fuzzing) and Multiple Attacker Fuzzing (MA-Fuzzing), which employ single and multiple attackers, respectively, during fuzzing to disturb swarm mission execution. We evaluated RSFuzz's performance with three popular swarm algorithms in simulated environments. The results show that RSFuzz outperforms the state-of-the-art with an average improvement of 17.75\% in effectiveness and a 38.4\% increase in efficiency. We validated some vulnerabilities in real world.