The study of the kinetic bottlenecks that hinder the rare transitions between long-lived metastable states is a major challenge in atomistic simulations. We propose a method to explore the transition state ensemble, which is the distribution of configurations that the system passes as it translocates from one metastable basin to another. We base our method on the committor function and the variational principle to which it obeys. We find its minimum through a self-consistent procedure that starts from information limited to the initial and final states. Right from the start, our procedure allows sampling very many transition state configurations. With the help of the variational principle, we perform a detailed analysis of the transition state ensemble, ranking quantitatively the degrees of freedom mostly involved in the transition and enabling for a systematic approach for the interpretation of simulation results and the construction of efficient physics-informed collective variables.