This article proposes a novel control strategy based on a broad fuzzy neural network (BFNN) which is subjected to contact with the unknown environment. Compared with the conventional fuzzy neural network (NN), a prominent feature can be achieved by taking the advantage of the broad learning system (BLS) to explicitly tackle the problem of how to choose a sufficient number of NN units to approximate the unknown dynamic model. Aiming at providing a soft compliant contact scheme without the requirement of the environment model, an adaptive impedance learning is developed to establish the optimal interaction between the robot and the environment. Meanwhile, the problems related to the state constraints are addressed by incorporating a barrier Lyapunov function (BLF) into the design of a trajectory tracking controller. The proposed method can achieve desired tracking and interaction performance while guaranteeing the stability of the closed-loop system. In addition, simulation and experimental studies are performed to verify the effectiveness of BFNN under optimal impedance control with a two degree-of-freedom (DOF) manipulator and a Baxter robot, respectively.