This article presents a neural network based admittance control scheme for robotic manipulators when interacting with the unknown environment in the presence of the actuator deadzone without needing force sensing. A compliant behavior of robotic manipulators in response to external torques from the unknown environment is achieved by admittance control. Inspired by broad learning system, a flatted neural network structure using radial basis function (RBF) with incremental learning algorithm is proposed to estimate the external torque, which can avoid retraining process if the system is modeled insufficiently. To deal with uncertainties in the robot system, an adaptive neural controller with dynamic learning framework is developed to ensure the tracking performance. Experiments on the Baxter robot have been implemented to test the effectiveness of the proposed method.