This paper proposes a new method for real-time terrain recognition-based navigation for mobile robots. Mobile robots performing tasks in unstructured environments need to adapt their trajectories in real-time to achieve safe and efficient navigation in complex terrains. However, current methods largely depend on visual and IMU (inertial measurement units) that demand high computational resources for real-time applications. In this paper, a real-time terrain identification-based navigation method is proposed using an on-board tapered whisker-based reservoir computing system. The nonlinear dynamic response of the tapered whisker was investigated in various analytical and Finite Element Analysis frameworks to demonstrate its reservoir computing capabilities. Numerical simulations and experiments were cross-checked with each other to verify that whisker sensors can separate different frequency signals directly in the time domain and demonstrate the computational superiority of the proposed system, and that different whisker axis locations and motion velocities provide variable dynamical response information. Terrain surface-following experiments demonstrated that our system could accurately identify changes in the terrain in real-time and adjust its trajectory to stay on specific terrain.