Enhancing Spiral Microrobot Dynamics in Ratchet Potentials: The Role of Gaussian Colored Noise

Abstract Random disturbances in microfluidic environments often cause pronounced trajectory deviations in microrobots, posing challenges for robust control. However, most existing models either neglect these disturbances or idealize them as Gaussian white noise (GWN), limiting their applicability. To address this, we investigate the influence of Gaussian colored noise (GCN) on the dynamics of a spiral microrobot navigating a ratchet potential. A stochastic dynamic model grounded in resistive force theory is proposed, and the system’s response is analyzed using the steady-state probability density function. We systematically examine how variations in ratchet potential, fluid viscosity, and noise intensity affect the microrobot’s average velocity and mean first passage time (MFPT). Moreover, we explore how geometric design impacts propulsion efficiency under stochastic excitation. Results reveal that GCN can significantly enhance propulsion efficiency and promote directional transport, with these effects strongly dependent on the noise correlation time. These findings not only enrich the theoretical framework of noise-induced microrobot dynamics but also provide practical guidance for optimizing design and environmental parameters.