It is challenging to model a four-wheeled Mecanum robot with an input-signal frequency that is limited to 10 Hz by design, owing to the low-frequency input and unknown motor dynamics. To address this issue, Nakagawa et al. proposed a reduced-order exhaustive search approach, which is limited by low high-speed accuracy and long computation times. Therefore, this study represented the wheel dynamics as a discrete difference equation and estimated relevant parameters using the gradient descent method. Additionally, Routh–Hurwitz stability constraints were incorporated using Karush–Kuhn–Tucker conditions: whenever an updated solution violated stability, it was projected back into the feasible region to ensure all system poles stay in the left half-plane. The proposed method achieved an almost zero relative steady-state error of -4.41×10^-8, representing an improvement of 2–5 orders of magnitude compared to those obtained using the method proposed by Nakagawa et al. (2.79×10^-6) and standard gradient descent method (1.09×10^-2). It also maintained comparable dynamic performance with a rise time of 0.12 s and a settling time of 0.23 s, aligning with the rise time (0.11 s) and settling time of the robot (0.25 s), respectively. These results indicated the effectiveness of introducing stability constraints into parameter estimation for low input signal frequency systems, ensuring both accuracy and system stability.

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