Stability-Constrained Parameter Estimation for Mecanum Cart with Limited Input Frequency

The purpose of this study is to model a 4 -wheeled Mecanum cart, with the input signal frequency designed to be 10 Hz and its overall motion derived by considering the mounting angles of the rollers on wheels. By integrating stability constraints into the parameter estimation process, this study aims to ensure both the model's accuracy and its system stability. The cart model consists of two parts: the kinematic equation between the wheel rotational speed and the overall motion of the cart and the relationship between the input driving signal and the wheel rotational speed which was represented as a difference equation. The parameters of difference equation were estimated using the gradient descent method, with the Routh-Hurwitz stability criterion incorporated as a constraint via the Karush-KuhnTucker conditions to guide the system's stability during the estimation process. Test data measured from real cart rotation, consisting of 13 sets of step signals (ranging from 10 rpm to 130 rpm in increments of 10 rpm) with 5 experimental repetitions per set, were used to compare the dynamic and steady-state characteristics of models obtained with and without stability constraints. Also 5 trials of random input experiments were performed to compare the dynamic and steady-state response of the models obtained from 2 methods. Results showed a decrease in the gradient descent success rate from 90% to 60%, while the system stability rate, defined as the ratio of the number of stable models to the total number of parameter estimate trials, improved from 30% to 60%. Additionally, a t-test on the mean errors between model outputs and the real cart output revealed no significant difference between the two methods. These results indicated that the effectiveness of introducing stability checks into parameter estimation for limit input signal frequency systems, ensuring both accuracy and system stability.