Indirect Adaptive Control Using Neural Network and Discrete Extended Kalman Filter for Wheeled Mobile Robot

This paper presents a novel approach to address the challenges associated with the trajectory tracking control of wheeled mobile robots (WMRs). The proposed control approach is based on an indirect adaptive control PID using a neural network and discrete extended Kalman filter (IAPIDNN-DEKF). The proposed IAPIDNN-DEKF scheme uses the NN to identify the system Jacobian, which is used for tuning the PID gains using the stochastic gradient descent algorithm (SGD). The DEKF is proposed for state estimation (localization), and the NN adaptation improves the tracking error performance. By augmenting the state vector, the NN captures higher-order dynamics, enabling more accurate estimations, which improves trajectory tracking. Simulation studies in which a WMR is used in different scenarios are conducted to evaluate the effectiveness of the IAPIDNN-DEKF control. In order to demonstrate the effectiveness of the IAPIDNN-DEKF control, its performance is compared with direct adaptive NN (DA-NN) control, backstepping control (BSC) and an adaptive PID. On lemniscate, IAPIDNN-DEKF achieves RMSE values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.078769</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.12086</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.1672</mn></mrow></semantics></math></inline-formula>. On sinusoidal trajectories, the method yields RMSE values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.01233</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.015138</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.088707</mn></mrow></semantics></math></inline-formula>, and on sinusoidal with perturbation, RMSE values are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.021495</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.016504</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.090142</mn></mrow></semantics></math></inline-formula> in <i>x</i>, <i>y</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>, respectively. These results demonstrate the superior performance of IAPIDNN-DEKF for achieving accurate control and state estimation. The proposed IAPIDNN-DEKF offers advantages in terms of accurate estimation, adaptability to dynamic environments and computational efficiency. This research contributes to the advancement of robust control techniques for WMRs and showcases the potential of IAPIDNN-DEKF to enhance trajectory tracking and state estimation capabilities in real-world applications.