This work proposes a leader–follower formation framework comprising three differential-drive mobile robots that are equipped with geometry-aware kinematics coupled with adaptive dynamics. The leader robot is directed by a nonlinear body frame tracking controller that is enhanced with an online radial basis function neural network. This network compensates for residual error in velocity-domain effects from the current position error, which enhances feedforward compensation without affecting stability. The dynamics of each robot are driven by an interval type-2 adaptive fuzzy-PID controller that adapts membership-function centers and footprint of uncertainty bounds in real time to deal with model mismatch and disturbances. As a result, the controller yields low chatter and ensures smooth control actions. The followers preserve formation using a geometric partial feedback linearization (PFL) design that integrates effectively with the adaptive layers. Controller gains for the leader and PFL formation kinematic controllers are tuned using the Secretary Bird Optimization Algorithm. A Lyapunov analysis for all the proposed controllers guarantees convergence and boundedness under nonholonomic constraints. Overall, the framework exhibits reliable path tracking and formation preservation, enhanced design for disturbance rejection, and smooth-behaved control effort through diverse operating conditions, such as robot dynamic model parameter uncertainties and control signals disturbances. Results show that all controllers ensured system stability and achieved low root mean square error values. Compared with existing works, the path accuracy for the leader was enhanced by 57%, while followers 1 and 2 achieved accuracy gains of 42.25% and 37.33%, respectively.
Karam et al. (Tue,) studied this question.