A novel saturated PID-type observer-based controller for wheeled mobile robots with a guaranteed performance considering path curvature

This article proposes a novel saturated PID-type formation controller for a class of nonholonomic wheeled mobile robots (WMRs) of type (m, s) with mobility m and steerability s. Since the path curvature causes a severe deviation of the followers from the leaders' trajectory in the corners, a new definition of output equations is suggested to construct the coordinates of a virtual reference point in the front of each follower based on the concept of the extended look-ahead control that utilizes a corrective angle to compensate the trajectory curvature efficiently. A nonlinear transformation and the robot's kinematic and dynamic equations are heuristically combined to develop a novel second-order Euler-Lagrange formulation of unconstrained errors from constrained errors. Then, a novel saturated PID-type controller is proposed for WMRs to build a desirable formation with a prescribed performance. An innovative nonlinear observer is presented to estimate followers' velocities. An efficient mixture of a radial basis function neural network (RBFNN) and an adaptive mechanism is proposed to compensate for model uncertainties, external disturbances, and network approximation errors. Lyapunov's direct method verifies semi-global uniform ultimate boundedness stability by estimating a gain-dependent region of attraction. Numerical simulations finally show the efficiency of the proposed controller.