A finite‐time adaptive Taylor series tracking control of electrically‐driven wheeled mobile robots

Abstract

This research seeks to address a new integrated kinematic/dynamic adaptive Taylor series‐based control design for the robust tracking of electrically‐driven differential drive wheeled mobile robots (WMRs). This control design includes two loops, namely the outer loop (a kinematic control law) and the inner loop (a dynamic controller). Being capable of compensating for far initial conditions from a desired trajectory, a new kinematic control law is designed to make the posture tracking error converge to zero asymptotically as well as to generate a desired trajectory for a dynamic controller. The key role of the dynamic controller is to compensate for lumped uncertainties. To do this, the proposed chattering‐free dynamic controller guarantees that the defined sliding surface which is a function of tracking error and its time derivative will be converged to zero within a finite time. The exact stability analysis of inner closed‐loop system is developed via two Lyapunov‐like positive definite functions to ensure not only the boundedness of all signals but also the finite‐time convergence of sliding surface to zero. The proposed control algorithm is validated by means of various simulations, including comparisons with well‐designed kinematic and integrated kinematic/dynamic control literature.

Taylor‐based adaptive sliding mode control method for robot manipulators

“…Theorem 1. The sliding surface S i → 0 as t → ∞, for i = 1, … , n using the control law (37) and the adaptation laws (44) utilized on system (16). Proof: The Barbalat Lemma is used to prove S → 0 as t → ∞.…”

“…Proof: The Barbalat Lemma is used to prove S → 0 as t → ∞. The closed-loop system (38) is formed by substituting the control law (37) with adaptation laws (44) into system (16). Then, choosing the Lyapunov function (39) results in (46).…”

“…In order to completely overcome the chattering phenomenon, the sign-function may be removed in the close vicinity of the sliding surface S = 0 as the uncertainty estimation is solely performed by the Taylor expansion. Consequently, a new Taylor-based boundary layer ASMC scheme is derived from the control laws ( 36) and (37) as…”

“…In this section, the proposed control law expressed by the Taylor-based ASMC scheme in (37) is denoted as PCL (37) and the time delay ASMC [20] expressed by ( 59) is denoted as TASMC (59). The control design parameters for the PCL (37) are shown in Table 1.…”

“…Taylor expansion has found various applications in control methods such as model predictive control [33], near-optimal control [34,35], model-based proportional integral derivative control [36], and Taylor-based adaptive control [30,31,37]. It is pointed out that the Taylor expansion can only be applied for a differentiable function around a given point.…”