A state augmented adaptive backstepping control of wheeled mobile robots

Abstract

The present paper aims to design an integrated kinematic/dynamic-based tracking controller for wheeled mobile robots (WMRs) considering motors’ dynamics. By defining a reference WMR, the role of kinematic controller is to not only minimize the posture error which indicates the difference between the reference and actual WMRs, but also to generate a desired path for the actual WMR. The kinematic tracking control problem of WMRs is so challenging if motors’ dynamics, parametric and nonparametric uncertainties and external disturbances are considered. Thus, proposing a dynamic control law alongside a kinematic control is unavoidable. In this study, we propose a new dynamic controller, namely, a state augmented adaptive backstepping such that the desired path is asymptotically tracked. Several numerical results accompanied by 3D simulations of trajectory tracking control of a WMR in ‘Simscape Multibody’ environment and comparisons with two well-designed controllers in the literature are reported to show the high performance of proposed control structure.

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

“…The voltage equation of geared PMDC motors is formulated by (26) in which U pm ∈ ℝ 2×1 represents the voltage of motors, U dis ∈ ℝ 2×1 denotes disturbances applied externally to the voltage inputs, and…”

“…, serve as matrices in diagonal form, namely back-emf coefficients, resistances and inductance of armatures, respectively. Applying (19) to (26), we have…”

“…Since the diagonal matrix of gear reduction ratio, r gm , consists of scalar constants, φpm and φpm are bounded via Equations ( 11), (12), respectively. Considering the stable linear voltage Equation (26), the boundedness of U pm , U dis (according to Assumption 2), φpm and motor parameters, including K b , R pm and L pm , results in the boundedness of I pm . Now turning to the state space Equation (28), the boundedness of U pm , c and  (𝚵) conclude the boundedness of Ξ accordingly.…”

“…• Contrary to the refs. [15,26,52,55], which have utilized the classic kinematic control law proposed by Kanayama, et al [30], a new kinematic control law as an outer loop is designed in this research article to not only make the posture tracking error converge asymptotically to zero, but also generate a desired trajectory for a dynamic controller. • Motivated by [46,52,54,56], which have employed universal approximators, namely fuzzy systems or neural networks to deal with different types of uncertainties, A new modelfree and simple dynamic controller is developed as an inner loop to effectively compensate for lumped (parametric and non-parametric) uncertainty and external disturbances using an adaptive Taylor series system.…”

“…Despite all benefits which dynamic‐based control designs bring about, they fail to work properly when initial positions are selected relatively far from the desired path [26]. A practical solution for this problem is to take both the kinematic and dynamic model of WMRs into account for developing control laws, which this combination can be called as a kinematic‐dynamic control design.…”