Second-Order Sliding Mode Formation Control of Multiple Robots by Extreme Learning Machine

Abstract

This paper addresses a second-order sliding mode control method for the formation problem of multirobot systems. The formation patterns are usually symmetrical. This sliding mode control is based on the super-twisting law. In many real-world applications, the robots suffer from a great diversity of uncertainties and disturbances that greatly challenge super-twisting sliding mode formation maneuvers. In particular, such a challenge has adverse effects on the formation performance when the uncertainties and disturbances have an unknown bound. This paper focuses on this issue and utilizes the technique of an extreme learning machine to meet this challenge. Within the leader–follower framework, this paper investigates the integration of the super-twisting sliding mode control method and the extreme learning machine. The output weights of this extreme learning machine are adaptively adjusted so that this integrated formation design has guaranteed closed-loop stability in the sense of Lyaponov. In the end, some simulations are implemented via a multirobot platform, illustrating the superiority and effectiveness of the integrated formation design in spite of uncertainties and disturbances.

Practical Prescribed Tracking Control of n-DOF Robotic Manipulator with Uncertainties via Friction Compensation Approach

“…In addition to robustness, control algorithms must also exhibit accuracy. Two types of methods are commonly used to achieve high-accuracy performance: model-based strategies [7,8] and traditional high-gain control algorithms, such as various sliding mode controllers [15][16][17]. However, completely modeling the robot dynamics is laborious, and modelbased control strategies are computationally demanding.…”

“…Theorem 1. Consider the error system (17) and the VGFESO (15). If ω(t) ≥ 4c∥P∥, then the scale estimation error η is uniformly ultimately bounded.…”

“…Theorem 2. For the robotic systems (1), the proposed controller (26), TD (25), and VGFESO (15) can guarantee that the error z and ε are ultimately bounded, and the tracking error e can converge to the region defined by the prescribed performance bound (4).…”

Switching Perfect Control Algorithm

“…Interestingly, the idea of having different sets of the closed-loop properties obtained in a single control task is not a new one. For example, the switching systems or sliding mode controllers have already been developed with a plethora of possible applications [14,[17][18][19]. With time-varying controller parameters, the possibility to influence the closed-loop system intentionally was given to the control designer.…”