Logcosh Super-Twisting Control for Path Planning and Following

Output singularities and slow error convergence are two critical factors that cause sliding mode control failure. This paper proposes LogCosh Super-Twisting Control (LCSTC), a super-twisting sliding mode controller constructed with a nonsingular terminal sliding manifold that incorporates the LogCosh function In (cosh (x)). LCSTC avoids singular behavior and guarantees practical finite-time stability of the sliding dynamics. We also apply LCSTC to path following tasks and compare it with two baseline controllers to assess its performance by simulations. The simulation results show that LCSTC keeps the lateral-distance RMSE below 1.2 mm throughout the path-following task. LCSTC Experiments conducted on a magnetic microrobot further strengthen the dependable effects of the LCSTC in real-world scenarios. Based on this controller, we develop two planners. One is based on the upgraded RRT∗(URRT∗) method for static scenes, and the other is based on the bi-robot APF(BiRAPF) method for dynamic scenes. Both planners generate short paths while maintaining a safe distance, and they couple with LCSTC to form integrated planand-follow schemes. The effectiveness of two plan-and-follow schemes is also demonstrated by simulations.