Prescribed Performance Control of Mobile Wheeled Inverted Pendulum Systems Under Arbitrary Initial Conditions

Mobile wheeled inverted pendulum (MWIP) is a typical naturally unstable underactuated system and it is very necessary to constrain its transient response to improve the overall safety. Prescribed performance control (PPC) is an effective method, however the system initial conditions are usually required to be known and constraint, otherwise it can lead to singularity problems. In practical systems, it is often difficult to obtain the exact initial state leading to limitations in the application of PPC. To overcome this issue, this paper presented a composite error transformation function to address the problem of initial condition dependence. A continuous bounded function was designed to compress the arbitrary initial error into the predefined bound to avoid singularities. After a set time, it was degraded to an original system error. Based on this composite transformation, a state feedback controller was proposed for the underactuated MWIP system to achieve the constraint outputs. Then, by employing the Lyapunov theorem, it was guaranteed that the closed-loop system would remain stable. Various numerical simulations under different initial conditions were carried out to prove the validity of the proposed controller.