Zero dynamics stabilisation and adaptive trajectory tracking for WIP vehicles through feedback linearisation and LQR technique

ABSTRACT

This paper presents a composite control strategy integrating adaptive sliding-mode control and the linear quadratic regulator (LQR) technology for a wheeled inverted pendulum (WIP) vehicle system. The system can be partitioned into an actuated rotational subsystem and an underactuated longitudinal subsystem based on the different control input in the mathematical model. In particular, the instability analysis of zero dynamic for the underactuated longitudinal subsystem is investigated in detail using the feedback linearisation technology. Then, an adaptive sliding-mode control is designed for the trajectory tracking, where an adaptive algorithm is developed to handle with the parameter uncertainties. In addition, the LQR technique is employed to guarantee zero dynamics stability so as to achieve simultaneously the vehicle body stabilisation at the upright position. Simulation results show the good performance and strong robustness of the proposed control schemes.

KEYWORDS:

• Feedback linearisation
• linear quadratic regulator (LQR)
• sliding-mode control
• unstable zero dynamics
• wheeled inverted pendulum

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by grants from the National Natural Science Foundation of China [grant number 61573078], [grant number 61175101], [grant number 61573147]; the International S&T Cooperation Program of China [grant number 2014DFB70120]; and the State Key Laboratory of Robotics and System [grant number SKLRS2015ZD06].