Abstract
This paper presents a control design method for implementing planar turning motion of a two-wheeled inverted pendulum with an input delay. The control task requires that the inverted pendulum is kept stabilized during the whole turning motion process along a pre-settled curve. Firstly, by using the theory of planar curve, key observations about the motion law of the two-wheeled mobile chassis are made and they are used to set up a dynamical trajectory tracking target. Then, by adjusting the parameters in the tracking target and the weights in the quadratic performance criterion, the optimal integral sliding mode controller based on a linear quadratic regulator is designed for keeping the vehicle body stabilized and tracking a circular path for the two-wheeled inverted pendulum. An illustrative example is given to demonstrate the validity of the theory with numerical simulation.
Highlights
Two-wheeled inverted pendulum (TWIP, for short) is a general term for mechanical models driven by two wheels with a rod of pendulum mounted on the chassis
The designed controllers based on these kinds of normal forms are focused on speeds, rather than forces or moment of force, which are more aligned with an actual motion control problem of the nonholonomic mechanical system
One is that in order to keep the TWIP walking along the target trajectory curve accurately, it is important to have the curvature of the target trajectory curve well tracked
Summary
Two-wheeled inverted pendulum (TWIP, for short) is a general term for mechanical models driven by two wheels with a rod of pendulum mounted on the chassis It is a self-balancing system and has some remarkable superiorities, such as simple structure, good dexterity, true zero turning radius, small footprint, low cost and low energy consumption [1]. Based on the dynamics equations of the TWIP, neural networkbased control [16], fuzzy logic control [17] and adaptive control combined with some classical control methods have been proposed to design trajectory tracking controllers to track the given longitudinal and yaw rotational speeds target [18,19,20,21,22].
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