Robust control of two-wheeled self-balanced transporter on sloping ground: A Takagi-Sugeno descriptor approach

Abstract

A commonly asked question in the field of autonomous robotics and intelligent vehicles is : How to design and control an urban transporter able to investigate narrow spaces ? From a mechanical point of view, a two wheeled transporter seems to be a good alternative due to its small footprint and its ability to manoeuvre on tight turns. However, the design of this vehicle requires two level of control : One, for the auto-balancing. The second ensures a velocity tracking. The use of linear control law requires a linearisation of the model around an a priori known equilibrium point under the assumption that the vehicle moves on a plane surface. Now, assume that the vehicle is moving along an unknown slope. Then, the equilibrium point is not known while designing the controller. The linearized model becomes unrepresentative. This work present a control of self-balanced two wheeled transporter. The aim is to design a robust controller able to stabilize the transporter on its natural equilibrium along an unknown slope. A quasi LPV approach, through the so-called TS fuzzy model and LMI constraints will be proposed. Moreover, The natural descriptor form of the mechanical system will be used to design the control law. This last choice allows reducing the conservatism of the LMI conditions. Finally a simulation tests showed the effectiveness of our approach.

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

“…In practice, some mechanical systems, such as, double inverted pendulum model of human standing in [43], twowheeled self-balanced transporter in [44] and 2-DOF planar parallel robot in [45], can be modelled as nonlinear descriptor systems (43). Applying the established sliding mode control methodology [7], [9], [12], [35], [36] to system (43) involves transformatiom to the nonlinear normal system described bẏ…”

“…It should be noted that the difference in the input matrices in (45) results from the inverse operation of the derivative-term coefficient E(x(t)), which makes the sliding mode control problem difficult. In addition, the descriptor model of the system (43) has a more simple structure than its normal model (44) and inverse operation of derivative-term matrix is avoid.…”