The Design and Implementation of a Wheeled Inverted Pendulum Using an Adaptive Output Recurrent Cerebellar Model Articulation Controller

A novel adaptive output recurrent cerebellar model articulation controller (AORCMAC) is utilized to control wheeled inverted pendulums (WIPs) that have a pendulum mounted on two coaxial wheels. This paper focuses mainly on adopting a self-dynamic balancing control strategy for such WIPs. Since the AORCMAC captures system dynamics, it is superior to conventional CMACs in terms of efficient learning and dynamic response. The AORCMAC parameters are adjusted online using the dynamic gradient descent method. The learning rates of the AORCMAC are determined using an analytical method based on a Lyapunov function, such that system convergence is achieved. The variable and optimal learning rates are derived to achieve rapid tracking-error convergence. A WIP standing control is utilized to experimentally verify the effectiveness of the proposed control system. Experimental results indicate that WIPs can stand upright stably with external disturbances via the proposed AORCMAC.

Nomenclature

Reference signal.

Error signal at th sampling interval.

Error change signal at th sampling interval.

th input state variable.

Resolution of input space.

Number of blocks.

Receptive-field basis function.

and

Mean and variance of basis function, respectively.

and

Recurrent and output weights, respectively.

Associated with the th receptive field.

Output of the ORCMAC.

and

Learning rates for mean and variance, respectively.

and

Learning rates for recurrent and output weights, respectively.

and

Modification value for mean and variance, respectively.

and

Modification value for recurrent and output weights, respectively.

Small positive constant.