Adaptive control of 2-wheeled balancing robot by two hemispheric cerebellar neuronal network model

Abstract

Major attention has been given to the cerebellum owingto its principal role during motor learning, sensory-motor transformations, and cognitive functioning. As aresult, its neuronal circuitry and learning capabilitieshave been well identified [1,2], and various mathematicalmodels have been proposed to explain experimental data.Previously we have configured a physio-anatomicallyinspired cerebellar neuronal network (CNN) controller,and demonstrated that the controller can govern anunstable plant, namely a 2-wheeled balancing robot [3].The CNN controller followed anatomical cerebellar corti-cal structure and included granular (Gr), Golgi (Go), bas-ket/stellate (Ba/St), and Purkinje (Pk) cells. Excitatoryinputs to the CNN carried by mossy fibers provided thedesired motion trajectories. Inhibitory feedback loopbetween Gr and Go, and feed-forward inhibitory loopbetween Ba/St and Pk were also included. Inferior olivary(IO) nucleus innervation to Pk via climbing fibers wasimplemented to convey error signal to the CNN. A pro-portional and differential (PD) controller sharing thesame mossy fiber inputs was introduced to work in tan-dem while the CNN controller is learning. As such, theerror signal via climbing fibers to the Pk was the outputof the PD controller. A simple learning rule that adjuststhe efficacy of the Gr-Pk synapses was employed to mimiclong-term depression and potentiation discovered at thissynapse in vitro and in vivo. Real time simulations andreal-world testing evinced that the CNN controller wassuccessful in controlling the unstable plant. Currently afurther refinement of the CNN controller was made toenhance its learning capability.Firstly, exalted by observations of bilateral plasticity dur-ing unilateral learning paradigms [4,5], right and left hemi-spheres of the cerebellum were separately modeled.Secondly the learning rule was modified to include thevery low spontaneous spike activity (~ 2 spikes/s) at theclimbing fiber input [5,6]. The error signal originated fromthe concurrent PD controller was split into two by usinghalf-wave rectifiers. The negative and positive waves arefed into right and left hemisphere models, respectivelyafter adding a DC value to mimic the climbing fiber spon-taneous firing. Each hemisphere comprises 120 Gr, 1 Go,6 Ba/St and 1 Pk cell [3]. The desired trajectory tested wasa single sinusoid (0.1 Hz) and a band limited (~ 0.3 Hz)noise.Real time simulation of a 2-wheel balancing robotdemonstrated that the proposed two hemispheric CNNnot only successfully controlled the robot but also com-pensated for abrupt perturbations (weight increase) thatthe PD controller alone cannot manage. Interestingly, inthe learning stage, a gradual substitution of the PD outputby the CNN controller was observed and eventually thePD output was almost diminished, meaning that the CNNcontroller successfully took over the PD controller.ConclusionsA two hemispheric cerebellar neuronal network control-ler was constructed and applied to the control of anunstable 2-wheel balancing robot. It was proved that theCNN controller can reproduce a basic form of unilaterallearning similar to the real cerebellum. These results arebeing further evaluated on the real world.