Adaptive control of 2-wheeled balancing robot by cerebellar neuronal network model Yoshiyuki Tanaka, Yohei Ohata, Tomohiro Kawamoto, and Yutaka Hirata, Member, IEEE Abstract��� A new adaptive motor controller was constructed, and tested on the control of a 2-wheeled balancing robot in simulation and real world. The controller consists of a feedback (PD) controller and a cerebellar neuronal network model. The structure of the cerebellar model was configured based upon known anatomical neuronal connection in the cerebellar cortex. Namely it consists of 120 granular (Gr) cells, 1 Golgi cell, 6 basket/stellate cells, and 1 Purkinje (Pk) cell. Each cell is described by a typical artificial neuron model that outputs a weighted sum of inputs after a sigmoidal nonlinear transformation. The 2 components of the proposed controller work in parallel, in a way that the cerebellar model adaptively modifies the synaptic weights between Gr and Pk as in the real cerebellum to minimize the output of the PD controller. We demonstrate that the proposed controller successfully controls a 2-wheeled balancing robot, and the cerebellar model rapidly takes over the PD controller in simulation. We also show that an abrupt load change on the robot, which the PD controller alone cannot compensate for, can be adaptively compensated by the cerebellar model. We further confirmed that the proposed controller can be applied to the control of the robot in real world. I. INTRODUCTION The cerebellum is known to play a pivotal role in biologi- cal adaptive motor control. Its anatomical neuronal circuitry is among the best identified in the brain, and the basic structure of the cerebellum is shared from fish to primate [1]. Further, the synaptic plasticity in cerebellar cortical neuronal circuitry has been physiologically well character- ized as an underlying neural mechanism of the cerebellar adaptive motor control [1] and its plausible learning rule has been proposed [2]. Thus many researchers have constructed mathematical models of the cerebellum to reproduce and explain various experimental data [3]. However, little attempt has been made to employ those models for engineering applications. Here we constructed a new cerebellar neuronal network model for engineering application, especially for a 2-wheeled balancing robot. We configured the model based upon anatomical and physiological evidence of the cerebellum, enabling a real-time adaptive robot control. A 2-wheeled balancing robot was chosen to test validity of the cerebellar model as an adaptive motor controller for unstable systems. This research was supported in part by MEXT Grant-in-Aid for Scientific Research (C 18500231, 21500298), the Hori Information Science Promotion Foundation, and Research Institute for Information Science of Chubu University. Y. Tanaka, Y. Ohata and Y. Hirata are with the Department of Com- puter Science, Chubu University Graduate School of Engineering, 1200 Matsumoto Kasugai Aichi, Japan yutaka@isc.chubu.ac.jp T. Kawamoto is with Bosch Corporation, Tokyo, Japan Go Pk Desired trajectory cf mf Gr pf & Control error PD controller output Ba/St Desired trajectory Motion trajectory + PD two-wheeled robot Current [A] Cerebeller controller model Error signal A B Fig. 1. The proposed controller (A) and configuration of the cerebellar model (B). II. METHODS A. Structure of the proposed controller The proposed adaptive controller consists of the cerebellar neuronal network model and a PD controller (Fig.1A). We used a 2-wheeled balancing robot ���e-nuvo Wheel��� (ZMP inc.) as a control object. The parameters of the PD controller ( K p and K d ) were adjusted so that the PD controller alone can initially balance the robot. The cerebellum model was configured based upon anatomical connection of each neuron type (Fig.1B). Namely, granular (Gr) cells and Golgi (Go) cells receive mossy fiber (mf) inputs that carry a desired trajectory of the robot, and a control error (desired trajectory - actual trajectory). Go cells receive excitatory input from Gr cells as well, and simultaneously inhibit Gr cells, forming a negative feedback loop. The excitatory outputs of Gr are also received by Purkinje (Pk) cells, and basket and stellate (Ba/St) cells. Ba/St cells inhibit Pk cells, forming a negative feed-forward pathway. Pk is the sole output cell type from the cerebellar cortex. Each Pk cell receives another input from inferior olivary nucleus through a climbing fiber (cf) that is considered to convey a control error signal [1]. The output of a Pk is considered to be modified to reduce the error signal by adjusting the synaptic efficacies between Gr and Pk. When Gr and cf are co-activated the synaptic efficacies decrease (Long-term depression: LTD) whereas when Gr alone is active they increase (Long-term potentiation: LTP) [4]. The 32nd Annual International Conference of the IEEE EMBS Buenos Aires, Argentina, August 31 - September 4, 2010 978-1-4244-4124-2/10/$25.00 ��2010 IEEE 1589