Mathematical Problems in Engineering

Volume 2015, Article ID 793208, 9 pages

http://dx.doi.org/10.1155/2015/793208

## Research on Walking Gait of Biped Robot Based on a Modified CPG Model

College of Information and Engineering, Taishan Medical University, Taian 271016, China

Received 27 October 2014; Revised 17 December 2014; Accepted 21 December 2014

Academic Editor: Victor Santibáñez

Copyright © 2015 Qiang Lu and Juan Tian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The neurophysiological studies of animals locomotion have verified that the fundamental rhythmic movements of animals are generated by the central pattern generator (CPG). Many CPG models have been proposed by scientific researchers. In this paper, a modified CPG model whose output function is is presented. The paper proves that the modified model has stable periodic solution and characteristics of the rhythmic movement using the Lyapunov judgement theorem and the phase diagram. A modified locomotion model is established in which the credit-assignment cerebellar model articulation controller (CA-CMAC) algorithm is used to realize the pattern mapping between the CPG output and the musculoskeletal system. And a seven-link biped robot is employed to simulate cyclic walking gait in order to test the validity of the locomotion model. The main findings include the following. (1) The modified CPG model can generate spontaneous oscillations which correspond to biological signals. (2) The analysis of the modified locomotion model reveals that the CA-CMAC algorithm can be used to realize the pattern mapping between the CPG output and the musculoskeletal system.

#### 1. Introduction

Through works of scientific researchers, people have realized that the CPG can generate rhythmic movements. In order to represent the CPG and generate required signals, several nonlinear oscillators that are coupled together have been developed, such as the Hopf Rayleigh, Van del Pol, and Matsuoka oscillators [1–3]. Due to their simplicity and effectiveness, these CPG models have widely been used in robot control and motion simulation of human [4–6].

Humanoid robots have become quite popular and are used as a research tool in many groups worldwide. Among the various motions of a humanoid robot, the most basic and important motion is bipedal walking [7–11]. Chevallereau et al. [7] presented three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D bipedal robot. Shimmyo et al. [8] proposed the biped walking pattern generation by using preview control based on a three-mass model. Liu et al. [9] presented biped walking control using a library of optimal trajectories. Wang et al. [10] showed an energy-efficient support vector machine learning control system considering the energy cost of each training sample of biped dynamic in order to realize energy efficient biped walking. Li et al. [11] showed a walking pattern generator based on the control of the center of mass states.

When the CPG model is applied to walking gait, the outputs of the CPG are changed to positions and angles which inspire the musculoskeletal system. Therefore, the outputs of the CPG should correspond to biological signals. But the outputs of Matsuoka model are smoother than biological signals [12]. Taga [13] showed that many parameters which include the body parameters, the parameters in the neural oscillators, the strength of the neural connections, the magnitude of the coefficients in the rhythmic force controller, the strength of the sensory inputs, and the impedance parameters decide the conversion from the CPG to musculoskeletal system in the design of planning gait. Kim et al. [14] showed that the nonparametric estimation based particle swarm optimization is to effectively search the parameters of the CPG. Therefore, they are important works to study the central pattern generator corresponding to biological signals and establish the method to realize the mapping from the CPG to the musculoskeletal system in the fields of robot motor control. The motivations behind this research are to generate control signals inspired by biological ones for the robot motions and develop bionic technologies of robots.

This paper is organized as follows. In Section 2, a modified CPG model and a CPG network model are presented. The modified locomotion model and the CA-CMAC algorithm are shown in Section 3. Simulations and results are discussed in Section 4, and the conclusions and future works are made in Section 5.

#### 2. Modified CPG Model and CPG Network

##### 2.1. Modified CPG Model

Kimura et al. [15] constructed an oscillator based on Matsuoka’s neuron model [1, 2]. The CPG model is shown in Figure 1. This model consists of two mutually inhibiting neurons that correspond to a flexor neuron and an extensor neuron in animals, respectively. These two neurons alternately induce torque proportional to the inner state in opposite directions. Each neuron is composed of two identical spontaneously firing neurons which remain active even when an animal is at rest and this activity can persist even when synaptic transmission is blocked and is thus endogenously generated. The two neurons are coupled together in such a way that the output of one neuron suppresses the other neuron’s activity and vice versa. Together with a certain adaptation or fatigue property of the neurons, the reciprocal inhibition works to produce a stable oscillation [16]. In Figure 1, the filled black circles indicate inhibitory action and the unfilled circles represent excitatory action.