20
Biologically Inspired Robotics
From the above discussion, we know that it is more convenient to obtain
a uniform output from the CPG network by feeding one of the CPG signals
back to the first module. This kind of closed-loop network can be applied to
snake-like robot control without any additional modification on the output
signals of the CPG. Thus, the system computation is decreased dramatically.
Moreover, the characteristic of the phase difference as stated in Equation
(2.5) can be used to control the number of S-shapes in snake-like robot locomotion. Therefore, this network with the feedback connection is more suitable for the control of a snake-like robot.
2.3.2 Analysis of a CPG Network
To figure out how to employ the CPG network to control locomotion of a
snake-like robot, the influence of each CPG parameter on the signal output
has to be investigated. In Matsuoka’s early work (Matsuoka 1985, 1987), some
partial and qualitative conclusions on the influence of the parameters on the
oscillator behavior were indicated. But a detailed analysis of the CPG characteristics to generate the desired rhythmic signals in the network was not provided. Because there is a strong coupling relation between the parameters
and the output, herein a numerical method is used to obtain the characteristics of the CPG model. To determine the influence of each parameter on the
output, the output characteristic is studied with the value of one parameter
varied in a certain range while the rest of the parameters remain unchanged.
From the mathematical model of the CPG model in Equation (2.1), the
output is mainly determined by several parameters. The influence of these
parameters on the amplitude and the period of oscillator output are primarily investigated. A cyclic inhibitory CPG model with three neurons is
selected to study the influence of parameters, and the numerical results are
shown in Figure 2.5. The value ranges of these parameters conform to the
mathematical analysis for stable oscillation in Matsuoka (1987), where every
parameter should meet the following numerical condition:
⎧ Z /(1 + ≤
β) 1
⎪
⎨
(2.6)
⎩ 1 τ τ 2
⎪ + 1 / < Z
Summarizing these characteristics, a concise conclusion can be obtained
from Table 2.2. Two important linear relations can be easily found: output
amplitude increases linearly with the driving input u 0 ; time constant τ 1 , τ 2
keeps a linear relation with the period of output while the value of τ 1 /τ 2 is a
constant. However, if τ 1 /τ 2 is not a constant, the linear relation between time
constant τ 1 , τ 2 and the period of output will be broken. The change of parameter u 0 does not influence the period of the output, whereas the change of τ 1 ,
τ 2 has no influence on the amplitude of the output. Furthermore, the basic
Biologically Inspired Robotics
From the above discussion, we know that it is more convenient to obtain
a uniform output from the CPG network by feeding one of the CPG signals
back to the first module. This kind of closed-loop network can be applied to
snake-like robot control without any additional modification on the output
signals of the CPG. Thus, the system computation is decreased dramatically.
Moreover, the characteristic of the phase difference as stated in Equation
(2.5) can be used to control the number of S-shapes in snake-like robot locomotion. Therefore, this network with the feedback connection is more suitable for the control of a snake-like robot.
2.3.2 Analysis of a CPG Network
To figure out how to employ the CPG network to control locomotion of a
snake-like robot, the influence of each CPG parameter on the signal output
has to be investigated. In Matsuoka’s early work (Matsuoka 1985, 1987), some
partial and qualitative conclusions on the influence of the parameters on the
oscillator behavior were indicated. But a detailed analysis of the CPG characteristics to generate the desired rhythmic signals in the network was not provided. Because there is a strong coupling relation between the parameters
and the output, herein a numerical method is used to obtain the characteristics of the CPG model. To determine the influence of each parameter on the
output, the output characteristic is studied with the value of one parameter
varied in a certain range while the rest of the parameters remain unchanged.
From the mathematical model of the CPG model in Equation (2.1), the
output is mainly determined by several parameters. The influence of these
parameters on the amplitude and the period of oscillator output are primarily investigated. A cyclic inhibitory CPG model with three neurons is
selected to study the influence of parameters, and the numerical results are
shown in Figure 2.5. The value ranges of these parameters conform to the
mathematical analysis for stable oscillation in Matsuoka (1987), where every
parameter should meet the following numerical condition:
⎧ Z /(1 + ≤
β) 1
⎪
⎨
(2.6)
⎩ 1 τ τ 2
⎪ + 1 / < Z
Summarizing these characteristics, a concise conclusion can be obtained
from Table 2.2. Two important linear relations can be easily found: output
amplitude increases linearly with the driving input u 0 ; time constant τ 1 , τ 2
keeps a linear relation with the period of output while the value of τ 1 /τ 2 is a
constant. However, if τ 1 /τ 2 is not a constant, the linear relation between time
constant τ 1 , τ 2 and the period of output will be broken. The change of parameter u 0 does not influence the period of the output, whereas the change of τ 1 ,
τ 2 has no influence on the amplitude of the output. Furthermore, the basic