15
CPG-Based Control of Serpentine Locomotion of a Snake-Like Robot
of a snake-like robot was verified through both simulation and experiment.
The relation between the locomotion patterns and the CPG parameters were
additionally obtained. In addition, how to obtain a different number of locomotive S-shapes was analyzed for this kind of CPG network.
2.2 CPG Models for Generation of Rhythmic Motion
Various models of a CPG neuron have been proposed (Ekeberg 1993; Matsuoka
1985). The CPG model proposed by Ekeberg (1993) is structurally complicated
and difficult to analyze numerically. However, the model of a CPG neuron
proposed by Matsuoka (1985) has the features of continuous-time and continuous-variable in its simple structure and can thus be easily implemented into
the control of the robot. Moreover, because Matsuoka’s (1985) CPG model has
been proven mathematically to generate rhythmic output, this neuron model
was thus adopted for the control of our snake-like robot.
Several neurons are usually included in a CPG model (Matsuoka 1985).
The neurons of the CPG are affected by each other. Through the interaction
of neurons, a group of rhythmic outputs is provided. The structure of the
individual neuron model is shown in Figure 2.1a. The mathematical model
of each neuron can be expressed as
m
β ∑
τ 1 u u
q + = u 0 − v −
wy j
j=1
(2.1)
τ 2 v v
q + = y
y g
= (u) = max(0, u) )
where u is the membrane potential of the neuron; v is the variable that represents the degree of adaptation; y is the output of the CPG neuron, and its
value is always positive; u 0 is the tonic driving input; τ 1 and τ 2 are the parameters that specify the time constants for membrane potential and adaptation
degree, respectively; β is the adaptation coefficient; w is the weight between
neurons; ∑ wy j represents the input from other neurons; and m is the number of all of the neurons in the CPG model.
Usually, there are several ways to construct a CPG model by connecting different numbers of neurons. For instance, a dual-neuron model and
a tri-neuron CPG model are shown in Figures 2.1b and 2.1c, respectively.
These two CPG models have been adopted in the control systems of many
bionic robots (Kimura, Akiyama, and Sakurama 1999; Lu et al. 2005). Due to
the complicated structure and numerous computations, a CPG model with
four or more neurons is not often used in practical applications. Because the
CPG-Based Control of Serpentine Locomotion of a Snake-Like Robot
of a snake-like robot was verified through both simulation and experiment.
The relation between the locomotion patterns and the CPG parameters were
additionally obtained. In addition, how to obtain a different number of locomotive S-shapes was analyzed for this kind of CPG network.
2.2 CPG Models for Generation of Rhythmic Motion
Various models of a CPG neuron have been proposed (Ekeberg 1993; Matsuoka
1985). The CPG model proposed by Ekeberg (1993) is structurally complicated
and difficult to analyze numerically. However, the model of a CPG neuron
proposed by Matsuoka (1985) has the features of continuous-time and continuous-variable in its simple structure and can thus be easily implemented into
the control of the robot. Moreover, because Matsuoka’s (1985) CPG model has
been proven mathematically to generate rhythmic output, this neuron model
was thus adopted for the control of our snake-like robot.
Several neurons are usually included in a CPG model (Matsuoka 1985).
The neurons of the CPG are affected by each other. Through the interaction
of neurons, a group of rhythmic outputs is provided. The structure of the
individual neuron model is shown in Figure 2.1a. The mathematical model
of each neuron can be expressed as
m
β ∑
τ 1 u u
q + = u 0 − v −
wy j
j=1
(2.1)
τ 2 v v
q + = y
y g
= (u) = max(0, u) )
where u is the membrane potential of the neuron; v is the variable that represents the degree of adaptation; y is the output of the CPG neuron, and its
value is always positive; u 0 is the tonic driving input; τ 1 and τ 2 are the parameters that specify the time constants for membrane potential and adaptation
degree, respectively; β is the adaptation coefficient; w is the weight between
neurons; ∑ wy j represents the input from other neurons; and m is the number of all of the neurons in the CPG model.
Usually, there are several ways to construct a CPG model by connecting different numbers of neurons. For instance, a dual-neuron model and
a tri-neuron CPG model are shown in Figures 2.1b and 2.1c, respectively.
These two CPG models have been adopted in the control systems of many
bionic robots (Kimura, Akiyama, and Sakurama 1999; Lu et al. 2005). Due to
the complicated structure and numerous computations, a CPG model with
four or more neurons is not often used in practical applications. Because the