Gait movement of human being is a kind of rhythmic movement of organisms generated by a central pattern generator (CPG). Biology found that a CPG is a biological neural circuit located in the abdominal ganglia of invertebrates or the spinal cord of vertebrates. For human being's motion control system, a CPG generates rhythmic outputs by the way of self-oscillation, driving the rhythmic movement of corresponding body parts. It can also regulate the gait movement outputs in real time with the sensory feedback by receiving external environment information it senses, ensuring the adaptability and stability of rhythmic gait movement^{[1, 2]}. As a typical rhythmic movement, gait movement, with the property of cyclic and phase complementary, has different kinds of movement frequencies and modes that can be regulated by CPG to help adapt to the environment^{[3, 4, 5]}. Previous studies on the CPG gait movement control model and the related theory play a significant role in building human being's motion control theory and its engineering application^{[6, 7, 8, 9, 10, 11, 12]}.

Attention selection is such an important property of human visual perception that researchers have put forward in a number of models on the basis of the physiological experimental data and analysis^{[13, 14, 15, 16, 17, 18]}, which were used to explain attention selection mechanism and functions.

The model proposed by Chik et al.^[17] contains two central neurons and several peripheral neurons, which are used to simulate basic and advanced activities of neurons in the visual cortex.

In this paper, the neurons that generate the attention selection signals were considered as central neurons, and the model that was built can realize the selection of two or more goals. Qu et al.^[18] amended the model proposed in the paper by Chik et al.^[17], taking into account the orientation selectivity in the primary visual cortex.

The Japanese researcher Matsuoka^{[19, 20, 21]} proposed the neural oscillator model containing two mutually inhibitory neurons, which can be used to simulate biological properties of CPG. They further analyzed the relationships between model parameters and the gait movement frequency and amplitude when the neural oscillator was applied to robot control^[21]. The gait movement model that Taga et al.^{[22, 23]} and Taga^[23] built included the musculoskeletal system, the neural oscillator, and the signal transmission network structures. They researched on the adaptation of the model in different environments and tasks, and the model generated gait movement outputs with a stable cycle when applied to computer simulation. Zhang et al.^[24] and Zhang and Zhu^{[25, 26]} built a new musculoskeletal control model based on functional electrical stimulation^[25] and its application in engineering, which can be used to assist the paraplegia to walk normally^[26]. Dong et al.^[27] amended the CPG model raised by Zhang et al.^[24] and gained a stable CPG gait movement output by simplifying the input of CPG network. The model by Dong and Wang^[28] built the relationship between input signal and internal model parameters, which reflected the regulation of control signal from the cerebral cortex to gait movement output.

The attention selection model, brought up in Refs. ^[17] and ^[18], is based on the H-H model by Hodgkin and Huxley^[29], comprising two central neurons and a population of peripheral neurons, in which the central neurons are responsible for receiving the synaptic input from peripheral neurons, and the synchronization phenomena between central neurons and peripheral neurons can be taken as the target selection of attention. To acquire the attention selection signal, the attention selection model with only one central neuron can be obtained by simplifying the peripheral neurons and their input into central neurons, which can be expressed as follows:

Click Browse formula

In this expression, I_ion indicates the neuronal ion currents, including the sodium current, the potassium current, and the leakage current, I_ext indicates the external current, and I_syn indicates the synaptic current that the central neuron receives. The detailed expression is as follows:

Click Browse formula

Click Browse formula

Click Browse formula

Moreover, ω₁ indicates the strength of connections that the central neurons have with their neighboring neurons, which is set as a unique constant. The parameter V_syn, exc indicates the reverse voltage of excitatory synapse conductance. The parameter R_a means the linear summation of synaptic current response of all the peripheral neurons at every moment, indicating the synapse current input central neuron received from all the peripheral neurons.

In real life, human beings practice different kinds of gait movements with different modes and frequencies, such as running, walking, and stepping. Attention selection mechanism is an important property of human motion, in which an attention selection signal is generated by processing and analyzing the external environment information obtained during the gait movement, which can adjust the gait movement frequency and amplitude in turn, regulating human being's gait movement finally.

The leg musculoskeletal model of human being's gait movement, widely used in engineering applications, is shown in Fig. 1(a)^{[22, 23]}. This model was developed based on the muscle model^{[30, 31]}. A total of 6 joints and 18 muscles exist in this musculoskeletal model, in which the muscle groups Ⅰ and Ⅱ represent stretching muscles and contracting muscles of the hips, respectively, the muscle groups Ⅲ and Ⅳ represent extension muscles of the knee, the muscle groups Ⅴ and Ⅵ represent extension muscles in the ankle, and the muscle groups Ⅶ, Ⅷ, and Ⅸ represent bi-articular muscles, which are used to connect two joints.

Fig. 1 Structure of CPG model under condition of attention selection[22, 23]

Figure options

The structure figure of the CPG model under the condition of attention selection based on the leg musculoskeletal model^[23], Matsuoka oscillator neurons^{[19, 20, 21]}, and the attention selection mechanism^{[17, 18]} is shown in Fig. 1(b)^{[22, 23]}. This model contains 6 Matsuoka neural oscillators, each of which includes two neurons, corresponding to the hip joints, knee joints, and ankle joints in both legs, respectively. The rhythmic output of oscillator neurons is used to generate joint torque and stiffness by complex calculations to drive the stretching muscles and body movement in corresponding joints. Thus, the gait movement is generated accordingly. From that, we can see gait movement of human beings can be described as rhythmic output of oscillator neurons in the CPG model, in which bi-articular muscles are driven by the combined effect of their corresponding neurons in these two joints.

The existing studies^[32] have already revealed that the gait movement would change, if the stable gait movement of the CPG model is affected by attention selection, while the new gait movement pattern can maintain a certain time and then revert to the original gait movement. At the same time, the regulation role of attention selection signal varies with different frequencies,

Click Browse formula

In this article, further research is conducted on the control strategy of attention selection on the CPG movement. As the internal parameters and structure of the CPG model control the gait movement output mode, the changes of parameters and structure should cause the changes in the frequency and amplitude of gait movement accordingly. To achieve a control on gait movement, the CPG model is amended under the condition of attention selection, optimizing the connections between attention selection and internal parameters of the CPG model, which enhances the regulation of attention selection on the model's internal parameters.

The amended model can achieve the control on the CPG model made by attention selection in three ways, making the CPG model adaptable and controllable, which have significant meanings for engineering application such as gait control for robots.

Control strategy of CPG gait movement under condition of attention selection 961 The amended CPG model under the condition of attention selection is shown in (5). In this equation, k_f denotes the induction gain, k_t is the tonic input gain, x_i are the two states of neurons (extensor muscle and constrictor muscle), v_i is the adaptability in the recovery process, ω_ij is the connection weight between neurons, τ is the state parameter, T is the adaptation parameter, r_i is the tonic input, V_L is the noise coefficient, and r_as is the attention selection signal, while A, V₀, and V_r denote normalized parameters of attention selection signal. More details can be found in Refs. ^[17]-^[18], ^[22]-^[24], and ^[28].

The amended CPG model under conditions of attention selection contains the CPG model based on the Matsuoka neural oscillators and the attention selection model. The CPG model parameters are adjusted under the effect of attention selection signals, which will regulate the oscillator neurons' output accordingly, achieving the regulation on gait movement ultimately.

The amplitude of neurons' output is controlled by the tonic input r_i in the CPG model, which means that the stride and limb posture are controlled by the joint torque and stiffness. Therefore, the stride and motion trail of gait movement are regulated by r_i as the torquestiffness parameter. The frequency of neurons' output is controlled by the oscillator parameters τ and T , indicating that the regulation on the gait movement frequency is realized by τ and T as the frequency parameters. The connection weight ω_ij controls the amplitude and frequency of oscillator neurons' output, which is adopted as the mode parameter to achieve the selection of gait movement mode.

The amendment to the CPG model under the condition of attention selection is realized by building the connection relationships between attention selection and CPG model parameters. The connection expression equation between the attention selection signal r_as and the CPG model parameters is the fifth to ninth equations in (5). In the amended model, r_{as_ b} is the integration of attention selection signal r_as, b and c are the regulation coefficients to the model parameters τ and T by attention selection, while ai is the regulation coefficient to the tonic input r_i of neuron i by attention selection. The parameter h_ij indicates the coefficient matrix to the connection weight ω_ij regulated by attention selection. The regulation on the model parameter by the attention selection signal is expressed through the expression above.

The control strategy on the CPG gait movement under the condition of attention selection can be studied in the following three aspects in the model. The study on the regulation effect on the gait movement frequency by changing the model parameters τ and T is conducted by introducing r_{as_ b} into the model parameters τ and T . The study on the regulation effect on the gait movement amplitude by changing the tonic input is conducted by introducing r_{as_ b} into the tonic input r_i. The study on the regulation effect on the gait movement mode is made by adjusting the neurons connection weight ω_ij in the CPG model by introducing r_{as_ b} into ω_ij .

The stable rhythmic output mode of the CPG model can be generated by adjusting its parameters^{[22, 23, 24, 28]}, which can embody not only the rhythmicity of the leg gait movement but also the complementary property of the output. The gait movement output mode with the expected frequency can be realized by adjusting the relevant parameters. The ideal attention selection signals are obtained by normalizing the parameters of the attention selection model, which are set according to the previous studies^{[17, 18]}.

According to the simulation results, the CPG model parameters τ and T can change under the regulation of attention selection signal, which can cause frequency changes of gait movement output consequentially. As shown in Fig. 2, time intervals of attention selection are labeled by dashed lines from 3.5 s to 7.5 s. Under the effect of attention selection, the frequency of CPG gait movement output y₁ and y₇ increase with the original amplitude. At the same time, the CPG gait movement output keeps the rhythm and complementary characteristics.

Fig. 2 Frequency changes of CPG model gait movement output and rhythmicity of leg gait movement under condition of attention selection

Figure options

The gait movement output of all neurons in the CPG model is shown in Fig. 3, which has consistent change laws of gait movement with y₁ and y₇. It is seen that the adjustment of model parameters τ and T can regulate the frequency of CPG gait movement output, without affecting the gait movement output amplitude.

Fig. 3 CPG gait movement output under condition of attention selection

Figure options

The spatial movement amplitude of legs is different when human beings are in different gait movements. According to the simulation results, the tonic input r_i can be controlled by the attention selection signal to regulate the amplitude of gait movement of neuron i in the CPG model. Take data in Fig. 4 as an example, under the effect of attention selection, the amplitudes of oscillator neurons output of hip joints (y₁, y₇, y₂, y₈) increase obviously, while the amplitudes of the rest of the oscillators remain constant. The regulation on the amplitude of gait movement in the model increases the controllability of CPG gait movement.

Fig. 4 Amplitude changes of CPG model gait movement output when attention selection regulates model parameter ri (a1 = 10, a2 = 10, a3 = 1, a4 = 1, a5 = 2, a6 = 1, a7 = 10, a8 = 10, a9 = 1, a10 = 1, a11 = 2, a12 = 1)

Figure options

The simulation results show that the connection weight changes when attention selection comes into play, and remains until the effect disappears, which causes the movement output mode to change sequentially in the same way. The movement output changes of four neurons y₁, y₇, y₂, and y₈ are listed in Fig. 5, from which it is seen that attention selection can control the CPG gait movement by adjusting the connection weight ω_ij .

Fig. 5 Output mode changes of CPG model gait movement when attention selection regulates connection weight ωij

Figure options

Every single research on the regulation effect of attention selection is carried out under the condition that the other two regulation effects remain small. In this paragraph, these three kinds of regulation effect are combined together to study the control strategy on the CPG gait movement, which can achieve the ideal gait movement mode by simulation. A part of neuron gait movement output is shown in Fig. 6, in which the CPG model keeps yielding stable gait movement before attention selection impacted.

Fig. 6 Part of neuron gait movement output of CPG model

Figure options

Figure 7 shows the data of a study^[33], in which the surface of electromyography signal of muscle groups in legs when walked naturally on flat ground was gained by the experiment carried out on 30 normal young people. They are right/left tibia anterior muscle, right/left biceps femur muscle, and right/left medial gastrocnemius from U₁ , U₂ , · · · , U₆ in turn, which correspond to muscle groups Ⅴ/Ⅳ/Ⅸ in the musculoskeletal model. This experiment showed that the electromyography activities in natural gait movement of normal young people are with characteristics of rhythm and alternation by left and right. The comparison of the gait movement period before attention selection impacted in Fig. 6 and the electromyography shown in Fig. 7 shows that they both have a consistent rhythmic cycle and complementary characteristics, which indicates that the simulation results are highly consistent with the experimental results.

Fig. 7 Original electromyography of muscle groups in both legs[33]

Figure options

Based on the amendment of the CPG model under attention selection with the neural oscillator theory, the present paper optimizes the connection between the attention selection signal and the CPG model parameters, building the interconnections of attention selection and the tonic input ri, the model parameters τ and T , and the connection weight ω_ij , which therefore enhances the regulation effect on the CPG inside parameters by attention selection. Moreover, the control strategy of CPG gait movement under the condition of attention selection is also studied. The simulation results are as follows. First, the adjustment of model parameters τ and T can regulate the frequency of gait movement, but cannot change the amplitude of gait movement. Second, the changes of the tonic input r_i can regulate the amplitude of CPG gait movement under attention selection. Third, the output modes of CPG gait movement under the condition of attention selection shift when attention selection impacts on the connection weight ω_ij . In conclusion, the output of gait movement in different modes can be realized by adjusting the regulation parameters and method. In addition, the simulation results and the experimental data are with the same features, which is also consistent with the biological reality.