3.4. Hardware neural networks for quadruped robot

Figure 10 shows the four sets of the excitatory-inhibitory neuron pair model connected by an inhibitory synaptic model. Figure 10a shows the connection diagram, and Figure 10b and c shows the output waveforms during the walking and trotting sequences in Figure 2, respectively. The motion sequences are initiated by an external trigger pulse. These results show that to generate a locomotion rhythm of the quadruped robot, the four sets of the excitatoryinhibitory neuron pair model must be connected to the inhibitory synaptic model. The sequences of the gait pattern differ between walk and gallop and between pace/bound and trot. The sequences are easily changed by changing the external trigger pulse.

#### 3.5. Hardware neural networks for hexapod robot

Figure 10. Four sets of excitatory-inhibitory neuron pair models connected by an inhibitory synaptic model. (a) Connection diagram, (b) output waveform when the external trigger pulse generates a walk sequence, (c) output waveform when the external trigger pulse generates a trot sequence (The waveforms in panels (b) and (c) are the simulation results).

38 Advanced Applications for Artificial Neural Networks

Figure 11 shows the circuit diagrams of the pulse-type hardware neuron model with CMOS circuit. Given that circuit of Figure 6 is difficult to construct in an IC with a limited layout area, it

Figure 11. Circuit diagram of the pulse-type hardware neuron model (equivalent CMOS circuit). (a) Cell body model, (b) excitatory synaptic model, and (c) inhibitory synaptic model.

is replaced by a CMOS with an equivalent circuit. In the CMOS circuit, RL and RG in Figure 6a become the MOS resistors M4C and M3C, respectively. Furthermore, the operational amplifier is replaced by a simple current mirror circuit. However, the basic characteristics of Figure 11 are unaffected by changing the circuit elements. The circuit parameters are CGC = 10 μF, CMC = 2.2 μF, M1C, M2C: W/L = 10, M3C: W/L = 0.1, and M4C: W/L = 0.3 for the cell body model and CESC = CIS<sup>C</sup> = 1 pF, MES1C-3C, and MIS1C-5C: W/L = 1 for the synaptic model. The voltage sources of the cell body and synaptic models are VAC = 3.0 V and VDD = 3.0 V, respectively.

Figure 12a shows the connection diagram of the inhibitory mutual coupling in the pulse-type hardware neuron model. Four sets of the model are coupled by 12 inhibitory synaptic models. Figure 12b shows a typical output waveform of the equivalent CMOS circuit. The inhibitory mutual coupling generates anti-phase synchronization, thus confirming that this coupling will achieve four anti-phase synchronizations. However, the random sequence of the output waveforms must be corrected to the repetitive sequence as shown in Figure 5. The correction is made by applying a single external trigger pulse.

Figure 12. Inhibitory mutual coupling of four pulse-type hardware neuron models. (a) Connection diagram of inhibitory mutual coupling and (b) simulated output waveform of the CMOS equivalent circuit (anti-phase synchronization).

Gait Generation of Multilegged Robots by using Hardware Artificial Neural Networks http://dx.doi.org/10.5772/intechopen.70693 41

is replaced by a CMOS with an equivalent circuit. In the CMOS circuit, RL and RG in Figure 6a become the MOS resistors M4C and M3C, respectively. Furthermore, the operational amplifier is replaced by a simple current mirror circuit. However, the basic characteristics of Figure 11 are unaffected by changing the circuit elements. The circuit parameters are CGC = 10 μF, CMC = 2.2 μF, M1C, M2C: W/L = 10, M3C: W/L = 0.1, and M4C: W/L = 0.3 for the cell body model and CESC = CIS<sup>C</sup> = 1 pF, MES1C-3C, and MIS1C-5C: W/L = 1 for the synaptic model. The voltage sources

Figure 12a shows the connection diagram of the inhibitory mutual coupling in the pulse-type hardware neuron model. Four sets of the model are coupled by 12 inhibitory synaptic models. Figure 12b shows a typical output waveform of the equivalent CMOS circuit. The inhibitory mutual coupling generates anti-phase synchronization, thus confirming that this coupling will achieve four anti-phase synchronizations. However, the random sequence of the output waveforms must be corrected to the repetitive sequence as shown in Figure 5. The correction is

Figure 12. Inhibitory mutual coupling of four pulse-type hardware neuron models. (a) Connection diagram of inhibitory mutual coupling and (b) simulated output waveform of the CMOS equivalent circuit (anti-phase synchronization).

of the cell body and synaptic models are VAC = 3.0 V and VDD = 3.0 V, respectively.

made by applying a single external trigger pulse.

40 Advanced Applications for Artificial Neural Networks

Figure 13. Applying the external trigger pulse to inhibitory mutual coupling of pulse-type hardware neuron models corrected by an external trigger pulse. (a) Connection diagram of inhibitory mutual coupling, (b) output waveform under an external trigger pulse (forward walk sequence in Figure 5), and (c) output waveform under an external trigger pulse (bound sequence in Figure 2). The waveforms in panels (b) and (c) are simulation results.

Figure 13 shows the inhibitory mutual coupling of the pulse-type hardware neuron models subjected to a single external trigger pulse. (a) The connection diagram of this system, and (b) a typical output waveform under the sequence vext1, vext2, vext3, and vext<sup>4</sup> of the trigger pulse (the forward walk sequence in Figure 5). Before applying the external trigger pulse, the output sequence was vI1, vI2, vI4, and vI3. After applying the pulse, it was corrected to vI1, vI2, vI3, and vI4. Therefore, the single-pulse correction realizes the forward and backward locomotion patterns in Figure 5. Note that walking and galloping in Figure 2 and forward and backward locomotion patterns in Figure 5 are all realized by the four-phase alternating oscillation and differ only in the order of their output sequences. Figure 13c shows a typical output waveform when the sequence of the external trigger pulse is vext1, vext2 and (simultaneously) Vext3, Vext4 (the bound sequence in Figure 2). The bound sequence is not realized by the external trigger pulse. The inhibitory mutual coupling of the pulse-type hardware neuron model cannot by itself generate the locomotion patterns of trot, pace, and bound because these motions are two-phase alternating oscillations.
