Living organisms can act autonomously because biological neural networks process the environmental information in continuous time. Therefore, living organisms have inspired many applications of autonomous control to small-sized robots. In this chapter, a small-sized robot is controlled by a hardware artificial neural network (ANN) without software programs. Previously, the authors constructed a multilegged walking robot. The link mechanism of the limbs was designed to reduce the number of actuators. The current paper describes the basic characteristics of hardware ANNs that generate the gait for multilegged robots. The pulses emitted by the hardware ANN generate oscillating patterns of electrical activity. The pulse-type hardware ANN model has the basic features of a class II neuron model, which behaves like a resonator. Thus, gait generation by the hardware ANNs mimics the synchronization phenomena in biological neural networks. Consequently, our constructed hardware ANNs can generate multilegged robot gaits without requiring software programs.
- hardware artificial neural networks
- pulse-type hardware neuron model
- multilegged robot
- link mechanism
- class II neuron model
- synchronization phenomena
Many types of multilegged robots have been developed for various applications [1, 2, 3]. Most of these robots were bioinspired by the structures, features, and excellent functionalities of living organisms [4, 5]. Living organisms autonomously operate under the control of small-sized neural networks. Therefore, researchers have begun studying artificial neural networks (ANNs) for robot control [6, 7, 8, 9, 10]. Biological neural networks are universally characterized by oscillatory patterns of electrical activity. These patterns govern several functions of living organisms, such as heart rhythms, movements, and swallowing [11, 12]. The oscillatory patterns of living organisms can be clarified through coupled neuron models, which have two categories: class I and class II . Given that the class II model is more easily synchronized than the class I model, the class II model is applied in studies of synchronization phenomena. Famous class II neuron models include the Hodgkin-Huxley model  and Bonhoeffer-van der Pol model , mathematical neuron models that form the basis of bioinspired oscillatory pattern generation [16, 17, 18]. Most of the central pattern generators (CPGs) designed for the synchronized locomotion control of multilegged robots [6, 7, 8] are also constructed by mathematical neuron models. A CPG model using mathematical neuron models can be implemented on a field programmable gate array (FPGA). However, an FPGA board cannot be mounted on a millimeter-sized robot system because of its size. Instead, oscillatory patterns for very small robots can be generated by hardware neuron models. Hardware rings of coupled oscillators, which can generate various oscillatory patterns by using the synchronization phenomena [19, 20], have been employed as the structural elements of ANNs. However, given that most of the hardware neuron models contain inductors in their circuit architectures [19, 20, 21, 22], they are difficult to implement in an integrated circuit (IC); thus, the use of such models is disadvantageous on the circuit scale . In particular, ICs can be combined with mechanical parts of the robot by using microelectromechanical system (MEMS) technology, which can reduce the robot size to the millimeter scale.
The authors are studying hardware ANNs based on a pulse-type hardware neuron model [24, 25, 26, 27] with the same basic features as biological neurons. Specifically, this model possesses spatiotemporal summation characteristics, a threshold period, and a refractory period and generates oscillating patterns of electrical activity. Furthermore, the pulse-type hardware neuron model requires no inductors; therefore, the system is easily implemented in an IC.
Previously, the authors proposed two types of prototype multilegged robots: a quadruped robot approximately 10 cm in size  and a hexapod robot approximately 5 mm in size . Both multilegged robots move their limbs by stepping motions. A multilegged robot usually needs actuators for each joint. In our multilegged robots, the number of actuators is reduced by a link mechanism, and the gait is controlled by a hardware ANN. The hardware ANN consists of 4 excitatory synaptic models, 16 inhibitory synaptic models, and 8 cell body models for the quadruped robot , and 12 inhibitory synaptic models and 4 cell body models for the hexapod robot [27, 28, 29].
This chapter describes the basic characteristics of the hardware ANNs that generate the gait of multilegged robots. After briefly introducing both types of multilegged robots, it discusses the hardware ANNs and mathematically describes the characteristics of the pulse-type hardware neuron model. The oscillation characteristic of the model requires a negative resistance and is described in a phase plane. The synchronization characteristics of connected hardware ANNs are also discussed. Finally, the hardware ANNs are validated in locomotion tests of the multilegged robot.
2. Multilegged robots
2.1. Quadruped robot
The width, length, and height dimensions of the quadruped robot are 130, 140, and 90 mm, respectively (see Figure 1 ). The quadruped robot is constructed from mechanical and electrical components. The mechanical components comprise the body frame, four servo motors, link mechanisms, and four legs. The electrical components consist of the control board, hardware ANNs, and battery. The limbs and body frame are made from aluminum base alloy 2017 and aluminum base alloy 5052, respectively. The mechanical parts are fabricated by a computerized numerical control machining system. The four legs of the quadruped robot system are actuated by four servo motors, and the stepping motion of each leg is generated by the link mechanisms. The servo motor is an HSR-8498HB (Hitec Multiplex Japan) model, which generates sufficient maximum torque to actuate the robot. The mechanical components of the quadruped robot are detailed in .
Figure 2 shows the relative phase difference of the quadruped gait pattern under a given driving rhythm of the actuators. The relative phase difference is referenced to the left forelimb (0°). Under various actuation rhythms, the quadruped robot generates different gait patterns. Figure 2 displays five typical gait patterns: walk, trot, pace, bound, and gallop. The directional changes and turning of the quadruped robot are not realized at present. The robot gait is easily controlled by software programs implemented on a control board. However, in the proposed robot control, the software program for generating the locomotion rhythms is replaced by a hardware ANN.
2.2. Hexapod robot
The fabricated hexapod robot is displayed in Figure 3 . The robot is 4.0 mm wide, 2.7 mm long, and 2.5 mm high. Two ground (GND) wires and eight signal wires (all made of copper) extend above the robot. The hexapod robot walks when the signal wires are connected to the hardware ANNs. The structure and stepping motion of the robot mimic those of an ant. The ant-like stepping motion is a series of tripod configurations in which two groups of three legs alternate between swing and stance phases (see Figure 5 in ). The hexapod robot comprises the frame parts, small-sized actuators, and link mechanisms. The small-sized actuators are constructed from artificial muscle wire. All mechanical parts are made from silicon wafers of various thicknesses (100, 200, 385, and 500 μm). The parts were shaped by dry etching by photolithography-based inductively coupled plasma . The small-sized actuator consists of four pieces of artificial muscle wire, as well as the shaft, rotor, and GND wire. The frame components and rotors are connected by the artificial muscle wire, which functions as a shape memory alloy . The artificial muscle wire is BMX50 (BioMetal® Helix, available online at
Figure 4 shows the leg motions of the hexapod robot. The artificial muscle wire shrinks at high temperatures and extends at low temperatures. Therefore, when an electric current is applied through the wire, the resulting heat displaces the four pieces of artificial muscle wire, and the rotor rotates. The wire is cooled by stopping the current flow. Thus, the actuator is rotated by changing the sequence of the input current. The link mechanism transmits the rotational movements of the rotor to the three legs on one side. This design requires only two small-sized actuators (one on each side of the robot) to actuate the six legs.
Figure 5 shows the relative phase differences of the hexapod gait patterns for different driving rhythms of the actuator. To heat the artificial muscle wires, an input pulse of amplitude 50–100 mA, period 2 s, and width 0.5 s is required. Therefore, the hexapod robot requires 2 s to complete one locomotion cycle. As mentioned above, the length of the artificial muscle wire depends on the temperature. Specifically, the wire shrinks when heated and extends when cooled. Heating the artificial muscle wires from A to D and from D to A in Figure 4 drives the hexapod robot forward and backward, respectively. The locomotion pattern is a 180° phase shift at each side, which mimics the locomotion of an ant. If the input pulse is narrower than 0.5 s, the thermal heating by the driving current is insufficient to shrink the wire. By contrast, if the input pulse is wider than 2 s, the thermal heating by the driving current is excessive, and the cooling is insufficient to extend the wire.
3. Hardware artificial neural networks
The hardware ANNs are based on a pulse-type hardware neuron model of class II, specifically, a Hodgkin-Huxley model and a Bonhoeffer-van der Pol model . This section describes the circuit diagrams and the basic characteristics of the pulse-type hardware neuron model. The synchronization phenomena of the hardware ANNs are also discussed.
3.1. Pulse-type hardware neuron model
Figure 6 shows the circuit diagrams of the pulse-type hardware neuron model, which comprises a cell body model and two synaptic models. The cell body model ( Figure 6a ) includes a voltage control-type negative resistance, an equivalent inductance, resistors R 1 and R 2, and a membrane capacitor CM . The voltage control-type negative resistance circuit with equivalent inductance consists of an n-channel MOSFET M 1, a p-channel MOSFET M 2, a voltage source VA , a leak resistor RL , another resistor RG , and a capacitor CG . The cell body model generates oscillating patterns of electrical activity vM (t). vG (t) is the voltage between both ends of capacitor CG . vM (t) and vG (t) are, respectively, governed by the following simultaneous differential equations.
A time-dependent nonlinear current i Λ(vM (t),vG (t)) flows through the negative resistance circuit. The governing equations of i Λ(vM (t),vG (t)) under the three possible conditions are given by the following:
where VTn and VTp are the threshold voltages of the n and p-channel MOSFETs, respectively. VGp is the gate voltage of MOSFET M 2. β is the conductance constant of the MOSFETs (with carrier mobility μ, dielectric constant ε of the gate insulator, oxide channel thickness t, channel width Wand channel length L). Although the value of β differs in the n-type and p-type MOSFETs, Eqs. (3–5) become intractable unless the βs are approximated by the same value. The complex case with different βs is considered in the following numerical analysis.
The circuit parameters of the cell body model are as follows: CG = 4.7 μF, CM = 470 nF, R G = 680 kΩ, R L = 10 kΩ, R 1 = 15 kΩ, R 2 = 20 kΩ, and R in = 50 kΩ. The voltage source VA = 3.5 V. The authors have used the BSS83 and BSH205 for M 1 and M 2, respectively. These circuit parameters are set to allow the cell body model to generate oscillation with amplitude 3.5 V, period 8 s, and width of 2 s.
Figure 6b and c displays the circuits of the excitatory and inhibitory synaptic models, respectively. The spatiotemporal summation characteristics of the synaptic model resemble those of biological systems. The output vS (t) of the synaptic model is the spatiotemporal summation of the output voltages of the cell body model vM (t). vES (t) and vIS (t) are described by the following equations.
The spatial summation is performed by the inverting amplifier, whose amplification factor imitates the synaptic weight. Suffixes E and I denote excitatory and inhibitory, respectively. The temporal summation is realized by the operational amplifier RC integrator. The resistors and capacitors in the synaptic model are valued at 1 MΩ and 1 pF, respectively. The operational amplifier is an RC4558D.
3.2. Basic characteristics of the cell body model
Figure 7 shows the negative resistance characteristics of the cell body model. The N-shape characteristic indicates that the negative resistance is voltage control type negative resistance. When 2.3 < vM (t) < 3.5 (vG (t) = 2.5 V), the negative resistance is provided by the negative resistance circuit. The amplitude of the negative resistance characteristic can be changed by varying the vG (t).
Figure 8 shows the phase plane of the cell body model. The attractor (solid line in Figure 8 ) is the limit cycle. The shapes of the vM (t)- and vG (t)-nullclines confirm the class II neuron characteristics of the cell body model. The same characteristics are observed in the Hodgkin-Huxley and Bonhoeffer-van der Pol models. The vM (t)- and vG (t)-nullclines intersect at the equilibrium point. When the equilibrium point dvM /dvG > 0, the cell body model becomes unstable and self-oscillates. By contrast, when dvM /dvG < 0, the cell body model becomes stable. In this chapter, the equilibrium point is set to the unstable condition dvM /dvG > 0. The unstable and stable conditions can be switched by varying VA .
3.3. Excitatory-inhibitory neuron pair model
The excitatory-inhibitory neuron pair model comprises two cell body models and two synaptic models and generates several oscillatory patterns by using the synchronization phenomena.
Figure 9 shows the circuit diagram of the excitatory-inhibitory neuron pair model. The cell body models are mutually coupled by the synaptic models. The excitatory synaptic model sums the excitatory inputs (output voltage of the cell body model vME and the external input voltage vextinE ). Meanwhile, the inhibitory synaptic model sums the inhibitory inputs (output voltage of the cell body model vMI and the external input voltage vextinI ). Both cell body models are assigned the same circuit parameters (The synchronization phenomena and oscillatory patterns of the mutually coupled excitatory-inhibitory neuron pair model are provided in ).
The synchronization phenomena of the excitatory-inhibitory neuron pair circuit depend on the connection type of the synaptic model. When the synaptic model connection is excitatory or inhibitory, the synchronization is in-phase and anti-phase, respectively. The excitatory-inhibitory neuron pair circuit was incorporated into the hardware ANN for the quadruped robot.
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 excitatory-inhibitory 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 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 is replaced by a CMOS with an equivalent circuit. In the CMOS circuit, RL and RG in Figure 6a become the MOS resistors M 4C and M 3C, 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, M 1C , M 2C : W/L = 10, M 3C : W/L = 0.1, and M 4C : W/L = 0.3 for the cell body model and C ESC = C ISC = 1 pF, M ES1C-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 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 v ext1, v ext2, v ext3, and v ext4 of the trigger pulse (the forward walk sequence in Figure 5 ). Before applying the external trigger pulse, the output sequence was v I1, vI2 , vI4 , and vI3 . After applying the pulse, it was corrected to v I1, 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.
4. Results and discussion
In this section, the gait rhythms generated by the hardware ANNs are tested in a multilegged robot.
4.1. Locomotion of the quadruped robot
Figure 14 shows the discrete circuits of the hardware ANNs. The electrical components were mounted on a frame-retardant type 4 (FR4) circuit board (The circuit diagram is shown in Figures 6 and 9 .) The hardware ANN consisted of four sets of an excitatory-inhibitory neuron pair model connected as shown in Figure 10a . The width and length of the mounted hardware ANNs are 100 and 80 mm, respectively; therefore, the hardware ANNs are sufficiently small to install on the quadruped robot.
Figure 15 shows the quadruped robot mounted with the hardware ANN circuit board. The quadruped robot system is 130 mm wide, 140 mm long, 100 mm high, and 530 g in weight. The power consumption of the hardware ANNs was approximately 360 mWh.
Walk sequence is the basic motion of the quadruped robot. Figure 16 shows the generated gait pattern and leg motion of a quadruped robot. Panels (a) and (b) show the driving rhythm of the (measured) walking gait pattern and the leg motion of the robot, respectively. Under the waveform shown in Figure 16a , the legs move as shown in Figure 16b . In other words, the generated driving rhythm is a four-phase alternating oscillation with the sequence left foreleg (LF), right hindleg (RH), right foreleg (RF), and left hindleg (LH).
The locomotion of a walking quadruped robot driven by the hardware ANNs is captured in Figure 17 . The motion patterns resemble those of a quadruped animal, thus confirming that the driving rhythms generated by the hardware ANNs can realize proper walking behavior. Moreover, the hardware ANNs can generate various oscillatory patterns without requiring computer programs.
Under an external trigger pulse, the constructed hardware ANNs can change the gait pattern of the quadruped robot. A walk-to-trot gait change is illustrated in Figure 18 . The external trigger pulse is generated by a waveform generator applied to the input port (see Figure 10 ). Considering that the hardware ANNs can memorize the applied gait rhythm, the quadruped robot can switch its locomotion pattern by applying an external input to its hardware ANNs.
4.2. Locomotion of the hexapod robot
Figure 19 shows the IC of the hardware ANNs. Panel (a) shows the layout pattern of the bare IC chip of the hardware ANNs. The design rule of the bare IC chip is four-metal two-poly CMOS (0.35 μm). The chip is sized (2.45 × 2.45) mm2. The hardware ANNs are connected as shown in Figure 13 . Four cell body models are mutually coupled by 12 inhibitory synaptic models. The driving waveform of the hexapod robot is generated by the outputs extracted from the hardware ANNs and the current mirror circuit. Four trigger pulse input ports are also extracted from the hardware ANNs. The sequence of the locomotion rhythm depends on the timing of the single external trigger pulse. Figure 19b shows the constructed bare IC chip, which is fixed to the cavity of an FR4 circuit board by wire bonding.
Figure 20 shows the measured output waveform of the designed IC. The hardware ANNs can generate the locomotion rhythms observed in living organisms. To sufficiently heat and cool the artificial muscle wires, the pulse width, period, and amplitude were set to 0.5 s, 2 s, and 75 mA, respectively. The connected helical artificial muscle wires are approximately 50 Ω. As shown in Figure 20 , the output waveform effectively actuates the actuator of the hexapod robot. The approximate power consumptions of the hardware ANNs and the current mirror circuit were 0.708 and 488 mWh, respectively. The former almost matches the power consumption of biological neural networks, but the power consumption of the artificial muscle wire was excessive.
The circuit in Figure 19b was mounted on the hexapod robot. Figure 21 shows snapshots of the walking hexapod robot system. The driving waveforms generated by the hardware ANNs actuate the hexapod robot, thus enabling successful locomotion.
This chapter describes the basic characteristics of the hardware ANNs as gait generators of multilegged robots.
The main findings are summarized below.
The basic component of the hardware ANN (namely, the cell body model) has the basic features of a class II neuron model.
Gait generation by the hardware ANNs uses synchronization phenomena, as observed in biological neural networks.
The hardware ANNs successfully guided the locomotion of two types of multilegged robots without requiring software programs or analog digital converters.
Currently, the authors consider replacing the artificial muscle wire by an electrostatic actuator to reduce the actuating power. The electrostatic actuator will be powered by high-voltage silicon photovoltaic cells installed in the microrobot system. In future works, the ANNs, actuator, power source system, and sensory system will be directly integrated into the silicon frame parts of the microrobot.
The authors like to thank Prof. Liwei Lin and the members of Lin laboratory. The VLSI chip in this study was fabricated by Digian Technology Inc. This work was supported by VLSI Design and Education Center (VDEC), the University of Tokyo in collaboration with Synopsys Inc., Cadence Design Systems Inc., and Mentor Graphics Inc. The fabrication of the hexapod robot was supported by the Research Center for Micro Functional Devices, Nihon University. The authors appreciate to all above supports.