5.2 Neural Control of Walking Machines
5.2.1 The Neural Oscillator Network
Neural oscillators for the walking machines have often been studied [29, 65, 131, 132, 140, 197]. Inter alia, H. Kimura et al. [111] constructed a neural
(a)
Fig. 5.22. Comparison of the “hysteresis effects” with different self-connection weights at the output neuron. (a) The output signal (dashed line) decreases from
≈ +1 to ≈ −1 when the input signal (solid line) is inactive (≈ −1). This effect corresponds to a very small turning angle of the walking machine in avoiding an ob-stacle. (b) The output signal (dashed line) stays longer at≈+1 and then decreases to≈ −1 when the input signal (solid line) is inactive. This effect corresponds to an appropriate turning angle of the walking machine in avoiding an obstacle. (c) The output signal (dashed line) stays longest at≈+1 and then decreases to≈ −1. This effect corresponds to a larger turning angle of the walking machine in avoiding an obstacle
oscillator network with four neurons. The network has been applied to con-trol the four-legged walking machineT EKKEN where each hip joint of the machine is driven by one of the neurons. J. Ayers et al. [12] used a
neu-5.2 Neural Control of Walking Machines 91
Fig. 5.23. (a)–(d) The input signals (solid line) of the sensors and the output signals (dashed line) of the output neurons. Due to the inhibitory synapses and the high activity of Output1 (a), the Output2 (b) is still inactive although Input2 is active. (c) and (d) show the switching condition between Output1 and Output2 when the activity of Input1 is low, meaning “no obstacles detected” and the activity of Input2 is still high, meaning “obstacles detected”. This phenomenon is responsible for escaping from sharp corners as well as deadlock situations
ral oscillator consisting of so-called elevator and depressor synergies. They are arranged as an endogenous pacemaker network with reciprocal inhibi-tion, and are used to generate walking patterns for the eight-legged Lobster robot. Here a so-called two-neuron network [154] is employed. It is used as a CPG [101, 113, 171, 198] which follows one principle of locomotion control in walking animals (cf. Sect. 2.3). It generates the rhythmic movement for basic locomotion of the walking machines without the requirement of sensory feedback. The network structure is shown in Fig. 5.24.
The network parameters are experimentally adjusted via the ISEE to ac-quire the optimal oscillating output signals for generating locomotion of the walking machines. The parameter set is selected with respect to the dynam-ics of the two-neuron system staying near the Neimark–Sacker bifurcation, where the quasi-periodic attractors occur [154]. Examples of different oscillat-ing output signals generated by different weights and bias terms are presented in Fig. 5.25.
Figure 5.25 shows that such a network has the capability to generate var-ious oscillating outputs depending on the weights and the bias terms. For instance, if the bias terms are small (cf. Fig. 5.25a), the initial output
sig-B2 B1
W2 W3
W4
W1
Output2 Output1
Fig. 5.24.The structure of the two-neuron network
nals will oscillate with a very small amplitude and then the amplitude will increase during a transient time, while the amplitude of the output signals for large bias terms is high right from the beginning (cf. Fig. 5.25b). Fur-thermore, different bias terms also affect the waveform of the output signals.
Different self-connection weights result in different amplitude and waveforms of the oscillating output signals (compare Figs. 5.25c and 5.25d). To adjust the oscillating frequency of the outputs, one can also control the connection weights between two output neurons; i.e., for small connection weights (ab-solute values), the output signals oscillate at low frequency, while the large connection weights (absolute values) make the outputs oscillate at high fre-quency with different waveforms (compare Figs. 5.25e and 5.25f). However, one can utilize this modifiable oscillating output behavior with respect to the weights and the bias terms in the field of neural control, e.g., for controlling the type of walking and the walking speed of legged robots.
Here, the actual parameter set for the network controller is given byB1= B2= 0.01,W1 =−0.4,W2 = 0.4 andW3=W4 = 1.5, where the sinusoidal outputs correspond to a quasi-periodic attractor (Fig. 5.26). They are used to drive the motor neurons directly to generate the appropriate locomotion of the walking machines [74, 128, 130].
The output of neuron 1 (Output1) is used to drive all thoracic joints and an additional backbone joint, and the output of neuron 2 (Output2) is used to drive all basal joints (and all distal joints for a three DOF leg). This oscil-lator network is implemented on a PDA with an update frequency of 25.6 Hz.
It generates a sinusoidal output with a frequency of approximately 0.8 Hz (Fig. 5.27) analyzed by the free scientific software package Scilab-3.0.6
By using asymmetric connections from the oscillator outputs to corre-sponding motor neurons, a typical trot gait for a four-legged walking machine and a typical tripod gait for a six-legged walking machine are obtained which
6 See also: http://scilabsoft.inria.fr/. Cited 18 December 2005.
5.2 Neural Control of Walking Machines 93
Fig. 5.25. The oscillating output signals of neurons 1 (dashed line) and 2 (solid line) from the network having different weights and bias terms. (a) For small bias terms (B1 =B2 = 0.0001) while W1 =−0.4,W2 = 0.4 andW3 =W4 = 1.5. (b) For larger bias terms (B1 =B2 = 0.1) and all weights as in (a). (c) For smaller self-connection weights (W3=W4= 1) whileW1=−0.4,W2= 0.4 and bias terms
= 0.01. (d) For larger self-connection weights (W3 = W4 = 1.7) and all weights together with bias terms as in (c). (e) For smaller absolute values of connection weights between two output neurons (W1=−0.25,W2= 0.25) whileW3=W4= 1.5 and the bias terms = 0.01. (f) For larger absolute values of connection weights between two output neurons (W1 =−0.8,W2= 0.8) and all weights together with bias terms as in (e)
(a) (b)
Fig. 5.26.(a) The output signals of neurons 1 (dashed line) and 2 (solid line) from the neural oscillator network. (b) The phase space with quasi-periodic attractor of the oscillator network which is used to drive the legs of the machines
(a) (b)
Fig. 5.27. (a) The sinusoidal output generated by the neural oscillator network is recorded for 5 seconds. (b) The FFT spectrum of the recorded sinusoidal out-put shows that the outout-put has the eigenfrequency around 4 Hz. Then, the walking frequency of the machines can be approximately (4/5) 0.8 Hz
are similar to the gaits of a cat and a cockroach, respectively (described in Sect. 2.3). In a trot gait as well as a tripod gait, (Figs. 5.28 and 5.29), the diagonal legs are paired and move together (see also Sect. 2.3). These typical gaits will enable efficient forward motions.