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Li et al. Intell Robot 2021;1(1):58-83 I http://dx.doi.org/10.20517/ir.2021.08 Page 62

Figure 2. A gated dipole model.

Another essential neurodynamics model is the gated dipole model, which is shown in Figure 2. A basic gated
dipole model is consisted of the opponent on-channel and off-channel. An arousal signal can stimulate both
on- and off- channels. The extra inputs and stimulate the on-channel and off-channel, respectively. The
dynamics of the available transmitters are characterized by

on (5)
= ( − on ) − ( + ) on
( )
off
= − off − ( + ) off (6)

where on and off arethenumberofavailabletransmittersin theon-andoff-channels, respectively; and are
the transmitter production and depletion rates, respectively; and represents the total amount of transmitter.
The on-cells receive excitatory inputs from the on-channel, while receive inhibitory inputs from its opponent
channel (off-channel). Similar to the off-channel, the off-cells receive excitatory inputs from the off-channel,
while receive inhibitory inputs from its opponent channel (on-channel). Thus, the dynamics of the on- and
off-channels are characterized by the following shunting equations

on
= − on + ( − on ) ( + ) on − ( + on ) ( + ) off (7)

off ( ) ( )
= − off + − off ( + ) off − + off ( + ) on (8)

where on and off are the activities of the on-channel and the off-channels, respectively. In the on-channel,
the available transmitters decrease exponentially to a plateau when the extra light is on, and goes back to its
initial resting level in the same manner after the offset of the light. The available transmitter in the off-channel
staysconstantsincethereisnochangeoflight. Intheon-channel, whentheextralight turnson, thereismore
available transmitter depleted, and the response of the on-cell initially overshoot. However, after the onset of
light,theavailabletransmitterdecreasesexponentiallyduetotemporaladaptation,theactivityofon-celldecays
exponentiallytoaplateau. Attheoffsetoftheextrainput, theon-andoff-channelshavethesameinput , while
the available transmitter in the on-channel is used up by the depletion during the on-light, the activity of the
on-channel appears a rebound which is called antagonistic rebound. After the extra light-off, due to temporal
adaption, the available transmitter rises exponentially to its resting level, the activity of the on-channel climbs
exponentially back also. The gated dipole model was successfully used to explain many biological phenomena
that involve agonist and antagonist interaction [27] , and had applications for robotic research of path planning
and tracking control [16,28] .