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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] .
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