Figure 1.
Model of the locust LGMD system.
Left column depicts the modelled anatomical organization of the pathway to the LGMD (A–E) while the right column indicates the physiological responses to a looming stimulus in terms of the mean population activity averaged over 25 repetitions for each layer of the model. (A) is the photoreceptor layer, (B) a centre/surround architecture in the lamina, (C) the on-off neurons of the medulla, (D) the neurons connecting to the excitatory pathway of the LGMD, and (E) the LGMD/DCMD output. The data was fitted (dashed line) with the instantaneous angular size of the object in (C) and (D), and with the multiplicative model of the LGMD proposed by Gabbiani et al. (1999) in (E).
Figure 2.
Responses of the LGMD model to a looming stimulus (solid square).
(A) Upper panel: Stimulus' angular size versus time. The looming stimulus shape and parameters are indicated on the top-left corner of the graph. Middle panel: firing rate of our model over time (circles) and the corresponding fit by the multiplicative model derived from LGMD recordings (dashed line). The fit parameters and the obtained correlation values are indicated. Lower panel: Raster plot of the responses of our model over 20 trials. (B) Fit of the Peak Firing Rate of the LGMD model with eq. 1 versus the l/|v| ratio of the stimulus. (C) Time To Collision (TTC) versus the l/|v| ratio and its linear regression. The experiments were done for three different model parameters, i.e. angular threshold values, to show how this parameter affects the peak firing rate. A total of 10 experiments per l/|v| ratio and condition were performed (N = 300). Error bars indicate data variance.
Figure 3.
Analysis of shape and texture effect on the peak firing rate relative to the Time To Contact (TTC).
(A) to (C): TTC versus the l/|v| ratio is invariant to stimulus shape and texture for the entire set of l/|v| ratios; (A) concentric squares, (B) checkerboard texture, (C) solid circular stimulus. The error bars indicate data variance; r is the correlation coefficient of the data with its linear regression.
Figure 4.
Responses of the model for different approach angles of the looming stimulus.
(A) The mean number of spikes per trial is calculated for four different approach angles. At least 20 repetitions have been performed per angle/speed pair. The l/|v| ratio was varied from 10ms (circles), to 30ms (triangles) and 50ms (diamonds). (B) The difference of the TTC of peak firing rate with respect to the l/|v| ratio between a frontal approaching trajectory and one at an angle representing 75% of the visual field. Error bars indicate data variance.
Figure 5.
Mean population responses of the different layers of our model to a uniformly expanding or receding stimulus.
The right most panel depicts the modelled anatomical organization of the pathway to the LGMD (A–E) where (A) is the photoreceptor layer, (B) the lamina (the centre/surround architecture), (C) the medulla (containing the on-off neurons), (D) the neurons connecting to the excitatory pathway of the LGMD, and (E) the LGMD/DCMD output. Left panel: Average population response for each of the layers of our model (depicted in the right most diagram) to an object that is uniformly increasing in size (10 repetitions). The curves in (E) show the different responses predicted by our model (solid line) and generated by the model proposed by Gabbiani et al. (1999) (dashed grey line) to the same stimulus. Right panel: Population responses for each of the layers of our model to receding stimuli (32 repetitions). The gain of the excitatory input to the LGMD was fixed to 0.2 while 4 different gains of the inhibition were tested (0.02, 0.01, 0.005, and 0.001). (E) shows the 4 predictions for the responses of the LGMD depending on the inhibitory weight to a receding stimulus. The input data to the LGMD was fitted with the instantaneous angular size of the object in (C) and (D) (red dashed line). The half-length of the objects for both linearly increasing and receding stimulation experiments was fixed to 30cm. In the case of the receding experiment, the simulated object was moving away from the camera at 10m/s.
Figure 6.
Trajectories and behavioural analysis of the “Strider” robot controlled by our LGMD model and a fly EMD based course stabilization system.
(A) Representative traces of the behaviour of the robot. Left panel shows the behaviour of the robot controlled by the LGMD model in combination with an EMD-based course stabilization system, as in [37]. Right panel shows the behaviour in absence of course stabilization. The blue traces indicate the position of the robot and the red segments indicate the detection of imminent collisions. The black dashed lines are obtained by fitting linear segments to the robot traces, minimizing the Mean Square Error (MSE). Inserted into both panels are polar plots of the heading direction. (B) Collision detections between 20cm and 100cm away from the wall were classified as correct, those detected closer than 20cm from the wall (solid gray area in A) as missed, and collisions detected at a distance over 100cm as false positives (dashed area in A). (C) Detected collisions vs. distance. Bar colors correspond to the classification of the collision detection defined in panel B. (D) Segment length: Histogram of the length of the linear segments identified with the fitting procedure in (A). This measures the straightness of the traces of the robot in the control situation and when controlled by the combined course stabilization and collision avoidance system. The error bars indicate data variance. The data in (B) and (C) corresponds to 16 experiments with the combined course stabilization and collision avoidance system and 5 control experiments (LGMD alone) in (D).
Figure 7.
The insect robot and its test arena.
Left panel: The “Strider” robot with its components. Right panel: Schema of the arena used to test the LGMD model including the “AnTS” tracking system setup. See text for further explanation.
Figure 8.
Neural connectivity that accounts for the on-off sensitive cell responses.
This network makes use of the interaction of delayed and non-delayed excitatory and inhibitory pathways.
Figure 9.
Schema of the connectivity between the medulla and the LGMD pre-synaptic fan.
(A) Connectivity pattern for each of the neurons connecting medulla and lobula that mediate the excitatory pathway to the LGMD. In the case of our model, the angular threshold is defined by the size of the surrounding excitation (red neurons), where the edges of a looming object would sit to provide the maximum excitation (δx, δy). (B) Example of how a looming square stimulus would excite the on-off neurons in the medulla and the pre-synaptic excitatory fan of the LGMD. The activity is color-coded. The cells placed in the centre of the object maximally excited during the approach movement, and poorly otherwise.