Decentralized control of insect walking: A simple neural network explains a wide range of behavioral and neurophysiological results

Abstract

Controlling the six legs of an insect walking in an unpredictable environment is a challenging task, as many degrees of freedom have to be coordinated. Solutions proposed to deal with this task are usually based on the highly influential concept that (sensory-modulated) central pattern generators (CPG) are required to control the rhythmic movements of walking legs. Here, we investigate a different view. To this end, we introduce a sensor based controller operating on artificial neurons, being applied to a (simulated) insectoid robot required to exploit the "loop through the world" allowing for simplification of neural computation. We show that such a decentralized solution leads to adaptive behavior when facing uncertain environments which we demonstrate for a broad range of behaviors never dealt with in a single system by earlier approaches. This includes the ability to produce footfall patterns such as velocity dependent "tripod", "tetrapod", "pentapod" as well as various stable intermediate patterns as observed in stick insects and in Drosophila. These patterns are found to be stable against disturbances and when starting from various leg configurations. Our neuronal architecture easily allows for starting or interrupting a walk, all being difficult for CPG controlled solutions. Furthermore, negotiation of curves and walking on a treadmill with various treatments of individual legs is possible as well as backward walking and performing short steps. This approach can as well account for the neurophysiological results usually interpreted to support the idea that CPGs form the basis of walking, although our approach is not relying on explicit CPG-like structures. Application of CPGs may however be required for very fast walking. Our neuronal structure allows to pinpoint specific neurons known from various insect studies. Interestingly, specific common properties observed in both insects and crustaceans suggest a significance of our controller beyond the realm of insects.

Fig 1

(a) Indian stick insect Carausius morosus. (b) Robot Hector which is used in simulation for testing the control principles derived.

Fig 2. Controller for one leg.

Artificial neurons are depicted as colored circles. Sensory input structure for swing: green, sensory input structure for stance: blue. Common output: red. Coordination channels: brown for rules 1–3, ocher for rule 5, light yellow for rule P (Pearson rule, see Supporting information) with connections in pink (Supporting information). Motivation units: light grey (swing–stance), dark grey (forward–backward), white (central units). SRP net and its’ connections (pink) are detailed in Supporting information (S2 PDF). Joint alpha (α): Pro–protractor, Ret–retractor; joint beta (β): Lev–levator, Dep–depressor; joint gamma (γ): Flex–flexor, Ext–extensor. Black dots: inhibitory synapses, open black triangles: excitatory synapses. For detailed explanations see text and Supporting information.

Fig 3

A-H. Footfall patterns for velocities driven by 50 mV, 40 mV, 30 mV, 25 mV, 20 mV, 15 mV 10 mV and 8 mV (G: the latter after disturbance of MR at about 8–11 s, see prolonged swing) and 8 mV (H: a stable pattern reached after more than 240 s). Apart from the last two runs all started with the same leg configuration. The corresponding transient phases for the last two runs are given in Supporting information (S3F and S3G Fig). Black bars show swing mode, Legs: FR front right, MR middle right, HR hind right, FL front left, ML middle left, HL hind left. For videos see Supporting information S1–S8 Videos. Abscissa: Time (s).

Fig 4. Footfall patterns with the velocity neuron set to 15 mV.

Upper panel (A) as in Fig 3F, after a stable pattern has been reached; lower panel which, after a disturbance of the right middle leg during swing, represents a mirror image version. B) illustrates which leg pairs are coupled together in either case.

Fig 5. Duration of lag 3L1 (time lag between beginning of swing in hind leg and beginning of swing in the following front leg), vs. period (duration of swing plus stance) as proposed by Graham [34].

Numbers attached to the red dots mark the velocity input (mV) given. Abscissa: time (s). The thin dashed line indicates slope 1. Bold dashed lines show the average data from Graham [34], his Fig 7; time *0.1). For short periods Graham observed a slight asymmetry between left and right legs, not observed in our simulations.

Fig 6. Negotiation of Curves.

A) Trajectory of leg end points during stance in curve walking (left) with respect to a body centered frame of reference, plotted over time window 50 s – 100 s. On the right, trajectories of leg end points during straight walking is shown for comparison. Dots mark position of leg basis. Front legs up. B) Footfall pattern. Global velocity neuron set to 45 mV, theta 75 deg. Ordinate: legs as in Fig 3, abscissa: time (s). For details see Methods.

Fig 7

A-D. Footfall patterns, backward walking for velocity neuron set to 50 mV, 40 mV, 30 mV or 20 mV (Supporting information S11–S14 Videos). Abscissa: time (s). For further details see Fig 3.

Fig 8

A-D. Simulation of experiments of deafferented locusts [69]. Black bars show activation of depressor muscle output (> 0 mV). A) all thoracic ganglia treated with pilocarpine, B) only prothoracic ganglion treated, C) only mesothoracic ganglion treated, D) only metathoracic ganglion treated. Last five periods show stable state. Abscissa: time (s).

Fig 9. Simulation of experiments with stick insects, one leg (FL) walking on a treadmill (velocity neuron set to 30 mV), while the other legs are deafferented and treated with pilocarpine (in Borgmann et al. [72], only ipsilateral legs were recorded).

Black bars show retractor muscle output (> 0 mV). For further velocities see Supporting information S4 Fig Abscissa: time (s).

Fig 10. Simulation of experiments where stick insects walk tethered on a treadmill with selected legs standing on force transducer platforms.

Shown are activations of retractor motor neurons (> 7 mV) over time (s) in A) to C). Corresponding experimental results [76,86] are given in D, E, F, respectively: Phase histograms of the beginning of the retraction in the walking legs (shown in white), force histograms of the maximum force in the standing legs (dark). Reference leg starting with the beginning of the retraction movement. In A) and D) both front legs and both middle legs are walking while both hind legs are standing. B) and E) shows left legs walking and right legs standing. C) and F) show both front legs standing, both middle legs and both hind legs walking [76,86]. Walking velocity neurons set to 30 mV.

Fig 11. Ring net.

A) Angle delta (leg position, angle alpha, and walking direction, theta) determines the contribution of alpha joint and gamma joint during stance. Column 1 (right) represents angle delta in spatial coding. Depending on desired velocity of the leg (vel) and angle delta the motor output for the retractor (O2), for flexor (O3) and for extensor (O4) are computed. Protraction (O1) is not yet implemented. Units marked with green dots show, as an example case, activation of the net by a delta value input of spatial code 6 (e.g., theta = 0 degrees and alpha = 25 mV). B) Organisation of ring net, schematically. Input: layers 1–3, green. Input delta = alpha–theta. The analog value delta (in mV) is transformed to the spatial coding version (Fig 2, box “spatial coding”), which is then given to the circle marked green. Output: Layer 4 (red, grey) controls the alpha joint (red: retractor, unit O2, green: protractor, unit O1, not used in the current version). Layer 5 (blue, yellow) controls the gamma joint (blue: flexor, unit O3, yellow: extensor, unit O4). Letter C (for numbers of circle units, Fig 11A) is not shown in Fig 11B.

Fig 12. Single leg controllers (shown in brown) and their connection via coordination rules (from [15]).

L1, L2, L3 left front, middle, and hind leg, respectively. R1, R2, and R3 stand for the corresponding right legs. The question mark indicates that there are ambiguous data concerning influence 3.