neuroWalknet, a controller for hexapod walking allowing for context dependent behavior

Decentralized control has been established as a key control principle in insect walking and has been successfully leveraged to account for a wide range of walking behaviors in the proposed neuroWalknet architecture. This controller allows for walking patterns at different velocities in both, forward and backward direction—quite similar to the behavior shown in stick insects—, for negotiation of curves, and for robustly dealing with various disturbances. While these simulations focus on the cooperation of different, decentrally controlled legs, here we consider a set of biological experiments not yet been tested by neuroWalknet, that focus on the function of the individual leg and are context dependent. These intraleg studies deal with four groups of interjoint reflexes. The reflexes are elicited by stimulation of the femoral chordotonal organ (fCO) or groups of campaniform sensilla (CS). Motor output signals are recorded from the alpha-joint, the beta-joint or the gamma-joint of the leg. Furthermore, the influence of these sensory inputs to artificially induced oscillations by application of pilocarpine has been studied. Although these biological data represent results obtained from different local reflexes in different contexts, they fit with and are embedded into the behavior shown by the global structure of neuroWalknet. In particular, a specific and intensively studied behavior, active reaction, has since long been assumed to represent a separate behavioral element, from which it is not clear why it occurs in some situations, but not in others. This question could now be explained as an emergent property of the holistic structure of neuroWalknet which has shown to be able to produce artificially elicited pilocarpine-driven oscillation that can be controlled by sensory input without the need of explicit innate CPG structures. As the simulation data result from a holistic system, further results were obtained that could be used as predictions to be tested in further biological experiments.


Standing
In the Introduction (sect. 2), we mention six motivation units, representing states Stand-Walk, Forward-Backward, Stance-Swing, but did not address examples concerning state Stand. As, however, Standing embraces an important aspect of behavior, in the following, we will briefly sketch cases concerning state Stand that form a necessary complement to walking behavior.
At first sight, standing seems to be a simple subcase of walking, as in the current version of neuroWalknet, just switching the global velocity value to zero is sufficient. However, the following will illustrate the complexity of this behavior, and will show that the structure of neuroWalknet based on motivation units, here Stand and Walk, may provide a relatively simple way to integrate both aspects, standing and walking. Four behaviors concerning the way how to deal with external forces will be addressed.
Biological Experiments: When the intact animal is standing freely and with all six legs each on a 3D force transducer platform, spontaneous changes of the torque in one joint can be observed in all legs, and other torques may change too, but in such a way that nonetheless the position of neither legs would change. This behavior led to the interpretation that in state Stand all 18 joints are controlled by negative feedback controllers each equipped with a position integrator [1,2]. As a consequence, the body and the leg positions stay absolutely fixed although the torques of the individual legs may change considerably and apparently seem to approaching a minimum value. The network studied by Schmitz and Stein [3] may provide a way to optimize these force distributions between the legs via minimizing cuticular stress.
However, over very long temporal periods another behavioral property, called "flexibilitas cerea", studied in detail by [4] shows that leg positions may change, too, but very slowly, possibly to minimize the sum of all torques even further (review [5]). When, however, not only-as in the cases mentioned above-the own body weight has to be supported, but stronger, permanent external forces have to be counteracted, further mechanisms are activated. To study this behavior in more detail, the reactions of individual leg joints to disturbances have been recorded, while the body was fixed to a holder. In this situation, first the joint develops a significant torque to counteract the external disturbance, but over time this force is decreasing. This behavior can be interpreted as a negative feedback controller with phasic-tonic dynamics ( [4,6,7], Simulations: [8]).
As a further case-as in the interim situation between dealing with small loads (in comparison with the own body weight, [1,2]) and stronger external forces as above [4]-, experiments have been performed, where the external forces where characterized by variable elasticity. When the external elasticity was low (i. e., stiffness high)-similar to case (2)-the joint controller showed a phasic behavior. However, with lower stiffness, the joint kept its position in place for a long time (for details see [9,10]). Some of these behaviors have been simulated individually, but not jet integrated into a global structure as neuroWalknet. These could be integrated into neuroWalknet via unit Stand and may thereby in future work combine walking with standing.

Searching
Searching movements have been studied in stick insects with fixed body and partly restrained legs (e.g. [11][12][13] in detail, but also in free walking animals [14][15][16]). In neuroWalknet, searching movements are assumed to be controlled by unit Walk and, as there is no ground contact, by unit Swing. Several hypotheses have been discussed concerning the swing movement as such, either as a property of the swing controller with negative feedback that may overshoot the target position if no ground contact has been found followed by a back swing [15], or an intrinsic central oscillatory system implemented in the swing controller [17]. Another model [18] showed that simulation of active reaction could also produce searching-like oscillations. Berg et al. [19] could show that the non-spiking interneuron I4 seems to control search movement (for a discussion, see [20]). As, however, details are not known yet, we did not implement a specific version in neuroWalknet.