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Abstract During behavior, the work done by actuators on the body can be resisted by the body's inertia, elastic forces, gravity, or viscosity. The dominant forces that resist actuation have major consequences on the control of that behavior. In the literature, features and actuation of locomotion, for example, have been successfully predicted by nondimensional numbers (e.g. Froude number and Reynolds number) that generally express the ratio between two of these forces (gravitational, inertial, elastic, and viscous). However, animals of different sizes or motions at different speeds may not share the same dominant forces within a behavior, making ratios of just two of these forces less useful. Thus, for a broad comparison of behavior across many orders of magnitude of limb length and cycle period, a dimensionless number that includes gravitational, inertial, elastic, and viscous forces is needed. This study proposes a nondimensional number that relates these four forces: the phase shift (ϕ) between the displacement of the limb and the actuator force that moves it. Using allometric scaling laws, ϕ for terrestrial walking is expressed as a function of the limb length and the cycle period at which the limb steps. Scale-dependent values of ϕ are used to explain and predict the electromyographic (EMG) patterns employed by different animals as they walk. 

Abstract Insects are highly capable walkers, but many questions remain regarding how the insect nervous system controls locomotion. One particular question is how information is communicated between the ‘lower level’ ventral nerve cord (VNC) and the ‘higher level’ head ganglia to facilitate control. In this work, we seek to explore this question by investigating how systems traditionally described as ‘positive feedback’ may initiate and maintain stepping in the VNC with limited information exchanged between lower and higher level centers. We focus on the ‘reflex reversal’ of the stick insect femur-tibia joint between a resistance reflex (RR) and an active reaction in response to joint flexion, as well as the activation of populations of descending dorsal median unpaired (desDUM) neurons from limb strain as our primary reflex loops. We present the development of a neuromechanical model of the stick insect ( Carausius morosus ) femur-tibia (FTi) and coxa-trochanter joint control networks ‘in-the-loop’ with a physical robotic limb. The control network generates motor commands for the robotic limb, whose motion and forces generate sensory feedback for the network. We based our network architecture on the anatomy of the non-spiking interneuron joint control network that controls the FTi joint, extrapolated network connectivity based on known muscle responses, and previously developed mechanisms to produce ‘sideways stepping’. Previous studies hypothesized that RR is enacted by selective inhibition of sensory afferents from the femoral chordotonal organ, but no study has tested this hypothesis with a model of an intact limb. We found that inhibiting the network’s flexion position and velocity afferents generated a reflex reversal in the robot limb’s FTi joint. We also explored the intact network’s ability to sustain steady locomotion on our test limb. Our results suggested that the reflex reversal and limb strain reinforcement mechanisms are both necessary but individually insufficient to produce and maintain rhythmic stepping in the limb, which can be initiated or halted by brief, transient descending signals. Removing portions of this feedback loop or creating a large enough disruption can halt stepping independent of the higher-level centers. We conclude by discussing why the nervous system might control motor output in this manner, as well as how to apply these findings to generalized nervous system understanding and improved robotic control. 

We introduce Drosophibot, a hexapod robot with legs designed based on the Common fruit fly, Drosophila melanogaster, built as a test platform for neural control development. The robot models anatomical aspects not present in other, similar bio-robots such as a retractable abdominal segment, insect-like dynamic scaling, and compliant feet segments in the hopes that more similar biomechanics will lead to more similar neural control and resulting behaviors. In increasing biomechanical modeling accuracy, we aim to gain further insight into the insect’s nervous system to inform the current model and subsequent neural controllers for legged robots. 

This work shows one way to tune a servomotor controller to make it perform in a similar way to a biomechanical model of an insect leg joint. Three key metrics were considered: the equilibrium angle of the joint as a function of antagonistic inputs; the dynamics of the free response when perturbed; and the dynamics of active motions. We model an insect leg joint as a hinge actuated by a pair of antagonistic linear Hill muscles that drive a rigid distal leg segment. Passive forces from the exoskeleton are also modeled as passive viscoelastic elements (PVE). We approximate parameter values for the model based on the biomechanics literature, and then dynamically scale them to the scale of our robot, Drosophibot. We show how to tune the servo’s control mapping and feedback gain to mimic the dynamically scaled model of the animal joint. 

Leg coordination is important for walking robots. Insects are able to effectively walk despite having small metabolisms and size, and understanding the neural mechanisms which govern their walking could prove useful for improving legged robots. In order to explore the possible neural systems responsible for inter-leg coordination, leg positional data for walking fruit flies of the species Drosophila melanogaster was recorded, where one individual leg was amputated at the base of the tibia. These experiments have shown that when amputated, the remaining stump oscillates in a speed-dependent manner. At low walking speeds there is a wide range of possible stump periods, and this variance collapses down to a minimum as walking speed increases. We believe this behavior can be explained by noisy pattern generation networks (CPGs) within the legs, with intra-leg load feedback and inter-leg global signals stabilizing the network. In this paper, this biological data will be analyzed so that a simplified neuromechanical model can be designed in order to explain this behavior.