Mechanical modeling of mechanosensitive insect strain sensors as a tool to investigate exoskeletal interfaces.

During walking, sensory information is measured and monitored by sensory organs that can be found on and within various limb segments. Strain can be monitored by insect load sensors, campaniform sensilla (CS), which have components embedded within the exoskeleton. CS vary in eccentricity, size, and orientation, which can affect their sensitivity to specific strains. Directly investigating the mechanical interfaces that these sensors utilize to encode changes in load bears various obstacles, such as modeling of viscoelastic properties. To circumvent the difficulties of modeling and performing biological experiments in small insects, we developed 3-dimensional printed resin models based on high-resolution imaging of CS. Through the utilization of strain gauges and a motorized tensile tester, physiologically plausible strain can be mimicked while investigating the compression and tension forces that CS experience; here, this was performed for a field of femoral CS inDrosophila melanogaster. Different loading scenarios differentially affected CS compression and the likely neuronal activity of these sensors and elucidate population coding of stresses acting on the cuticle.

Mechanosensory encoding of forces in walking uphill and downhill: force feedback can stabilize leg movements in stick insects.

Force feedback could be valuable in adapting walking to diverse terrains, but the effects of changes in substrate inclination on discharges of sensory receptors that encode forces have rarely been examined. In insects, force feedback is provided by campaniform sensilla, mechanoreceptors that monitor forces as cuticular strains. We neurographically recorded responses of stick insect tibial campaniform sensilla to "naturalistic" forces (joint torques) that occur at the hind leg femur-tibia (FT) joint in uphill, downhill, and level walking. The FT joint torques, obtained in a previous study that used inverse dynamics to analyze data from freely moving stick insects, are quite variable during level walking (including changes in sign) but are larger in magnitude and more consistent when traversing sloped surfaces. Similar to vertebrates, insects used predominantly extension torque in propulsion on uphill slopes and flexion torques to brake forward motion when going downhill. Sensory discharges to joint torques reflected the torque direction but, unexpectedly, often occurred as multiple bursts that encoded the rate of change of positive forces (dF/dt) even when force levels were high. All discharges also showed hysteresis (history dependence), as firing substantially decreased or ceased during transient force decrements. These findings have been tested in simulation in a mathematical model of the sensilla (Szczecinski NS, Dallmann CJ, Quinn RD, Zill SN. Bioinspir Biomim 16: 065001, 2021) that accurately reproduced the biological data. Our results suggest the hypothesis that sensory feedback from the femoro-tibial joint indicating force dynamics (dF/dt) can be used to counter the instability in traversing sloped surfaces in animals and, potentially, in walking machines.NEW & NOTEWORTHY Discharges of sensory receptors (campaniform sensilla) in the hind legs of stick insects can differentially signal forces that occur in walking uphill versus walking downhill. Unexpectedly, sensory firing most closely reflects the rate of change of force (dF/dt) even when the force levels are high. These signals have been replicated in a mathematical model of the receptors and could be used to stabilize leg movements both in the animal and in a walking robot.

SNS-Toolbox: An Open Source Tool for Designing Synthetic Nervous Systems and Interfacing Them with Cyber-Physical Systems.

One developing approach for robotic control is the use of networks of dynamic neurons connected with conductance-based synapses, also known as Synthetic Nervous Systems (SNS). These networks are often developed using cyclic topologies and heterogeneous mixtures of spiking and non-spiking neurons, which is a difficult proposition for existing neural simulation software. Most solutions apply to either one of two extremes, the detailed multi-compartment neural models in small networks, and the large-scale networks of greatly simplified neural models. In this work, we present our open-source Python package SNS-Toolbox, which is capable of simulating hundreds to thousands of spiking and non-spiking neurons in real-time or faster on consumer-grade computer hardware. We describe the neural and synaptic models supported by SNS-Toolbox, and provide performance on multiple software and hardware backends, including GPUs and embedded computing platforms. We also showcase two examples using the software, one for controlling a simulated limb with muscles in the physics simulator Mujoco, and another for a mobile robot using ROS. We hope that the availability of this software will reduce the barrier to entry when designing SNS networks, and will increase the prevalence of SNS networks in the field of robotic control.

Adaptive load feedback robustly signals force dynamics in robotic model of Carausius morosus stepping.

Animals utilize a number of neuronal systems to produce locomotion. One type of sensory organ that contributes in insects is the campaniform sensillum (CS) that measures the load on their legs. Groups of the receptors are found on high stress regions of the leg exoskeleton and they have significant effects in adapting walking behavior. Recording from these sensors in freely moving animals is limited by technical constraints. To better understand the load feedback signaled by CS to the nervous system, we have constructed a dynamically scaled robotic model of the Carausius morosus stick insect middle leg. The leg steps on a treadmill and supports weight during stance to simulate body weight. Strain gauges were mounted in the same positions and orientations as four key CS groups (Groups 3, 4, 6B, and 6A). Continuous data from the strain gauges were processed through a previously published dynamic computational model of CS discharge. Our experiments suggest that under different stepping conditions (e.g., changing "body" weight, phasic load stimuli, slipping foot), the CS sensory discharge robustly signals increases in force, such as at the beginning of stance, and decreases in force, such as at the end of stance or when the foot slips. Such signals would be crucial for an insect or robot to maintain intra- and inter-leg coordination while walking over extreme terrain.

Biomechanical and Sensory Feedback Regularize the Behavior of Different Locomotor Central Pattern Generators.

This work presents an in-depth numerical investigation into a hypothesized two-layer central pattern generator (CPG) that controls mammalian walking and how different parameter choices might affect the stepping of a simulated neuromechanical model. Particular attention is paid to the functional role of features that have not received a great deal of attention in previous work: the weak cross-excitatory connectivity within the rhythm generator and the synapse strength between the two layers. Sensitivity evaluations of deafferented CPG models and the combined neuromechanical model are performed. Locomotion frequency is increased in two different ways for both models to investigate whether the model's stability can be predicted by trends in the CPG's phase response curves (PRCs). Our results show that the weak cross-excitatory connection can make the CPG more sensitive to perturbations and that increasing the synaptic strength between the two layers results in a trade-off between forced phase locking and the amount of phase delay that can exist between the two layers. Additionally, although the models exhibit these differences in behavior when disconnected from the biomechanical model, these differences seem to disappear with the full neuromechanical model and result in similar behavior despite a variety of parameter combinations. This indicates that the neural variables do not have to be fixed precisely for stable walking; the biomechanical entrainment and sensory feedback may cancel out the strengths of excitatory connectivity in the neural circuit and play a critical role in shaping locomotor behavior. Our results support the importance of including biomechanical models in the development of computational neuroscience models that control mammalian locomotion.

Sensory signals of unloading in insects are tuned to distinguish leg slipping from load variations in gait: experimental and modeling studies.

In control of walking, sensory signals of decreasing forces are used to regulate leg lifting in initiation of swing and to detect loss of substrate grip (leg slipping). We used extracellular recordings in two insect species to characterize and model responses to force decrements of tibial campaniform sensilla, receptors that detect forces as cuticular strains. Discharges to decreasing forces did not occur upon direct stimulation of the sites of mechanotransduction (cuticular caps) but were readily elicited by bending forces applied to the leg. Responses to bending force decreases were phasic but had rate sensitivities similar to discharges elicited by force increases in the opposite direction. Application of stimuli of equivalent amplitude at different offset levels showed that discharges were strongly dependent upon the tonic level of loading: firing was maximal to complete unloading of the leg but substantially decreased or eliminated by sustained loads. The contribution of cuticle properties to sensory responses was also evaluated: discharges to force increases showed decreased adaptation when mechanical stress relaxation was minimized; firing to force decreases could be related to viscoelastic "creep" in the cuticle. Discharges to force decrements apparently occur due to cuticle viscoelasticity that generates transient strains similar to bending in the opposite direction. Tuning of sensory responses through cuticular and membrane properties effectively distinguishes loss of substrate grip/complete unloading from force variations due to gait in walking. We have successfully reproduced these properties in a mathematical model of the receptors. Sensors with similar tuning could fulfil these functions in legs of walking machines.NEW & NOTEWORTHY Decreases in loading of legs are important in the regulation of posture and walking in both vertebrates and invertebrates. Recordings of activities of tibial campaniform sensilla, which encode forces in insects, showed that their responses are specifically tuned to detect force decreases at the end of the stance phase of walking or when a leg slips. These results have been reproduced in a mathematical model of the receptors and also have potential applications in robotics.

Correlation between ranges of leg walking angles and passive rest angles among leg types in stick insects.

Because of scaling issues, passive muscle and joint forces become increasingly important as limb size decreases.1-3 In some small limbs, passive forces can drive swing in locomotion,4,5 and antagonist passive torques help control limb swing velocity.6 In stance, minimizing antagonist muscle and joint passive forces could save energy. These considerations predict that, for small limbs, evolution would result in the angle range over which passive forces are too small to cause limb movement (called "resting-state range" in prior insect work4 and "area of neutral equilibrium" in physics and engineering) correlating with the limb's typical working range, usually that in locomotion. We measured the most protracted and retracted thorax-femur (ThF) angles of the pro- (front), meso- (middle), and metathoracic (hind) leg during stick insect (Carausius morosus) walks. This ThF working range differed in the three leg types, being more posterior in more posterior legs. In other experiments, we manually protracted or retracted the denervated front, middle, and hind legs. Upon release, passive forces moved the leg in the opposite direction (retraction or protraction) until it reached the most protracted or most retracted edge of the ThF resting-state range. The ThF resting-state angle ranges correlated with the leg-type working range, being more posterior in more posterior legs. The most protracted ThF walking angles were more retracted than the post-protraction ThF angles, and the most retracted ThF walking angles were similar to the post-retraction ThF angles. These correlations of ThF working- and resting-state ranges could simplify motor control and save energy. These data also provide an example of evolution altering behavior by changing passive muscle and joint properties.7.

Internal state effects on behavioral shifts in freely behaving praying mantises (Tenodera sinensis).

How we interact with our environment largely depends on both the external cues presented by our surroundings and the internal state from within. Internal states are the ever-changing physiological conditions that communicate the immediate survival needs and motivate the animal to behaviorally fulfill them. Satiety level constitutes such a state, and therefore has a dynamic influence on the output behaviors of an animal. In predatory insects like the praying mantis, hunting tactics, grooming, and mating have been shown to change hierarchical organization of behaviors depending on satiety. Here, we analyze behavior sequences of freely hunting praying mantises (Tenodera sinensis) to explore potential differences in sequential patterning of behavior as a correlate of satiety. First, our data supports previous work that showed starved praying mantises were not just more often attentive to prey, but also more often attentive to further prey. This was indicated by the increased time fraction spent in attentive bouts such as prey monitoring, head turns (to track prey), translations (closing the distance to the prey), and more strike attempts. With increasing satiety, praying mantises showed reduced time in these behaviors and exhibited them primarily towards close-proximity prey. Furthermore, our data demonstrates that during states of starvation, the praying mantis exhibits a stereotyped pattern of behavior that is highly motivated by prey capture. As satiety increased, the sequenced behaviors became more variable, indicating a shift away from the necessity of prey capture to more fluid presentations of behavior assembly.

A computational model of insect campaniform sensilla predicts encoding of forces during walking.

Control of forces is essential in both animals and walking machines. Insects measure forces as strains in their exoskeletons via campaniform sensilla (CS). Deformations of cuticular caps embedded in the exoskeleton excite afferents that project to the central nervous system. CS afferent firing frequency (i.e. 'discharge') is highly dynamic, correlating with the rate of change of the force. Discharges adapt over time to tonic forces and exhibit hysteresis during cyclic loading.In this study we characterized a phenomenological model that predicts CS discharge, in which discharge is proportional to the instantaneous stimulus force relative to an adaptive variable. In contrast to previous studies of sensory adaptation, our model (1) is nonlinear and (2) reproduces the characteristic power-law adaptation with first order dynamics only (i.e. no 'fractional derivatives' are required to explain dynamics). We solve the response of the system analytically in multiple cases and use these solutions to derive the dynamics of the adaptive variable. We show that the model can reproduce responses of insect CS to many different force stimuli after being tuned to reproduce only one response, suggesting that the model captures the underlying dynamics of the system. We show that adaptation to tonic forces, rate-sensitivity, and hysteresis are different manifestations of the same underlying mechanism: the adaptive variable. We tune the model to replicate the dynamics of three different CS groups from two insects (cockroach and stick insect), demonstrating that it is generalizable. We also invert the model to estimate the stimulus force given the discharge recording from the animal. We discuss the adaptive neural and mechanical processes that the model may mimic and the model's use for understanding the role of load feedback in insect motor control. A preliminary model and results were previously published in the proceedings of the Conference on Biohybrid and Biomimetic Systems.

Extending the Functional Subnetwork Approach to a Generalized Linear Integrate-and-Fire Neuron Model.

Engineering neural networks to perform specific tasks often represents a monumental challenge in determining network architecture and parameter values. In this work, we extend our previously-developed method for tuning networks of non-spiking neurons, the "Functional subnetwork approach" (FSA), to the tuning of networks composed of spiking neurons. This extension enables the direct assembly and tuning of networks of spiking neurons and synapses based on the network's intended function, without the use of global optimization or machine learning. To extend the FSA, we show that the dynamics of a generalized linear integrate and fire (GLIF) neuron model have fundamental similarities to those of a non-spiking leaky integrator neuron model. We derive analytical expressions that show functional parallels between: (1) A spiking neuron's steady-state spiking frequency and a non-spiking neuron's steady-state voltage in response to an applied current; (2) a spiking neuron's transient spiking frequency and a non-spiking neuron's transient voltage in response to an applied current; and (3) a spiking synapse's average conductance during steady spiking and a non-spiking synapse's conductance. The models become more similar as additional spiking neurons are added to each population "node" in the network. We apply the FSA to model a neuromuscular reflex pathway two different ways: Via non-spiking components and then via spiking components. These results provide a concrete example of how a single non-spiking neuron may model the average spiking frequency of a population of spiking neurons. The resulting model also demonstrates that by using the FSA, models can be constructed that incorporate both spiking and non-spiking units. This work facilitates the construction of large networks of spiking neurons and synapses that perform specific functions, for example, those implemented with neuromorphic computing hardware, by providing an analytical method for directly tuning their parameters without time-consuming optimization or learning.

A neuromechanical model exploring the role of the common inhibitor motor neuron in insect locomotion.

In this work, we analyze a simplified, dynamical, closed-loop, neuromechanical simulation of insect joint control. We are specifically interested in two elements: (1) how slow muscle fibers may serve as temporal integrators of sensory feedback and (2) the role of common inhibitory (CI) motor neurons in resetting this integration when the commanded position changes, particularly during steady-state walking. Despite the simplicity of the model, we show that slow muscle fibers increase the accuracy of limb positioning, even for motions much shorter than the relaxation time of the fiber; this increase in accuracy is due to the slow dynamics of the fibers; the CI motor neuron plays a critical role in accelerating muscle relaxation when the limb moves to a new position; as in the animal, this architecture enables the control of the stance phase speed, independent of swing phase amplitude or duration, by changing the gain of sensory feedback to the stance phase muscles. We discuss how this relates to other models, and how it could be applied to robotic control.

Neuromechanical Model of Rat Hindlimb Walking with Two-Layer CPGs.

This work demonstrates a neuromechanical model of rat hindlimb locomotion undergoing nominal walking with perturbations. In the animal, two types of responses to perturbations are observed: resetting and non-resetting deletions. This suggests that the animal locomotor system contains a memory-like organization. To model this phenomenon, we built a synthetic nervous system that uses separate rhythm generator and pattern formation layers to activate antagonistic muscle pairs about each joint in the sagittal plane. Our model replicates the resetting and non-resetting deletions observed in the animal. In addition, in the intact (i.e., fully afferented) rat walking simulation, we observe slower recovery after perturbation, which is different from the deafferented animal experiment. These results demonstrate that our model is a biologically feasible description of some of the neural circuits in the mammalian spinal cord that control locomotion, and the difference between our simulation and fictive motion shows the importance of sensory feedback on motor output. This model also demonstrates how the pattern formation network can activate muscle synergies in a coordinated way to produce stable walking, which motivates the use of more complex synergies activating more muscles in the legs for three-dimensional limb motion.

Static stability predicts the continuum of interleg coordination patterns in Drosophila.

During walking, insects must coordinate the movements of their six legs for efficient locomotion. This interleg coordination is speed dependent: fast walking in insects is associated with tripod coordination patterns, whereas slow walking is associated with more variable, tetrapod-like patterns. To date, however, there has been no comprehensive explanation as to why these speed-dependent shifts in interleg coordination should occur in insects. Tripod coordination would be sufficient at low walking speeds. The fact that insects use a different interleg coordination pattern at lower speeds suggests that it is more optimal or advantageous at these speeds. Furthermore, previous studies focused on discrete tripod and tetrapod coordination patterns. Experimental data, however, suggest that changes observed in interleg coordination are part of a speed-dependent spectrum. Here, we explore these issues in relation to static stability as an important aspect for interleg coordination in Drosophila We created a model that uses basic experimentally measured parameters in fruit flies to find the interleg phase relationships that maximize stability for a given walking speed. The model predicted a continuum of interleg coordination patterns spanning the complete range of walking speeds as well as an anteriorly directed swing phase progression. Furthermore, for low walking speeds, the model predicted tetrapod-like patterns to be most stable, whereas at high walking speeds, tripod coordination emerged as most optimal. Finally, we validated the basic assumption of a continuum of interleg coordination patterns in a large set of experimental data from walking fruit flies and compared these data with the model-based predictions.

Leg-local neural mechanisms for searching and learning enhance robotic locomotion.

Adapting motor output based on environmental forces is critical for successful locomotion in the real world. Arthropods use at least two neural mechanisms to adjust muscle activation while walking based on detected forces. Mechanism 1 uses negative feedback of leg depressor force to ensure that each stance leg supports an appropriate amount of the body's weight. Mechanism 2 encourages searching for ground contact if the leg supports no body weight. We expand the neural controller for MantisBot, a robot based upon a praying mantis, to include these mechanisms by incorporating leg-local memory and command neurons, as observed in arthropods. We present results from MantisBot transitioning between searching and stepping, mimicking data from animals as reported in the literature.

A Functional Subnetwork Approach to Designing Synthetic Nervous Systems That Control Legged Robot Locomotion.

A dynamical model of an animal's nervous system, or synthetic nervous system (SNS), is a potentially transformational control method. Due to increasingly detailed data on the connectivity and dynamics of both mammalian and insect nervous systems, controlling a legged robot with an SNS is largely a problem of parameter tuning. Our approach to this problem is to design functional subnetworks that perform specific operations, and then assemble them into larger models of the nervous system. In this paper, we present networks that perform addition, subtraction, multiplication, division, differentiation, and integration of incoming signals. Parameters are set within each subnetwork to produce the desired output by utilizing the operating range of neural activity, R, the gain of the operation, k, and bounds based on biological values. The assembly of large networks from functional subnetworks underpins our recent results with MantisBot.

A neural network with central pattern generators entrained by sensory feedback controls walking of a bipedal model.

A neuromechanical simulation of a planar, bipedal walking robot has been developed. It is constructed as a simplified, planar musculoskeletal model of the biomechanics of the human lower body. The controller consists of a dynamic neural network with central pattern generators (CPGs) entrained by force and movement sensory feedback to generate appropriate muscle forces for walking. The CPG model is a two-level architecture, which consists of separate rhythm generator and pattern formation networks. The biped model walks stably in the sagittal plane without inertial sensors or a centralized posture controller or a 'baby walker' to help overcome gravity. Its gait is similar to humans' and it walks at speeds from 0.850 m s-1 up to 1.289 m s-1 with leg length of 0.84 m. The model walks over small unknown steps (6% of leg length) and up and down 5° slopes without any additional higher level control actions.

Template for the neural control of directed stepping generalized to all legs of MantisBot.

We previously developed a neural controller for one leg of our six-legged robot, MantisBot, that could direct locomotion toward a goal by modulating leg-local reflexes with simple descending commands from a head sensor. In this work, we successfully apply an automated method to tune the control network for all three pairs of legs of our hexapod robot MantisBot in only 90 s with a desktop computer. Each foot's motion changes appropriately as the body's intended direction of travel changes. In addition, several results from studies of walking insects are captured by this model. This paper both demonstrates the broad applicability of this control method for robots, and suggests neural mechanisms underlying observations from walking insects.

Mantisbot is a robotic model of visually guided motion in the praying mantis.

Insects use highly distributed nervous systems to process exteroception from head sensors, compare that information with state-based goals, and direct posture or locomotion toward those goals. To study how descending commands from brain centers produce coordinated, goal-directed motion in distributed nervous systems, we have constructed a conductance-based neural system for our robot MantisBot, a 29 degree-of-freedom, 13.3:1 scale praying mantis robot. Using the literature on mantis prey tracking and insect locomotion, we designed a hierarchical, distributed neural controller that establishes the goal, coordinates different joints, and executes prey-tracking motion. In our controller, brain networks perceive the location of prey and predict its future location, store this location in memory, and formulate descending commands for ballistic saccades like those seen in the animal. The descending commands are simple, indicating only 1) whether the robot should walk or stand still, and 2) the intended direction of motion. Each joint's controller uses the descending commands differently to alter sensory-motor interactions, changing the sensory pathways that coordinate the joints' central pattern generators into one cohesive motion. Experiments with one leg of MantisBot show that visual input produces simple descending commands that alter walking kinematics, change the walking direction in a predictable manner, enact reflex reversals when necessary, and can control both static posture and locomotion with the same network.

Design process and tools for dynamic neuromechanical models and robot controllers.

We present a serial design process with associated tools to select parameter values for a posture and locomotion controller for simulation of a robot. The controller is constructed from dynamic neuron and synapse models and simulated with the open-source neuromechanical simulator AnimatLab 2. Each joint has a central pattern generator (CPG), whose neurons possess persistent sodium channels. The CPG rhythmically inhibits motor neurons that control the servomotor's velocity. Sensory information coordinates the joints in the leg into a cohesive stepping motion. The parameter value design process is intended to run on a desktop computer, and has three steps. First, our tool FEEDBACKDESIGN uses classical control methods to find neural and synaptic parameter values that stably and robustly control servomotor output. This method is fast, testing over 100 parameter value variations per minute. Next, our tool CPGDESIGN generates bifurcation diagrams and phase response curves for the CPG model. This reveals neural and synaptic parameter values that produce robust oscillation cycles, whose phase can be rapidly entrained to sensory feedback. It also designs the synaptic conductance of inter-joint pathways. Finally, to understand sensitivity to parameters and how descending commands affect a leg's stepping motion, our tool SIMSCAN runs batches of neuromechanical simulations with specified parameter values, which is useful for searching the parameter space of a complicated simulation. These design tools are demonstrated on a simulation of a robot, but may be applied to neuromechanical animal models or physical robots as well.

Neuromechanical model of praying mantis explores the role of descending commands in pre-strike pivots.

Praying mantises hunt by standing on their meso- and metathoracic legs and using them to rotate and translate (together, 'pivot') their bodies toward prey. We have developed a neuromechanical software model of the praying mantis Tenodera sinensis to use as a platform for testing postural controllers that the animal may use while hunting. Previous results showed that a feedforward model was insufficient for capturing the diversity of posture observed in the animal (Szczecinski et al 2014 Biomimetic and Biohybrid Syst. 3 296-307). Therefore we have expanded upon this model to make a flexible controller with feedback that more closely mimics the animal. The controller actuates 24 joints in the legs of a dynamical model to orient the head and translate the thorax toward prey. It is controlled by a simulation of nonspiking neurons assembled as a highly simplified version of networks that may exist in the mantid central complex and thoracic ganglia. Because of the distributed nature of these networks, we hypothesize that descending commands that orient the mantis toward prey may be simple direction-of-intent signals, which are turned into motor commands by the structure of low-level networks in the thoracic ganglia. We verify this through a series of experiments with the model. It captures the speed and range of mantid pivots as reported in other work (Yamawaki et al 2011 J. Insect Physiol. 57 1010-6). It is capable of pivoting toward prey from a variety of initial postures, as seen in the animal. Finally, we compare the model's joint kinematics during pivots to preliminary 3D kinematics collected from Tenodera.