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A challenge in robotics is to control interactions with the environment by modulating the stiffness of a manipulator’s joints. Smart servos are controlled with proportional feedback gain that is analogous to torsional stiffness of an animal’s joint. In animals, antagonistic muscle groups can be temporarily coactivated to stiffen the joint to provide greater opposition to external forces. However, the joint properties for which coactivation increases the stiffness of the joint remain unknown. In this study, we explore possible mechanisms by building a mathematical model of the stick insect tibia actuated by two muscles, the extensor and flexor tibiae. Muscle geometry, passive properties, and active properties are extracted from the literature. Joint stiffness is calculated by tonically activating the antagonists, perturbing the joint from its equilibrium angle, and calculating the restoring moment generated by the muscles. No reflexes are modeled. We estimate how joint stiffness depends on parallel elastic element stiffness, the shape of the muscle activation curve, and properties of the force-length curve. We find that co-contracting antagonist muscles only stiffens the joint when the peak of the force-length curve occurs at a muscle length longer than that when the joint is at equilibrium and the muscle force versus activation curve is concave-up. We discuss how this information could be applied to the control of a smart servo actuator in a robot leg. 

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. 

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. 

It is unknown precisely how the nervous system of invertebrates combines multiple sensory inputs to calculate more abstract quantities, e.g., combining the angle of multiple leg joints to calculate the position of the foot relative to the body. In this paper, we suggest that non-spiking interneurons (NSIs) in the nervous system could calculate such quantities and construct a neuromechanical model to support the claim. Range fractionated sensory inputs are modeled as multiple integrate-and-fire neurons. The NSI is modeled as a multi-compartment dendritic tree and one large somatic compartment. Each dendritic compartment receives synaptic input from one sensory neuron from the knee and one from the hip. Every dendritic compartment connects to the soma. The model is constructed within the Animatlab 2 software. The neural representation of the system accurately follows the true position of the foot. We also discuss motivation for future research, which includes modeling other hypothetical networks in the insect nervous system and integrating this model into task-level robot control. 

This article is a historical perspective on how the study of the neuromechanics of insects and other arthropods has inspired the construction, and especially the control, of hexapod robots. Many hexapod robots’ control systems share common features, including: 1. Direction of motor output of each joint (i.e. to flex or extend) in the leg is gated by an oscillatory or bistable gating mechanism; 2. The relative phasing between each joint is influenced by proprioceptive feedback from the periphery (e.g. joint angles, leg load) or central connections between joint controllers; and 3. Behavior can be directed (e.g. transition from walking along a straight path to walking along a curve) via low-dimensional, broadly-acting descending inputs to the network. These distributed control schemes are inspired by, and in some robots, closely mimic the organization of the nervous systems of insects, the natural hexapods, as well as crustaceans. Nearly a century of research has revealed organizational principles such as central pattern generators, the role of proprioceptive feedback in control, and command neurons. These concepts have inspired the control systems of hexapod robots in the past, in which these structures were applied to robot controllers with neuromorphic (i.e. distributed) organization, but not neuromorphic computational units (i.e. neurons) or computational hardware (i.e. hardware-accelerated neurons). Presently, several hexapod robots are controlled with neuromorphic computational units with or without neuromorphic organization, almost always without neuromorphic hardware. In the near future, we expect to see hexapod robots whose controllers include neuromorphic organization, computational units, and hardware. Such robots may exhibit the full mobility of their insect counterparts thanks to a ‘biology-first’ approach to controller design. This perspective article is not a comprehensive review of the neuroscientific literature but is meant to give those with engineering backgrounds a gentle introduction into the neuroscientific principles that underlie models and inspire neuromorphic robot controllers. A historical summary of hexapod robots whose control systems and behaviors use neuromorphic elements is provided. Robots whose controllers closely model animals and may be used to generate concrete hypotheses for future animal experiments are of particular interest to the authors. The authors hope that by highlighting the decades of experimental research that has led to today’s accepted organization principles of arthropod nervous systems, engineers may better understand these systems and more fully apply biological details in their robots. To assist the interested reader, deeper reviews of particular topics from biology are suggested throughout.

 

Load sensing is critical for walking behavior in animals, who have evolved a number of sensory organs and neural systems to improve their agility. In particular, insects measure load on their legs using campaniform sensilla (CS), sensory neurons in the cuticle of high-stress portions of the leg. Extracellular recordings from these sensors in a behaving animal are difficult to collect due to interference from muscle potentials, and some CS groups are largely inaccessible due to their placement on the leg. To better understand what loads the insect leg experiences and what sensory feedback the nervous system may receive during walking, we constructed a dynamically-scaled robotic model of the leg of the stick insect Carausius morosus. We affixed strain gauges in the same positions and orientations as the major CS groups on the leg, i.e., 3, 4, 6A, and 6B. The robotic leg was mounted to a vertically-sliding linear guide and stepped on a treadmill to simulate walking. Data from the strain gauges was run through a dynamic model of CS discharge developed in a previous study. Our experiments reveal stereotypical loading patterns experienced by the leg, even as its weight and joint stiffness is altered. Furthermore, our simulated CS strongly signal the beginning and end of stance phase, two key events in the coordination of walking. 

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. 

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. 

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.