Integrative Biomimetics of Autonomous Hexapedal Locomotion

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.

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.

Continuous Online Adaptation of Bioinspired Adaptive Neuroendocrine Control for Autonomous Walking Robots

Walking animals can continuously adapt their locomotion to deal with unpredictable changing environments. They can also take proactive steps to avoid colliding with an obstacle. In this study, we aim to realize such features for autonomous walking robots so that they can efficiently traverse complex terrains. To achieve this, we propose novel bioinspired adaptive neuroendocrine control. In contrast to conventional locomotion control methods, this approach does not require robot and environmental models, exteroceptive feedback, or multiple learning trials. It integrates three main modular neural mechanisms, relying only on proprioceptive feedback and short-term memory, namely: 1) neural central pattern generator (CPG)-based control; 2) an artificial hormone network (AHN); and 3) unsupervised input correlation-based learning (ICO). The neural CPG-based control creates insect-like gaits, while the AHN can continuously adapt robot joint movement individually with respect to the terrain during the stance phase using only the torque feedback. In parallel, the ICO generates short-term memory for proactive obstacle negotiation during the swing phase, allowing the posterior legs to step over the obstacle before hitting it. The control approach is evaluated on a bioinspired hexapod robot walking on complex unpredictable terrains (e.g., gravel, grass, and extreme random stepfield). The results show that the robot can successfully perform energy-efficient autonomous locomotion and online continuous adaptation with proactivity to overcome such terrains. Since our adaptive neural control approach does not require a robot model, it is general and can be applied to other bioinspired walking robots to achieve a similar adaptive, autonomous, and versatile function.

Control of fore- and hindlimb movements and their coordination during quadrupedal locomotion across speeds in adult spinal cats

Coordinating the four limbs is critical for terrestrial mammalian locomotion. Thoracic spinal transection abolishes neural communication between the brain and spinal networks controlling hindlimb/leg movements. Several studies have shown that animal models of spinal transection (spinalization), such as mice, rats, cats and dogs recover hindlimb locomotion with the forelimbs stationary or suspended. However, we know less on the ability to generate quadrupedal locomotion after spinal transection. We collected kinematic and electromyography data in four adult cats during quadrupedal locomotion at five treadmill speeds before (intact cats) and after low-thoracic spinal transection (spinal cats). We show that adult spinal cats performed quadrupedal treadmill locomotion and modulated their speed from 0.4 m/s to 0.8 m/s but required perineal stimulation. During quadrupedal locomotion, several compensatory strategies occurred, such as postural adjustments of the head and neck and the appearance of new coordination patterns between the fore- and hindlimbs, where the hindlimbs took more steps than the forelimbs. We also observed temporal changes, such as shorter forelimb cycle/swing durations and shorter hindlimb cycle/stance durations in the spinal state. Forelimb double support periods occupied a greater proportion of the cycle in the spinal state and hindlimb stride length was shorter. Coordination between the fore- and hindlimbs was weakened and more variable in the spinal state. Changes in muscle activity reflected spatiotemporal changes in the locomotor pattern. Despite important changes in the pattern, our results indicate that biomechanical properties of the musculoskeletal system play an important role in quadrupedal locomotion and offset some of the loss in neural communication between networks controlling the fore- and hindlimbs following spinal transection.

Gait Transition from Pacing by a Quadrupedal Simulated Model and Robot with Phase Modulation by Vestibular Feedback

We propose a method to achieve autonomous gait transition according to speed for a quadruped robot pacing at medium speeds. We verified its effectiveness through experiments with the simulation model and the robot we developed. In our proposed method, a central pattern generator (CPG) is applied to each leg. Each leg is controlled by a PD controller based on output from the CPG. The four CPGs are coupled, and a hard-wired CPG network generates a pace pattern by default. In addition, we feed the body tilt back to the CPGs in order to adapt to the body oscillation that changes according to the speed. As a result, our model and robot achieve stable changes in speed while autonomously generating a walk at low speeds and a rotary gallop at high speeds, despite the fact that the walk and rotary gallop are not preprogramed. The body tilt angle feedback is the only factor involved in the autonomous generation of gaits, so it can be easily used for various quadruped robots. Therefore, it is expected that the proposed method will be an effective control method for quadruped robots.

Insect-Inspired Robots: Bridging Biological and Artificial Systems

This review article aims to address common research questions in hexapod robotics. How can we build intelligent autonomous hexapod robots that can exploit their biomechanics, morphology, and computational systems, to achieve autonomy, adaptability, and energy efficiency comparable to small living creatures, such as insects? Are insects good models for building such intelligent hexapod robots because they are the only animals with six legs? This review article is divided into three main sections to address these questions, as well as to assist roboticists in identifying relevant and future directions in the field of hexapod robotics over the next decade. After an introduction in section (1), the sections will respectively cover the following three key areas: (2) biomechanics focused on the design of smart legs; (3) locomotion control; and (4) high-level cognition control. These interconnected and interdependent areas are all crucial to improving the level of performance of hexapod robotics in terms of energy efficiency, terrain adaptability, autonomy, and operational range. We will also discuss how the next generation of bioroboticists will be able to transfer knowledge from biology to robotics and vice versa.

Investigating the role of low level reinforcement reflex loops in insect locomotion

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.

Decentralized control and local information for robust and adaptive decentralized Deep Reinforcement Learning

Decentralization is a central characteristic of biological motor control that allows for fast responses relying on local sensory information. In contrast, the current trend of Deep Reinforcement Learning (DRL) based approaches to motor control follows a centralized paradigm using a single, holistic controller that has to untangle the whole input information space. This motivates to ask whether decentralization as seen in biological control architectures might also be beneficial for embodied sensori-motor control systems when using DRL. To answer this question, we provide an analysis and comparison of eight control architectures for adaptive locomotion that were derived for a four-legged agent, but with their degree of decentralization varying systematically between the extremes of fully centralized and fully decentralized. Our comparison shows that learning speed is significantly enhanced in distributed architectures-while still reaching the same high performance level of centralized architectures-due to smaller search spaces and local costs providing more focused information for learning. Second, we find an increased robustness of the learning process in the decentralized cases-it is less demanding to hyperparameter selection and less prone to becoming trapped in poor local minima. Finally, when examining generalization to uneven terrains-not used during training-we find best performance for an intermediate architecture that is decentralized, but integrates only local information from both neighboring legs. Together, these findings demonstrate beneficial effects of distributing control into decentralized units and relying on local information. This appears as a promising approach towards more robust DRL and better generalization towards adaptive behavior.

User Local Coordinate-Based Accompanying Robot for Human Natural Movement of Daily Life

Considering the trend of aging societies, accompanying technology can help frail, elderly individuals participate in daily activities. The ideal accompanying robot should accompany the user in a proper position according to the activity scenarios and context; the prerequisite is that the accompanying robot should quickly move to a designated position and closely maintain it regardless of the direction in which the user moves. This paper proposes a user local coordinate-based strategy to satisfy this need. As a proof of concept, a novel “string-pot” approach was utilized to measure the position difference between the robot and the target. We implemented the control strategy and assessed its performance in our gait lab. The results showed that the robot can follow the user in the designated position while the user performs forward, backward, and lateral movements, turning, and walking along a curve.

Adaptive and Energy-Efficient Optimal Control in CPGs Through Tegotae-Based Feedback

To obtain biologically inspired robotic control, the architecture of central pattern generators (CPGs) has been extensively adopted to generate periodic patterns for locomotor control. This is attributed to the interesting properties of nonlinear oscillators. Although sensory feedback in CPGs is not necessary for the generation of patterns, it plays a central role in guaranteeing adaptivity to environmental conditions. Nonetheless, its inclusion significantly modifies the dynamics of the CPG architecture, which often leads to bifurcations. For instance, the force feedback can be exploited to derive information regarding the state of the system. In particular, the Tegotae approach can be adopted by coupling proprioceptive information with the state of the oscillation itself in the CPG model. This paper discusses this policy with respect to other types of feedback; it provides higher adaptivity and an optimal energy efficiency for reflex-like actuation. We believe this is the first attempt to analyse the optimal energy efficiency along with the adaptivity of the Tegotae approach.

From Motor-Output to Connectivity: An In-Depth Study of in-vitro Rhythmic Patterns in the Cockroach Periplaneta americana

The cockroach is an established model in the study of locomotion control. While previous work has offered important insights into the interplay among brain commands, thoracic central pattern generators, and the sensory feedback that shapes their motor output, there remains a need for a detailed description of the central pattern generators' motor output and their underlying connectivity scheme. To this end, we monitored pilocarpine-induced activity of levator and depressor motoneurons in two types of novel in-vitro cockroach preparations: isolated thoracic ganglia and a whole-chain preparation comprising the thoracic ganglia and the subesophageal ganglion. Our data analyses focused on the motoneuron firing patterns and the coordination among motoneuron types in the network. The burstiness and rhythmicity of the motoneurons were monitored, and phase relations, coherence, coupling strength, and frequency-dependent variability were analyzed. These parameters were all measured and compared among network units both within each preparation and among the preparations. Here, we report differences among the isolated ganglia, including asymmetries in phase and coupling strength, which indicate that they are wired to serve different functions. We also describe the intrinsic default gait and a frequency-dependent coordination. The depressor motoneurons showed mostly similar characteristics throughout the network regardless of interganglia connectivity; whereas the characteristics of the levator motoneurons activity were mostly ganglion-dependent, and influenced by the presence of interganglia connectivity. Asymmetries were also found between the anterior and posterior homolog parts of the thoracic network, as well as between ascending and descending connections. Our analyses further discover a frequency-dependent inversion of the interganglia coordination from alternations between ipsilateral homolog oscillators to simultaneous activity. We present a detailed scheme of the network couplings, formulate coupling rules, and review a previously suggested model of connectivity in light of our new findings. Our data support the notion that the inter-hemiganglia coordination derives from the levator networks and their coupling with local depressor interneurons. Our findings also support a dominant role of the metathoracic ganglion and its ascending output in governing the anterior ganglia motor output during locomotion in the behaving animal.

Effect of Thoracic Connective Lesion on Inter-Leg Coordination in Freely Walking Stick Insects

Multi-legged locomotion requires appropriate coordination of all legs with coincident ground contact. Whereas behaviourally derived coordination rules can adequately describe many aspects of inter-leg coordination, the neural mechanisms underlying these rules are still not entirely clear. The fact that inter-leg coordination is strongly affected by cut thoracic connectives in tethered walking insects, shows that neural information exchange among legs is important. As yet, recent studies have shown that load transfer among legs can contribute to inter-leg coordination through mechanical coupling alone, i.e., without neural information exchange among legs. Since naturalistic load transfer among legs works only in freely walking animals but not in tethered animals, we tested the hypothesis that connective lesions have less strong effects if mechanical coupling through load transfer among legs is possible. To do so, we recorded protraction/retraction angles of all legs in unrestrained walking stick insects that either had one thoracic connective cut or had undergone a corresponding sham operation. In lesioned animals, either a pro-to-mesothorax or a meso-to-metathorax connective was cut. Overall, our results on temporal coordination were similar to published reports on tethered walking animals, in that the phase relationship of the legs immediately adjacent to the lesion was much less precise, although the effect on mean phase was relatively weak or absent. Lesioned animals could walk at the same speed as the control group, though with a significant sideward bias toward the intact side. Detailed comparison of lesion effects in free-walking and supported animals reveal that the strongest differences concern the spatial coordination among legs. In free walking, lesioned animals, touch-down and lift-off positions shifted significantly in almost all legs, including legs of the intact body side. We conclude that insects with disrupted neural information transfer through one connective adjust to this disruption differently if they experience naturalistic load distribution. While mechanical load transfer cannot compensate for lesion-induced effects on temporal inter-leg coordination, several compensatory changes in spatial coordination occur only if animals carry their own weight.

Integrating Non-spiking Interneurons in Spiking Neural Networks

Researchers working with neural networks have historically focused on either non-spiking neurons tractable for running on computers or more biologically plausible spiking neurons typically requiring special hardware. However, in nature homogeneous networks of neurons do not exist. Instead, spiking and non-spiking neurons cooperate, each bringing a different set of advantages. A well-researched biological example of such a mixed network is a sensorimotor pathway, responsible for mapping sensory inputs to behavioral changes. This type of pathway is also well-researched in robotics where it is applied to achieve closed-loop operation of legged robots by adapting amplitude, frequency, and phase of the motor output. In this paper we investigate how spiking and non-spiking neurons can be combined to create a sensorimotor neuron pathway capable of shaping network output based on analog input. We propose sub-threshold operation of an existing spiking neuron model to create a non-spiking neuron able to interpret analog information and communicate with spiking neurons. The validity of this methodology is confirmed through a simulation of a closed-loop amplitude regulating network inspired by the internal feedback loops found in insects for posturing. Additionally, we show that non-spiking neurons can effectively manipulate post-synaptic spiking neurons in an event-based architecture. The ability to work with mixed networks provides an opportunity for researchers to investigate new network architectures for adaptive controllers, potentially improving locomotion strategies of legged robots.

Sprawling Quadruped Robot Driven by Decentralized Control With Cross-Coupled Sensory Feedback Between Legs and Trunk

Quadruped animals achieve agile and highly adaptive locomotion owing to the coordination between their legs and other body parts, such as the trunk, head, and tail, that is, body–limb coordination. This study aims to understand the sensorimotor control underlying body–limb coordination. To this end, we adopted sprawling locomotion in vertebrate animals as a model behavior. This is a quadruped walking gait with lateral body bending used by many amphibians and lizards. Our previous simulation study demonstrated that cross-coupled sensory feedback between the legs and trunk helps to rapidly establish body–limb coordination and improve locomotion performance. This paper presented an experimental validation of the cross-coupled sensory feedback control using a newly developed quadruped robot. The results show similar tendencies to the simulation study. Sensory feedback provides rapid convergence to stable gait, robustness against leg failure, and morphological changes. Our study suggests that sensory feedback potentially plays an essential role in body–limb coordination and provides a robust, sensory-driven control principle for quadruped robots.

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.

Framework for Developing Bio-Inspired Morphologies for Walking Robots

Morphology is a defining trait of any walking entity, animal or robot, and is crucial in obtaining movement versatility, dexterity and durability. Collaborations between biologist and engineers create opportunities for implementing bio-inspired morphologies in walking robots. However, there is little guidance for such interdisciplinary collaborations and what tools to use. We propose a development framework for transferring animal morphologies to robots and substantiate it with a replication of the ability of the dung beetle species Scarabaeus galenus to use the same morphology for both locomotion and object manipulation. As such, we demonstrate the advantages of a bio-inspired dung beetle-like robot, ALPHA, and how its morphology outperforms a conventional hexapod by increasing the (1) step length by 50.0%, (2) forward and upward reach by 95.5%, and by lowering the (3) overall motor acceleration by 7.9%, and (4) step frequency by 21.1% at the same walking speed. Thereby, the bio-inspired robot has longer and fewer steps that lower fatigue-inducing impulses, a greater variety of step patterns, and can potentially better utilise its workspace to overcome obstacles. Hence, we demonstrate how the framework can be used to develop legged robots with bio-inspired morphologies that embody greater movement versatility, dexterity and durability.

Neurodynamic modeling of the fruit fly Drosophila melanogaster

This manuscript describes neuromechanical modeling of the fruit fly Drosophila melanogaster in the form of a hexapod robot, Drosophibot, and an accompanying dynamic simulation. Drosophibot is a testbed for real-time dynamical neural controllers modeled after the anatomy and function of the insect nervous system. As such, Drosophibot has been designed to capture features of the animal's biomechanics in order to better test the neural controllers. These features include: dynamically scaling the robot to match the fruit fly by designing its joint elasticity and movement speed; a biomimetic actuator control scheme that converts neural activity into motion in the same way as observed in insects; biomimetic sensing, including proprioception from all leg joints and strain sensing from all leg segments; and passively compliant tarsi that mimic the animal's passive compliance to the walking substrate. We incorporated these features into a dynamical simulation of Drosophibot, and demonstrate that its actuators and sensors perform in an animal-like way. We used this simulation to test a neural walking controller based on anatomical and behavioral data from insects. Finally, we describe Drosophibot's hardware and show that the animal-like features of the simulation transfer to the physical robot.

Stepping pattern changes in the caterpillar Manduca sexta: the effects of orientation and substrate

Most animals can successfully travel across cluttered, uneven environments and cope with enormous changes in surface friction, deformability and stability. However, the mechanisms used to achieve such remarkable adaptability and robustness are not fully understood. Even more limited is the understanding of how soft, deformable animals such as tobacco hornworm Manduca sexta (caterpillars) can control their movements as they navigate surfaces that have varying stiffness and are oriented at different angles. To fill this gap, we analyzed the stepping patterns of caterpillars crawling on two different types of substrate (stiff and soft) and in three different orientations (horizontal and upward/downward vertical). Our results show that caterpillars adopt different stepping patterns (i.e. different sequences of transition between the swing and stance phases of prolegs in different body segments) based on substrate stiffness and orientation. These changes in stepping pattern occur more frequently in the upward vertical orientation. The results of this study suggest that caterpillars can detect differences in the material properties of the substrate on which they crawl and adjust their behavior to match those properties.

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

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.

Resource-efficient bio-inspired visual processing on the hexapod walking robot HECTOR

Emulating the highly resource-efficient processing of visual motion information in the brain of flying insects, a bio-inspired controller for collision avoidance and navigation was implemented on a novel, integrated System-on-Chip-based hardware module. The hardware module is used to control visually-guided navigation behavior of the stick insect-like hexapod robot HECTOR. By leveraging highly parallelized bio-inspired algorithms to extract nearness information from visual motion in dynamically reconfigurable logic, HECTOR is able to navigate to predefined goal positions without colliding with obstacles. The system drastically outperforms CPU- and graphics card-based implementations in terms of speed and resource efficiency, making it suitable to be also placed on fast moving robots, such as flying drones.

Evaluation of linear and non-linear activation dynamics models for insect muscle

In computational modelling of sensory-motor control, the dynamics of muscle contraction is an important determinant of movement timing and joint stiffness. This is particularly so in animals with many slow muscles, as is the case in insects-many of which are important models for sensory-motor control. A muscle model is generally used to transform motoneuronal input into muscle force. Although standard models exist for vertebrate muscle innervated by many motoneurons, there is no agreement on a parametric model for single motoneuron stimulation of invertebrate muscle. Although several different models have been proposed, they have never been evaluated using a common experimental data set. We evaluate five models for isometric force production of a well-studied model system: the locust hind leg tibial extensor muscle. The response of this muscle to motoneuron spikes is best modelled as a non-linear low-pass system. Linear first-order models can approximate isometric force time courses well at high spike rates, but they cannot account for appropriate force time courses at low spike rates. A linear third-order model performs better, but only non-linear models can account for frequency-dependent change of decay time and force potentiation at intermediate stimulus frequencies. Some of the differences among published models are due to differences among experimental data sets. We developed a comprehensive toolbox for modelling muscle activation dynamics, and optimised model parameters using one data set. The "Hatze-Zakotnik model" that emphasizes an accurate single-twitch time course and uses frequency-dependent modulation of the twitch for force potentiation performs best for the slow motoneuron. Frequency-dependent modulation of a single twitch works less well for the fast motoneuron. The non-linear "Wilson" model that optimises parameters to all data set parts simultaneously performs better here. Our open-access toolbox provides powerful tools for researchers to fit appropriate models to a range of insect muscles.