Legged animals still outperform many terrestrial robots due to the complex interplay of various component subsystems. Centralization is a potential integrated design axis to help improve the performance of legged robots in variable terrain environments. Centralization arises from the coupling of multiple limbs and joints through mechanics or feedback control. Strong couplings contribute to a whole-body coordinated response (centralized) and weak couplings result in localized responses (decentralized). Rarely are both mechanical and neural couplings considered together in designing centralization. In this study, we use an empirical information theory-based approach to evaluate the emergent centralization of a hexapod robot. We independently vary the mechanical and neural coupling through adjustable joint stiffness and variable coupling of leg controllers, respectively. We found an increase in centralization as neural coupling increased. Changes in mechanical coupling did not significantly affect centralization during walking, but did change the total information processing of the neuromechanical control architecture. Information-based centralization increased with robotic performance in terms of cost of transport and speed, implying that this may be a useful metric in robotic design.

Convergent and divergent structures in the networks that make up biological brains are found across many species and brain regions at various spatial scales. Neurons in these networks fire action potentials, or "spikes," whose precise timing is becoming increasingly appreciated as large sources of information about both sensory input and motor output. In this work, we investigate the extent to which feedforward convergent/divergent network structure is related to the gain in information of spike timing representations over spike count representations. While previous theories on coding in convergent and divergent networks have largely neglected the role of precise spike timing, our model and analyses place this aspect at the forefront. For a suite of stimuli with different timescales, we demonstrate that structural bottlenecks-small groups of neurons post-synaptic to network convergence-have a stronger preference for spike timing codes than expansion layers created by structural divergence. We further show that this relationship can be generalized across different spike-generating models and measures of coding capacity, implying a potentially fundamental link between network structure and coding strategy using spikes. Additionally, we found that a simple network model based on convergence and divergence ratios of a hawkmoth (Manduca sexta) nervous system can reproduce the relative contribution of spike timing information in its motor output, providing testable predictions on optimal temporal resolutions of spike coding across the moth sensory-motor pathway at both the single-neuron and population levels.

Crossbridge binding, state transitions, and force in active muscle is dependent on the radial spacing between the myosin-containing thick filament and the actin-containing thin filament in the filament lattice. This radial spacing has been previously shown through spatially explicit modeling and experimental efforts to greatly affect quasi-static, isometric, force production in muscle. It has recently been suggested that this radial spacing might also be able to drive differences in mechanical function, or net work, under dynamic oscillations like those which occur in muscles in vivo. However, previous spatially explicit models either had no radial spacing dependence, meaning the radial spacing could not be investigated, or did include radial spacing dependence but could not reproduce in vivo net work during dynamic oscillations and only investigated isometric contractions. Here we show the first spatially explicit model to include radial crossbridge dependence which can produce mechanical function similar to real muscle. Using this spatially explicit model of a half sarcomere, we show that when oscillated at strain amplitudes and frequencies like those in the main flight muscles of the hawkmoth Manduca sexta, mechanical function (net work) does depend on the lattice spacing. In addition, since the trajectory of lattice spacing changes during dynamic oscillation can vary from organism to organism, we can prescribe a trajectory of lattice spacing changes in the spatially explicit half sarcomere model and investigate the extent to which the time course of lattice spacing changes can affect mechanical function. We simulated a half sarcomere undergoing dynamic oscillations and prescribed the Poisson's ratio of the lattice to be either 0 (constant lattice spacing) or 0.5 (isovolumetric lattice spacing changes). We also simulated net work using lattice spacing data taken from M. sexta which has a variable Poisson's ratio. Our simulation results indicate that the lattice spacing can change the mechanical function of muscle, and that in some cases a 1 nm difference can switch the net work of the half sarcomere model from positive (motor-like) to negative (brake-like).

Traditional models of motor control typically operate in the domain of continuous signals such as spike rates, forces, and kinematics. However, there is growing evidence that precise spike timings encode significant information that coordinates and causally influences motor control. Some existing neural network models incorporate spike timing precision but they neither predict motor spikes coordinated across multiple motor units nor capture sensory-driven modulation of agile locomotor control. In this paper, we propose a visual encoder and model of a sensorimotor system based on a recurrent neural network (RNN) that utilizes spike timing encoding during smooth pursuit target tracking. We use this to predict a nearly complete, spike-resolved motor program of a hawkmoth that requires coordinated millisecond precision across 10 major flight motor units. Each motor unit enervates one muscle and utilizes both rate and timing encoding. Our model includes a motion detection mechanism inspired by the hawkmoth's compound eye, a convolutional encoder that compresses the sensory input, and a simple RNN that is sufficient to sequentially predict wingstroke-to-wingstroke modulation in millisecond-precise spike timings. The two-layer output architecture of the RNN separately predicts the occurrence and timing of each spike in the motor program. The dataset includes spikes recorded from all motor units during a tethered flight where the hawkmoth attends to a moving robotic flower, with a total of roughly 7000 wingstrokes from 16 trials on 5 hawkmoth subjects. Intra-trial and same-subject inter-trial predictions on the test data show that nearly every spike can be predicted within 2 ms of its known spike timing precision values. Whereas, spike occurrence prediction accuracy is about 90%. Overall, our model can predict the precise spike timing of a nearly complete motor program for hawkmoth flight with a precision comparable to that seen in agile flying insects. Such an encoding framework that captures visually-modulated precise spike timing codes and coordination can reveal how organisms process visual cues for agile movements. It can also drive the next generation of neuromorphic controllers for navigation in complex environments.

Sensory inputs in nervous systems are often encoded at the millisecond scale in a precise spike timing code. There is now growing evidence in behaviors ranging from slow breathing to rapid flight for the prevalence of precise timing encoding in motor systems. Despite this, we largely do not know at what scale timing matters in these circuits due to the difficulty of recording a complete set of spike-resolved motor signals and assessing spike timing precision for encoding continuous motor signals. We also do not know if the precision scale varies depending on the functional role of different motor units. We introduce a method to estimate spike timing precision in motor circuits using continuous MI estimation at increasing levels of added uniform noise. This method can assess spike timing precision at fine scales for encoding rich motor output variation. We demonstrate the advantages of this approach compared to a previously established discrete information theoretic method of assessing spike timing precision. We use this method to analyze the precision in a nearly complete, spike resolved recording of the 10 primary wing muscles control flight in an agile hawk moth, Manduca sexta. Tethered moths visually tracked a robotic flower producing a range of turning (yaw) torques. We know that all 10 muscles in this motor program encode the majority of information about yaw torque in spike timings, but we do not know whether individual muscles encode motor information at different levels of precision. We demonstrate that the scale of temporal precision in all motor units in this insect flight circuit is at the sub-millisecond or millisecond-scale, with variation in precision scale present between muscle types. This method can be applied broadly to estimate spike timing precision in sensory and motor circuits in both invertebrates and vertebrates.

In most instances, flapping wing robots have emulated the “synchronous” actuation of insects in which the wingbeat timing is generated from a time-dependent, rhythmic signal. The internal dynamics of asynchronous insect flight muscle enable high-frequency, adaptive wingbeats with minimal direct neural control. In this paper, we investigate how the delayed stretch-activation (dSA) response of asynchronous insect flight muscle can be transformed into a feedback control law for flapping wing robots that results in stable limit cycle wingbeats. We first demonstrate - in theory and simulation - the mechanism by which asynchronous wingbeats self-excite. Then, we implement the feedback law on a dynamically-scaled robophysical model as well as on an insect-scale robotic flapping wing. Experiments on large- and small-scale robots demonstrate good agreement with the theory results and highlight how dSA parameters govern wingbeat amplitude and frequency. Lastly, we demonstrate that asynchronous actuation has several advantages over synchronous actuation schemes, including the ability to rapidly adapt or halt wingbeats in response to external loads or collisions through low-level feedback control.

Spike train decoding is considered one of the grand challenges in reverse-engineering neural control systems as well as in the development of neuromorphic controllers. This paper presents a novel relative-time kernel design that accounts for not only individual spike train patterns, but also the relative spike timing between neuron pairs in the population. The new relative-time-kernel-based spike train decoding method proposed in this paper allows us to map the spike trains of a population of neurons onto a lower-dimensional manifold, in which continuous-time trajectories live. The effectiveness of our novel approach is demonstrated by comparing it with existing kernel-based and rate-based decoders, including the traditional reproducing kernel Hilbert space framework. In this paper, we use the data collected in hawk moth flower tracking experiments to test the importance of relative spike timing information for neural control, and focus on the problem of uncovering the mapping from the spike trains of ten primary flight muscles to the resulting forces and torques on the moth body. We show that our new relative-time-kernel-based decoder improves the prediction of the resulting forces and torques by up to 52.1 %. Our proposed relative-time-kernel-based decoder may be used to reverse-engineer neural control systems more accurately by incorporating precise relative spike timing information in spike trains.

What are the features of movement encoded by changing motor commands? Do motor commands encode movement independently or can they be represented in a reduced set of signals (i.e. synergies)? Motor encoding poses a computational and practical challenge because many muscles typically drive movement, and simultaneous electrophysiology recordings of all motor commands are typically not available. Moreover, during a single locomotor period (a stride or wingstroke) the variation in movement may have high dimensionality, even if only a few discrete signals activate the muscles. Here, we apply the method of partial least squares (PLS) to extract the encoded features of movement based on the cross-covariance of motor signals and movement. PLS simultaneously decomposes both datasets and identifies only the variation in movement that relates to the specific muscles of interest. We use this approach to explore how the main downstroke flight muscles of an insect, the hawkmoth Manduca sexta, encode torque during yaw turns. We simultaneously record muscle activity and turning torque in tethered flying moths experiencing wide-field visual stimuli. We ask whether this pair of muscles acts as a muscle synergy (a single linear combination of activity) consistent with their hypothesized function of producing a left-right power differential. Alternatively, each muscle might individually encode variation in movement. We show that PLS feature analysis produces an efficient reduction of dimensionality in torque variation within a wingstroke. At first, the two muscles appear to behave as a synergy when we consider only their wingstroke-averaged torque. However, when we consider the PLS features, the muscles reveal independent encoding of torque. Using these features we can predictably reconstruct the variation in torque corresponding to changes in muscle activation. PLS-based feature analysis provides a general two-sided dimensionality reduction that reveals encoding in high dimensional sensory or motor transformations.