Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches

Neural dynamics of robust legged robots

Legged robot control has improved in recent years with the rise of deep reinforcement learning, however, much of the underlying neural mechanisms remain difficult to interpret. Our aim is to leverage bio-inspired methods from computational neuroscience to better understand the neural activity of robust robot locomotion controllers. Similar to past work, we observe that terrain-based curriculum learning improves agent stability. We study the biomechanical responses and neural activity within our neural network controller by simultaneously pairing physical disturbances with targeted neural ablations. We identify an agile hip reflex that enables the robot to regain its balance and recover from lateral perturbations. Model gradients are employed to quantify the relative degree that various sensory feedback channels drive this reflexive behavior. We also find recurrent dynamics are implicated in robust behavior, and utilize sampling-based ablation methods to identify these key neurons. Our framework combines model-based and sampling-based methods for drawing causal relationships between neural network activity and robust embodied robot behavior.

Flies adaptively control flight to compensate for added inertia

Animal locomotion is highly adaptive, displaying a large degree of flexibility, yet how this flexibility arises from the integration of mechanics and neural control remains elusive. For instance, animals require flexible strategies to maintain performance as changes in mass or inertia impact stability. Compensatory strategies to mechanical loading are especially critical for animals that rely on flight for survival. To shed light on the capacity and flexibility of flight neuromechanics to mechanical loading, we pushed the performance of fruit flies (Drosophila) near its limit and implemented a control theoretic framework. Flies with added inertia were placed inside a virtual reality arena which permitted free rotation about the vertical (yaw) axis. Adding inertia increased the fly's response time yet had little influence on overall gaze stabilization performance. Flies maintained stability following the addition of inertia by adaptively modulating both visuomotor gain and damping. By contrast, mathematical modelling predicted a significant decrease in gaze stabilization performance. Adding inertia altered saccades, however, flies compensated for the added inertia by increasing saccade torque. Taken together, in response to added inertia flies increase reaction time but maintain flight performance through adaptive neural control. Overall, adding inertia decreases closed-loop flight robustness. Our work highlights the flexibility and capacity of motor control in flight.

Gait Entrainment to Torque Pulses from a Hip Exoskeleton Robot

Robot-aided locomotor rehabilitation has proven challenging. To facilitate progress, it is important to first understand the neuro-mechanical dynamics and control of unimpaired human locomotion. Our previous studies found that human gait entrained to periodic torque pulses at the ankle when the pulse period was close to preferred stride duration. Moreover, synchronized gait exhibited constant phase relation with the pulses so that the robot provided mechanical assistance. To test the generality of mechanical gait entrainment, this study characterized unimpaired human subjects' responses to periodic torque pulses during overground walking. The intervention was applied by a hip exoskeleton robot, Samsung GEMS-H. Gait entrainment was assessed based on the time-course of the phase at which torque pulses occurred within each stride. Experiments were conducted for two consecutive days to evaluate whether the second day elicited more entrainment. Whether entrainment was affected by the difference between pulse period and preferred stride duration was also assessed. Results indicated that the intervention evoked gait entrainment that occurred more often when the period of perturbation was closer to subjects' preferred stride duration, but the difference between consecutive days was insignificant. Entrainment was accompanied by convergence of pulse phase to a similar value across all conditions, where the robot maximized mechanical assistance. Clear evidence of motor adaptation indicated the potential of the intervention for rehabilitation. This study quantified important aspects of the nonlinear neuro-mechanical dynamics underlying unimpaired human walking, which will inform the development of effective approaches to robot-aided locomotor rehabilitation, exploiting natural dynamics in a minimally-encumbering way.

Challenges in dynamic mode decomposition

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov space closure when modelling nonlinear systems. Here, we investigate the combination of noise and nonlinearity in a controlled setting, by studying a class of systems with linear latent dynamics which are observed via multinomial observables. Our numerical models include system and measurement noise. We explore the influences of dataset metrics, the spectrum of the latent dynamics, the normality of the system matrix and the geometry of the dynamics. Our results show that even for these very mildly nonlinear conditions, DMD methods often fail to recover the spectrum and can have poor predictive ability. Our work is motivated by our experience modelling multilegged robot data, where we have encountered great difficulty in reconstructing time series for oscillatory systems with intermediate transients, which decay only slightly faster than a period.

Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

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.

Locomotor transitions in the potential energy landscape-dominated regime

To traverse complex three-dimensional terrain with large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize near-steady-state, single-mode locomotion (e.g. walk, run). We know little about how to use physical interaction to make robust locomotor transitions. Here, we review our progress towards filling this gap by discovering terradynamic principles of multi-legged locomotor transitions, using simplified model systems representing distinct challenges in complex three-dimensional terrain. Remarkably, general physical principles emerge across diverse model systems, by modelling locomotor-terrain interaction using a potential energy landscape approach. The animal and robots' stereotyped locomotor modes are constrained by physical interaction. Locomotor transitions are stochastic, destabilizing, barrier-crossing transitions on the landscape. They can be induced by feed-forward self-propulsion and are facilitated by feedback-controlled active adjustment. General physical principles and strategies from our systematic studies already advanced robot performance in simple model systems. Efforts remain to better understand the intelligence aspect of locomotor transitions and how to compose larger-scale potential energy landscapes of complex three-dimensional terrains from simple landscapes of abstracted challenges. This will elucidate how the neuromechanical control system mediates physical interaction to generate multi-pathway locomotor transitions and lead to advancements in biology, physics, robotics and dynamical systems theory.

An energy landscape approach to locomotor transitions in complex 3D terrain

Effective locomotion in nature happens by transitioning across multiple modes (e.g., walk, run, climb). Despite this, far more mechanistic understanding of terrestrial locomotion has been on how to generate and stabilize around near-steady-state movement in a single mode. We still know little about how locomotor transitions emerge from physical interaction with complex terrain. Consequently, robots largely rely on geometric maps to avoid obstacles, not traverse them. Recent studies revealed that locomotor transitions in complex three-dimensional (3D) terrain occur probabilistically via multiple pathways. Here, we show that an energy landscape approach elucidates the underlying physical principles. We discovered that locomotor transitions of animals and robots self-propelled through complex 3D terrain correspond to barrier-crossing transitions on a potential energy landscape. Locomotor modes are attracted to landscape basins separated by potential energy barriers. Kinetic energy fluctuation from oscillatory self-propulsion helps the system stochastically escape from one basin and reach another to make transitions. Escape is more likely toward lower barrier direction. These principles are surprisingly similar to those of near-equilibrium, microscopic systems. Analogous to free-energy landscapes for multipathway protein folding transitions, our energy landscape approach from first principles is the beginning of a statistical physics theory of multipathway locomotor transitions in complex terrain. This will not only help understand how the organization of animal behavior emerges from multiscale interactions between their neural and mechanical systems and the physical environment, but also guide robot design, control, and planning over the large, intractable locomotor-terrain parameter space to generate robust locomotor transitions through the real world.

Uneven substrates constrain walking speed in ants through modulation of stride frequency more than stride length

Natural terrain is rarely flat. Substrate irregularities challenge walking animals to maintain stability, yet we lack quantitative assessments of walking performance and limb kinematics on naturally uneven ground. We measured how continually uneven 3D-printed substrates influence walking performance of Argentine ants by measuring walking speeds of workers from laboratory colonies and by testing colony-wide substrate preference in field experiments. Tracking limb motion in over 8000 videos, we used statistical models that associate walking speed with limb kinematic parameters to compare movement over flat versus uneven ground of controlled dimensions. We found that uneven substrates reduced preferred and peak walking speeds by up to 42% and that ants actively avoided uneven terrain in the field. Observed speed reductions were modulated primarily by shifts in stride frequency instead of stride length (flat R 2: 0.91 versus 0.50), a pattern consistent across flat and uneven substrates. Mixed effect modelling revealed that walking speeds on uneven substrates were accurately predicted based on flat walking data for over 89% of strides. Those strides that were not well modelled primarily involved limb perturbations, including missteps, active foot repositioning and slipping. Together these findings relate kinematic mechanisms underlying walking performance on uneven terrain to ecologically relevant measures under field conditions.

Limping following limb loss increases locomotor stability

Although many arthropods have the ability to voluntarily lose limbs, how these animals rapidly adapt to such an extreme perturbation remains poorly understood. It is thought that moving with certain gaits can enable efficient, stable locomotion; however, switching gaits requires complex information flow between and coordination of an animal's limbs. We show here that upon losing two legs, spiders can switch to a novel, more statically stable gait, or use temporal adjustments without a gait change. The resulting gaits have higher overall static stability than the gaits that would be imposed by limb loss. By decreasing the time spent in a low-stability configuration - effectively 'limping' over less-stable phases of the stride - spiders increased the overall stability of the less statically stable gait with no observable reduction in speed, as compared with the intact condition. Our results shed light on how voluntary limb loss could have persisted evolutionarily among many animals, and provide bioinspired solutions for robots when they break or lose limbs.

The effects of feedback on stability and maneuverability of a phase-reduced model for cockroach locomotion

In previous work, we built a neuromechanical model for insect locomotion in the horizontal plane, containing a central pattern generator, motoneurons, muscles actuating jointed legs, and rudimentary proprioceptive feedback. This was subsequently simplified to a set of 24 phase oscillators describing motoneuronal activation of agonist-antagonist muscle pairs, which facilitates analyses and enables simulations over multi-dimensional parameter spaces. Here we use the phase-reduced model to study dynamics and stability over the typical speed range of the cockroach Blaberus discoidalis, the effects of feedback on response to perturbations, strategies for turning, and a trade-off between stability and maneuverability. We also compare model behavior with experiments on lateral perturbations, changes in body mass and moment of inertia, and climbing dynamics, and we present a simple control strategy for steering using exteroceptive feedback.

Sex differences in leg dexterity are not present in elite athletes

We studied whether the time-varying forces that control unstable foot-ground interactions provide insight into the neural control of dynamic leg function. Twenty elite (10F, 26.4±3.5yrs) and 20 recreational (10F, 24.8±2.4yrs) athletes used an isolated leg to maximally compress a slender spring designed to buckle at low forces while seated. The foot forces during the compression at the edge of instability quantify the maximal sensorimotor ability to control dynamic foot-ground interactions. Using the nonlinear analysis technique of attractor reconstruction, we characterized the spatial (interquartile range IQR) and geometric (trajectory length TL, volume V, and sum of edge lengths SE) features of the dynamical behavior of those force time series. ANOVA confirmed the already published effect of sex, and a new effect of athletic ability, respectively, in TL (p=0.014 and p<0.001), IQR (p=0.008 and p<0.001), V (p=0.034 and p=0.002), and SE (p=0.033 and p<0.001). Further analysis revealed that, for recreational athletes, females exhibited weaker corrective actions and greater stochasticity than males as per their greater mean values of TL (p=0.003), IQR (p=0.018), V (p=0.017), and SE (p=0.025). Importantly, sex differences disappeared in elite athletes. These results provide an empirical link between sex, athletic ability, and nonlinear dynamical control. This is a first step in understanding the sensorimotor mechanisms for control of unstable foot-ground interactions. Given that females suffer a greater incidence of non-contact knee ligament injuries, these non-invasive and practical metrics of leg dexterity may be both indicators of athletic ability, and predictors of risk of injury.

Longitudinal quasi-static stability predicts changes in dog gait on rough terrain

Legged animals utilize gait selection to move effectively and must recover from environmental perturbations. We show that on rough terrain, domestic dogs, Canis lupus familiaris, spend more time in longitudinal quasi-statically stable patterns of movement. Here, longitudinal refers to the rostro-caudal axis. We used an existing model in the literature to quantify the longitudinal quasi-static stability of gaits neighbouring the walk, and found that trot-like gaits are more stable. We thus hypothesized that when perturbed, the rate of return to a stable gait would depend on the direction of perturbation, such that perturbations towards less quasi-statically stable patterns of movement would be more rapid than those towards more stable patterns of movement. The net result of this would be greater time spent in longitudinally quasi-statically stable patterns of movement. Limb movement patterns in which diagonal limbs were more synchronized (those more like a trot) have higher longitudinal quasi-static stability. We therefore predicted that as dogs explored possible limb configurations on rough terrain at walking speeds, the walk would shift towards trot. We gathered experimental data quantifying dog gait when perturbed by rough terrain and confirmed this prediction using GPS and inertial sensors (n=6, P<0.05). By formulating gaits as trajectories on the n-torus we are able to make tractable the analysis of gait similarity. These methods can be applied in a comparative study of gait control which will inform the ultimate role of the constraints and costs impacting locomotion, and have applications in diagnostic procedures for gait abnormalities, and in the development of agile legged robots.

Summary: Dogs co-ordinate their limbs on rough terrain in a manner consistent with optimization for quasi-static longitudinal stability.

Constructing predictive models of human running

Running is an essential mode of human locomotion, during which ballistic aerial phases alternate with phases when a single foot contacts the ground. The spring-loaded inverted pendulum (SLIP) provides a starting point for modelling running, and generates ground reaction forces that resemble those of the centre of mass (CoM) of a human runner. Here, we show that while SLIP reproduces within-step kinematics of the CoM in three dimensions, it fails to reproduce stability and predict future motions. We construct SLIP control models using data-driven Floquet analysis, and show how these models may be used to obtain predictive models of human running with six additional states comprising the position and velocity of the swing-leg ankle. Our methods are general, and may be applied to any rhythmic physical system. We provide an approach for identifying an event-driven linear controller that approximates an observed stabilization strategy, and for producing a reduced-state model which closely recovers the observed dynamics.

Intersegmental coupling and recovery from perturbations in freely running cockroaches

Cockroaches are remarkably stable runners, exhibiting rapid recovery from external perturbations. To uncover the mechanisms behind this important behavioral trait, we recorded leg kinematics of freely running animals in both undisturbed and perturbed trials. Functional coupling underlying inter-leg coordination was monitored before and during localized perturbations, which were applied to single legs via magnetic impulses. The resulting transient effects on all legs and the recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architecture and strength by fitting experimental data to a six-leg-unit phase oscillator model. Using maximum-likelihood techniques, we found that a network with nearest-neighbor inter-leg coupling best fitted the data and that, although coupling strengths vary among preparations, the overall inputs entering each leg are approximately balanced and consistent. Simulations of models with different coupling strengths encountering perturbations suggest that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations.

Positive force feedback in development of substrate grip in the stick insect tarsus

The mechanics of substrate adhesion has recently been intensively studied in insects but less is known about the sensorimotor control of substrate engagement. We characterized the responses and motor effects of tarsal campaniform sensilla in stick insects to understand how sensory signals of force could contribute to substrate grip. The tarsi consist of a chain of segments linked by highly flexible articulations. Morphological studies showed that one to four campaniform sensilla are located on the distal end of each segment. Activities of the receptors were recorded neurographically and sensilla were identified by stimulation and ablation of their cuticular caps. Responses were characterized to bending forces and axial loads, muscle contractions and to forces applied to the retractor apodeme (tendon). The tarsal sensilla effectively encoded both the rate and amplitude of loads and muscle forces, but only when movement was resisted. Mechanical stimulation of the receptors produced activation of motor neurons in the retractor unguis and tibial flexor muscles. These findings indicate that campaniform sensilla can provide information about the effectiveness of the leg muscles in generating substrate adherence. They can also produce positive force feedback that could contribute to the development of substrate grip and stabilization of the tarsal chain.

WITHDRAWN: Positive force feedback in development of substrate grip in the stick insect tarsus

The Publisher regrets that this article is an accidental duplication of an article that has already been published, http://dx.doi.org/10.1016/j.asd.2014.06.002. The duplicate article has therefore been withdrawn.