This paper investigates the mathematical modeling and basic motion properties of planar seven-link robots that forms passive closed and active open chains. The passive closed model is formed by connecting seven rigid frames via seven viscoelastic joints, and the active open model is formed by connecting them via actuated joints. The former is a convex heptagonal model and can exhibit passive-dynamic rolling on a gentle downhill, whereas the latter virtually forms a forward-leaning octagonal shape by controlling the six relative joint angles. In the first half of this paper, we describe the model assumptions and develop the mathematical equations of motion and collision of the passive closed model, and numerically analyze the motion characteristics by changing the slope angle while checking the conditions necessary for stable motion generation. In the second half, we outline the active open model, develop the PD control system, and numerically analyze the motion characteristics by changing the target angle parameter that controls the degree of forward lean of the virtual octagon.

The authors have proposed a passive rotating locomotion robot that forms a convex heptagonal body by connecting seven identical linear rigid frames via viscoelastic rotational joints. In our previous study, it was confirmed through both numerical simulations and actual experiments that stable and passive rotating motion on a downhill could be generated. This paper proposes two new models in which the seven rigid frames are used as robust exoskeletons as they are, but the elastic elements attached to the rotating joints are removed and repositioned on the diagonals of the convex heptagon to reproduce the flexibility of the internal tissue. The elastic elements form a star-shaped polygon called a heptagram, which is formed by connecting seven vertices with a single stroke. The seven vertices can be connected in two different ways to form two different heptagram shapes. We report the basic numerical results of the change in the motion characteristics of the two models with respect to the slope angle and elastic modulus. An overview of the prototypes developed and the results of basic experiments are also reported.

This study introduces a novel burrowing robot that achieves effective locomotion inside granular media through the synergistic integration of high-frequency vibration-induced environmental-phase-transition (EPT) and adaptive morphing. The robotic system employs three key innovations: 1) an asymmetric arm trajectory mechanism generating directional propulsion, 2) a vibration-mediated granular fluidization system reducing environmental resistance, and 3) passively adaptive claws demonstrating phase-dependent configuration changes. Experimental results demonstrate that the synchronization of morphologically adaptive claws and high-frequency vibration significantly improves locomotion performance. Additionally, numerical simulations based on Adams-EDEM coupling provide deeper insights into the interaction mechanisms between the robot and granular media. This work advances fundamental understanding of terradynamic locomotion by demonstrating environmental modification as a viable strategy for resistance reduction, while providing a bio-inspired framework for developing versatile robotic systems capable of navigating complex particulate environments.

Quadrupedal locomotion involves coordinated interaction between limbs and torso, enabling them to achieve remarkable movement performance and adapt effectively to various environments. In previous studies, mathematical dynamic models of quadrupeds have been established to investigate the mechanisms of limb-torso interaction during walking. However, due to the strong nonlinearity within the model, analyzing how the torso’s motion, especially vibrations, affects walking remains a significant challenge. In this study, the linearization and frequency analysis methods are applied to the quadruped walker to analyze its vibration characteristics, including natural frequency and vibration amplitude. Subsequently, numerical simulations are conducted to examine the relationship between torso vibration and walking performance. Furthermore, a comparison between the vibration characteristics and the simulation results reveals a potential resonance phenomenon. This finding not only validates the effectiveness of the linearization approach but also offers new insights into the interaction between the limbs and torso.

The movement of the legs involves the interaction between the feet and the ground. Consequently, most animals possess a wide variety of foot morphologies and multifunctional capabilities. The selection and switching of these foot functions are passive and environment-dependent, ensuring environmental compliance. Despite this, current research on compliant feet lacks mathematical models that simultaneously encompass locomotion and foot compliance. Therefore, conducting in-depth studies on locomotion properties under current conditions is challenging. In this study, we present novel passive compliant feet applicable to the passive walking of a rimless wheel. We first introduce a dynamic model, achieve passive walking through numerical simulations, and subsequently analyze the gait patterns for compliance and multi-period gait. This study bridges a gap in understanding the interaction between motion and compliance in foot design, providing insights into the dynamics of compliant motion.

This paper mathematically conceives a novel walking support device that leverages passive dynamics and coupling effects. In this model, a passive human walker is flexibly connected to an active humanoid, where the coupling effect induces a stable walking gait of the human. To understand the key mechanism of such indirect gait regulation, different actuation modes are designed for the humanoid and compared via phase-plane analysis of the steady-state gaits. Moreover, stability analysis is conducted via Poincaré map. The results show that it is difficult to enhance the human walker's stability when coupled to a humanoid robot using additional sensory information, compared to using a humanoid robot actuated with a predetermined force that employs no state feedback. The present mathematical model and our theoretical findings contribute to analysis and control design for locomotion systems with robot-human or inter-robots cooperation.

Undulation is the most common gait generated by legless creatures, which enables their robust and efficient locomotion in various environments. Such advantages inspired the control design of many kinds of locomotion robots. Despite their technical details, most of them realize the undulation gait via tracking predetermined trajectories called serpenoid curves, which are a group of sinusoidal waveforms with specified phase differences. This technique, however, sounds quite redundant in terms of sensing and control. Here, we investigate the research question: whether the sinusoidal waveform is necessary to be encoded in the control signal to make the whole body an “S-shape”? We use a 4-link rigid body dynamics model as a simple example, by which numerical simulations are conducted. Together with theoretical analysis, we show that undulation gait emerges naturally based on embodied position controller and filter, where binary actuation torques are required only. Our results not only discover locomotion mechanisms for significantly reducing the sensing and control requirement of generating artificial undulation gait, but also provide additional understandings for biological systems from the mechanical engineering point of view.

Biological observations on tetrapods locomotion deduce that anti-phase synchronization (APS) between fore and rear parts is beneficial for achieving a high-speed walking. On the other hand, theoretical analysis and experimental studies on quadruped robots suggest that a flexible spine potentially improves the gait efficiency and adaptability via smoothing the ground collisions. However, these two mechanisms have never been placed together by a comprehensive investigation in terms of their synergetic effect. Namely, an advanced principle is still lacking in combining the APS and the spine flexibility for quadruped walking robots. To address this issue, we construct a mathematical model for a quadruped dynamic walker under different spine conditions. First, the APS effect is generated via entrainment-based control method under a rigid spine condition. Then, flexible spines realized by three kinds of springs are compared with the rigid one via theoretical analysis. The results suggest that the APS mechanism and the flexible spine can be synergized via an appropriate deformation control. The theoretical findings not only uncover locomotion control mechanisms for quadruped walking robots, but also provide additional understandings of tetrapods dynamic walking from a mechanical engineering point of view.

After occasional perturbation, it is crucial to spontaneously control the limit cycle walking so that it quickly returns to its closed orbit in phase space. Otherwise, its stability can not be sufficiently guaranteed if the speed of recovery is slow while successive perturbation is applied. The accumulated deviation may eventually drive the phase outside the basin of attraction, leading to failure of the walking. In this sense, a control law that quickly recovers the disturbed phase before encountering the following perturbations is indispensable. With this consideration, here we analytically derive an optimal fast entrainment waveform that maximizes the speed of phase recovery based on phase reduction theory. Our theoretical method is numerically evaluated using a limit cycle walker, which is indirectly controlled by the oscillation of a wobbling mass via entrainment effect. The obtained waveform is used as the desired trajectory of the wobbling motion. The simulation results show that the waveform we derived achieves the best performance among all candidates. Our method helps to enhance the stability of limit cycle walking.

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum.

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this "presumably transient" dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

With the purpose of achieving stable and energy efficient locomotion on the slippery road surface, a sliding locomotion robot without joint torque but indirectly controlled by an active wobbling mass is recently proposed. In this paper, we deepen the analysis of the mechanism of the indirectly controlled sliding locomotion for further optimization and generalization. First, we derive the equations of dynamics and control. Second, we estimate the natural frequency of the robot, the moving speed and energy efficiency are also evaluated with respect to forcing amplitude and frequency of the wobbling mass. Third, the Arnol'd tongue is introduced to analyze the relationship between achieving efficient locomotion and being entrained. In addition, phase oscillation and synchronization phenomenon are analyzed via hysteresis plot to further interpret the unusual shapes of the Arnol'd tongues. Finally, we analyze the entrained, however, inefficient locomotion by reconfirming the rolling constraints from the mechanical energy dissipation point of view. Our results help better understanding of the indirectly controlling mechanism, and the methods can be applied to other indirectly controlled locomotion robots.

Precisely manipulating the center of mass (CoM) of the underactuated locomotion robot can't be easily achieved by common control mechanisms which apply only joint torques. A novel and indirect method has been recently introduced using an active wobbling mass attached to limit cycle walkers. The next important issue is to design an optimal control input to reduce the forcing energy. In this paper, we use combined rimless wheels as a simplified example to apply our method, which is based on the theory of phase oscillators. First, we introduce the typical modeling and control of this underactuated robot. Second, we obtain the phase response curve by numerically applying perturbations at different phases of the walker's gait interval and calculating the deviations from the unperturbed. Third, we analytically derive an optimal forcing waveform for the wobbling mass to entrain the combined rimless wheel based on the phase response curve. As an ecological extension, an ideal forcing waveform for m: 1 entrainment was further generated. Finally, the proposed method was evaluated by locking range of the Arnold tongues. The results show that the optimal forcing waveform we derived achieves the best performance for 1:1 entrainment among all the candidates. One of the strongest advantages of our method is the easiness of its implementation, prompting its applicability to a wide variety of locomotion systems.

Circadian clocks are autonomous oscillators driving daily rhythms in physiology and behavior. In mammals, a network of coupled neurons in the suprachiasmatic nucleus (SCN) is entrained to environmental light-dark cycles and orchestrates the timing of peripheral organs. In each neuron, transcriptional feedbacks generate noisy oscillations. Coupling mediated by neuropeptides such as VIP and AVP lends precision and robustness to circadian rhythms. The detailed coupling mechanisms between SCN neurons are debated. We analyze organotypic SCN slices from neonatal and adult mice in wild-type and multiple knockout conditions. Different degrees of rhythmicity are quantified by pixel-level analysis of bioluminescence data. We use empirical orthogonal functions (EOFs) to characterize spatio-temporal patterns. Simulations of coupled stochastic single cell oscillators can reproduce the diversity of observed patterns. Our combination of data analysis and modeling provides deeper insight into the enormous complexity of the data: (1) Neonatal slices are typically stronger oscillators than adult slices pointing to developmental changes of coupling. (2) Wild-type slices are completely synchronized and exhibit specific spatio-temporal patterns of phases. (3) Some slices of Cry double knockouts obey impaired synchrony that can lead to co-existing rhythms ("splitting"). (4) The loss of VIP-coupling leads to desynchronized rhythms with few residual local clusters. Additional information was extracted from co-culturing slices with rhythmic neonatal wild-type SCNs. These co-culturing experiments were simulated using external forcing terms representing VIP and AVP signaling. The rescue of rhythmicity via co-culturing lead to surprising results, since a cocktail of AVP-antagonists improved synchrony. Our modeling suggests that these counter-intuitive observations are pointing to an antagonistic action of VIP and AVP coupling. Our systematic theoretical and experimental study shows that dual coupling mechanisms can explain the astonishing complexity of spatio-temporal patterns in SCN slices.

This paper investigates the roles and effects of dynamic absorbers attached to the leg frames on the gait properties of passive dynamic walking. First, we model a passive compass-like biped robot that consists of two identical leg frames with passive dynamic absorbers that represent micromechanical vibration or human flesh dynamics. We then conduct gait analysis through numerical simulations to observe how small oscillation of the leg frames affects the gait properties, and show that speeding-up is achieved by utilizing the indirect softness produced by the dynamic absorbers. Second, we investigate the dominant effect of small oscillation using the same model. The simulation results show high nonlinearity in the generated walking gait.

It was clarified that speeding-up of passive dynamic walking (PDW) of a combined rimless wheel (CRW) can be achieved by adjustment of the phase difference between the fore and rear legs. We discussed the mechanism from the viewpoint of overcoming potential barrier, and showed that the trajectory of the whole center of mass (CoM) is significantly flattened by choosing the phase difference. This paper investigates the potentiality of speeding-up the CRW without having the phase difference but by using a passive wobbling mass that vibrates up and down in the body in expectation of flattening the whole CoM trajectory. We show that the walking speed is increased by the effect of the wobbling mass and that a transition from anti-phase to in-phase oscillation arises with the increase of the elasticity. We also show nonlinear characteristics such a high sensitivity to initial conditions and hysteresis phenomenon. Furthermore, the validity of the simulation results is verified using an experimental CRW machine.

This paper investigates passive dynamic walking of a combined rimless wheel that consists of two identical 8-legged rimless wheels. By using the mathematical model, we numerically show that stable passive gaits can be generated on a gentle slope, and that the walking speed is dramatically improved by adjusting the phase difference between the fore and rear legs. We then discuss the inherent speeding-up mechanism from the potential barrier point of view. Furthermore, the validity of the derived results is evaluated by using an experimental machine.

In this paper, a novel stereo-endoscopic high-speed digital imaging system and a method to estimate the glottal area function are proposed. Glottal length, width, and area of one female participant were estimated in three different fundamental frequencies (F0s). Index Terms: glottal area function, stereoscopy, high-speed imaging