Model Of Locomotion Research Articles

Modeling and Analysis of a Soft Endoluminal Inchworm Robot Propelled by a Rotating Magnetic Dipole Field

Abstract In clinical practice, therapeutic and diagnostic endoluminal procedures of the human body often use a scope, catheter, or passive pill-shaped camera. Unfortunately, such devices used in the circulatory system and gastrointestinal tract are often uncomfortable, invasive, and require the patient to be sedated. With current technology, regions of the body are often inaccessible to the clinician. Herein, a magnetically actuated soft endoluminal inchworm robot that may extend clinicians’ ability to reach further into the human body and practice new procedures is described, modeled, and analyzed. A detailed locomotion model is proposed that takes into account the elastic deformation of the robot and its interactions with the environment. The model is validated with in vitro and ex vivo (pig intestine) physical experiments and is shown to capture the robot’s gait characteristics through a lumen. Utilizing dimensional analysis, the effects of the mechanical properties and design variables on the robot’s motion are investigated further to advance the understanding of this endoluminal robot concept.

Interactive Simulation Program for Autonomous Vehicles

The paper presents an interactive simulation program dedicated to autonomous vehicles. The program, developed in the form of an app and written in the Matlab programming language, is a didactic tool, which aims to better understand the phenomena that occur during locomotion. To achieve this goal, the user can easily perform interactive simulations by changing the model parameters. In addition to the mentioned flexibility, the user can perform case studies and scenarios. The structure of the program is obtained by aggregating seven objects (modules), dedicated to studying the contributions of each to the simulation. These modules are for different types of trajectories, for controllers, three types of locomotion models, sensors, different filters, environment models, and for simultaneous localization and mapping. The connection between them is possible through a database. This framework ensures the continuity of the simulations. At the end of the interactive visual simulation, the user is obtaining a holistic report with the results.

Cooperative Locomotion Via Supervisory Predictive Control and Distributed Nonlinear Controllers

Abstract This paper presents a hierarchical nonlinear control algorithm for the real-time planning and control of cooperative locomotion of legged robots that collaboratively carry objects. An innovative network of reduced-order models subject to holonomic constraints, referred to as interconnected linear inverted pendulum (LIP) dynamics, is presented to study cooperative locomotion. The higher level of the proposed algorithm employs a supervisory controller, based on event-based model predictive control (MPC), to effectively compute the optimal reduced-order trajectories for the interconnected LIP dynamics. The lower level of the proposed algorithm employs distributed nonlinear controllers to reduce the gap between reduced- and full-order complex models of cooperative locomotion. In particular, the distributed controllers are developed based on quadratic programing (QP) and virtual constraints to impose the full-order dynamical models of each agent to asymptotically track the reduced-order trajectories while having feasible contact forces at the leg ends. The paper numerically investigates the effectiveness of the proposed control algorithm via full-order simulations of a team of collaborative quadrupedal robots, each with a total of 22 degrees-of-freedom. The paper finally investigates the robustness of the proposed control algorithm against uncertainties in the payload mass and changes in the ground height profile. Numerical studies show that the cooperative agents can transport unknown payloads whose masses are up to 57%, 97%, and 137% of a single agent's mass with a team of two, three, and four legged robots.

Social Distancing with the Optimal Steps Model

With the Covid-19 pandemic, an urgent need has arisen to simulate social distancing. The Optimal Steps Model (OSM) is a pedestrian locomotion model that operationalizes an individual's need for personal space. We present new parameter values for personal space in the OSM to simulate social distancing in the pedestrian dynamics simulator Vadere. Our approach is pragmatic. We consider two use cases: in the first, we demand that a set social distance must never be violated. In the second the social distance can be violated temporarily for less than 10s. For each use case we conduct simulation studies in a typical bottleneck scenario and measure contact times, that is, violations of the social distance rule.We conduct regression analysis to assess how the parameter choice depends on the desired social distance and the corridor width. We find that evacuation time increases linearly with the width of the repulsion potential, which is an analogy to physics modeling the strength of the need for personal space. The evacuation time decreases linearly with larger corridor width. The influence of the corridor width on the evacuation time is smaller than the influence of the range of the repulsion, that is, the need for personal space. If the repulsion is too strong, we observe clogging effects. Our regression formulas enable Vadere users to conduct their own studies without understanding the intricacies of the OSM implementation and without extensive parameter adjustment.

Model of metameric locomotion in smooth active directional filaments with curvature fluctuations

Locomotion in segmented animals, such as annelids and myriapods (centipedes and millipedes), is generated by a coordinated movement known as metameric locomotion, which can be also implemented in robots designed to perform specific tasks. We introduce a theoretical model, based on an active directional motion of the head segment and a passive trailing of the rest of the body segments, in order to formalize and study the metameric locomotion. The model is specifically formulated as a steered Ornstein-Uhlenbeck curvature process, preserving the continuity of the curvature along the whole body filament, and thus supersedes the simple active Brownian model, which would be inapplicable in this case. We obtain the probability density by analytically solving the Fokker-Planck equation pertinent to the model. We also calculate explicitly the correlators, such as the mean-square orientational fluctuations, the orientational correlation function and the mean-square separation between the head and tail segments, both analytically either via the Fokker-Planck equation or directly by either solving analytically or implementing it numerically from the Langevin equations. The analytical and numerical results coincide. Our theoretical model can help understand the locomotion of metameric animals and instruct the design of metameric robots.

How big can a walking fish be? A theoretical inference based on observations on four land-dwelling fish genera of South Vietnam.

Comparative study of terrestrial locomotion of 4 fish genera including Anabas, Channa, Clarias, and Monopterus, was performed in experimental setting with the substrate surface of wet clay. No special adaptations for terrestrial locomotion were found. Every fish uses for propulsion on land what it already has. Eel-shaped Monopterus crawls by body undulations in a serpentine or sidewinding technique, the latter of which was not previously observed beyond snakes. The other 3 fish genera walk by body oscillations using stiff appendages as propulsors. When they are located anteriorly, as the serrate operculum in Anabas and the preaxial spine of the pectoral fin in Clarias, the propulsion is termed prolocomotor, when posteriorly, as the spiny anal fin in Channa-metalocomotor. Channa is the heaviest fish walking out of water in our days, quite comparable in size with first Devonian tetrapods Acanthostega and Tulerpeton. A theoretical calculation is suggested for the upper size limit of a fish capable of terrestrial walking without special locomotor adaptations. It should be roughly 20 cm in the vertical dimension of the trunk, which is just a little above the known size of Devonian tetrapodomorph fishes Panderichthys and Elpistostege. The metalocomotor walking technique of Channa is suggested as the closest extant model for terrestrial locomotion at the fish-tetrapod transition. The major difference is that the metalocomotor propulsor in Channa is represented by the anal fin, while in tetrapodomorphs by the pelvic fins. The sprawled pelvic fins were advantageous in respect of reduced requirement for side-to-side tail swinging.

Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle.

Jellyfish have been called one of the most energy-efficient animals in the world due to the ease in which they move through their fluid environment, by product of their bell kinematics coupled with their morphological, muscular, material properties. We investigated jellyfish locomotion by conducting in silico comparative studies and explored swimming performance across different fluid scales (i.e., Reynolds Number), bell contraction frequencies, and contraction phase kinematics (duty cycle) for a jellyfish with a fineness ratio of 1 (ratio of bell height to bell diameter). To study these relationships, an open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid-structure interaction problem of a flexible jellyfish bell in a viscous fluid. Thorough 2D parameter subspace explorations illustrated optimal parameter combinations in which give rise to enhanced swimming performance. All performance metrics indicated a higher sensitivity to bell actuation frequency than fluid scale or duty cycle, via Sobol sensitivity analysis, on a higher performance parameter subspace. Moreover, Pareto-like fronts were identified in the overall performance space involving the cost of transport and forward swimming speed. Patterns emerged within these performance spaces when highlighting different parameter regions, which complemented the global sensitivity results. Lastly, an open source computational model for jellyfish locomotion is offered to the science community that can be used as a starting place for future numerical experimentation.

Vertical locomotion in the arboreal salamander Aneides vagrans

AbstractSalamanders are often used as a model of early tetrapod locomotion, due to their generalized tetrapod body plan. We imaged five individuals of wandering salamander, Aneides vagrans, during horizontal and vertical locomotion and compared kinematic and gait adjustments made to compensate for each condition. We used ImageJ to calculate duty factor, stride length, stride frequency, contralateral foot spread, heading of climbing, and forward velocity. Like other terrestrial salamanders, A. vagrans use a diagonal couplet, lateral sequence walk on horizontal surfaces. When walking vertically, however, they use a single‐foot gait, taking smaller steps and extending the duty factor compared with level walking. Salamanders adjusted their limbs to have a wider contralateral foot spread between fore‐ and hindfeet when walking downward as compared to walking upward or horizontally. These gait adjustments may minimize the risk of slipping or falling by increasing the number of contact points during the stride cycle, and by bringing their center of mass closer to the surface. We found that salamanders moved at a significantly faster velocity when traveling horizontally compared to vertically. Furthermore, we found no significant difference between upward and downward velocity, despite greater stride lengths in upward locomotion; this was explained by a higher stride frequency in downward locomotion. We estimate travel time up or down an old‐growth redwood tree to be on the scale of hours, a significant time investment that may encourage alternatives when available. These results suggest that, in an ecological context, while salamanders are capable of traveling straight down a redwood tree, they may simply tend to jump.

Modeling Post-Scratching Locomotion with Two Rhythm Generators and a Shared Pattern Formation.

Simple SummaryPost-scratching locomotion in cats refers to the spontaneous occurrence of an episode of locomotion generated after an event of scratching. This phenomenon suggests the potential existence of shared neurons in the spinal cord mediating the transition from one rhythmic motor task to another. Here, we examine this possibility with a mathematical model, reproducing the experimental observations. Our findings reveal a possible mechanism in which the central nervous system could share neuronal circuits from two central pattern generators to produce a sequence of different rhythmic motor actions.This study aimed to present a model of post-scratching locomotion with two intermixed central pattern generator (CPG) networks, one for scratching and another for locomotion. We hypothesized that the rhythm generator layers for each CPG are different, with the condition that both CPGs share their supraspinal circuits and their motor outputs at the level of their pattern formation networks. We show that the model reproduces the post-scratching locomotion latency of 6.2 ± 3.5 s, and the mean cycle durations for scratching and post-scratching locomotion of 0.3 ± 0.09 s and 1.7 ± 0.6 s, respectively, which were observed in a previous experimental study. Our findings show how the transition of two rhythmic movements could be mediated by information exchanged between their CPG circuits through routes converging in a common pattern formation layer. This integrated organization may provide flexible and effective connectivity despite the rigidity of the anatomical connections in the spinal cord circuitry.

Amoebic Foraging Model of Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

A Mobile Mathieu Oscillator Model for Vibrational Locomotion of a Bristlebot

Abstract Terrestrial locomotion that is produced by creating and exploiting frictional anisotropy is common amongst animals such as snakes, gastropods, and limbless lizards. In this paper we present a model of a bristlebot that locomotes by generating frictional anisotropy due to the oscillatory motion of an internal mass and show that this is equivalent to a stick–slip Mathieu oscillator. Such vibrational robots have been available as toys and theoretical curiosities and have seen some applications such as the well-known kilobot and in pipe line inspection, but much remains unknown about this type of terrestrial locomotion. In this paper, motivated by a toy model of a bristlebot made from a toothbrush, we derive a theoretical model for its dynamics and show that its dynamics can be classified into four modes of motion: purely stick (no locomotion), slip, stick–slip, and hopping. In the stick mode, the dynamics of the system are those of a nonlinear Mathieu oscillator and large amplitude resonance oscillations lead to the slip mode of motion. The mode of motion depends on the amplitude and frequency of the periodic forcing. We compute a phase diagram that captures this behavior, which is reminiscent of the tongues of instability seen in a Mathieu oscillator. The broader result that emerges in this paper is that mobile limbless continuum or soft robots can exploit high-frequency parametric oscillations to generate fast and efficient terrestrial motion.

A comparative study on the two vibration driven locomotion systems in various friction levels

This paper presented comparison results of two locomotion models: a pure-vibration driven and a vibro-impact driven system. In experiments, the friction force can be varied without changing the internal and the body masses. The mathematical models of the two systems were developed and experimentally verified. Using dimensionless models, the results can be expanded to other sizes in practice. The two models were compared in the following aspects: the progression rate, the motion direction and the dynamics response. The effect of friction as an important variable on the dynamic response of the two scaled models were examined and compared by means of bifurcation analysis and basin of attraction. It has been found that, the pure-vibration can provide forward motion better than the vibro-impact does. The highest progression rate of the vibro-impact was less than that of the pure-vibration system in the investigated ranges of input parameters. Besides, the pure-vibration always has period-1 motion, whereas the vibro-impact system has a rich and complex dynamic response, including period-1, period-2 as well as chaotic motions. The results obtained would be useful for design and operating the self-propelled locomotion systems.

AQuRo: A Cat-like Adaptive Quadruped Robot With Novel Bio-Inspired Capabilities.

There are currently many quadruped robots suited to a wide range of applications, but traversing some terrains, such as vertical ladders, remains an open challenge. There is still a need to develop adaptive robots that can walk and climb efficiently. This paper presents an adaptive quadruped robot that, by mimicking feline structure, supports several novel capabilities. We design a novel paw structure and several point-cloud-based sensory structures incorporating a quad-composite time-of-flight sensor and a dual-laser range finder. The proposed robot is equipped with physical and cognitive capabilities which include: 1) a dynamic-density topological map building with attention model, 2) affordance perception using the topological map, and 3) a neural-based locomotion model. The novel capabilities show strong integration between locomotion and internal–external sensory information, enabling short-term adaptations in response to environmental changes. The robot performed well in several situations: walking on natural terrain, walking with a leg malfunction, avoiding a sudden obstacle, climbing a vertical ladder. Further, we consider current problems and future development.

Is Human Walking a Network Medicine Problem? An Analysis Using Symbolic Regression Models with Genetic Programming

Human walking is typically assessed using a sensor placed on the lower back or the hip. Such analyses often ignore that the arms, legs, and body trunk movements all have significant roles during walking; in other words, these body nodes with accelerometers form a body sensor network (BSN). BSN refers to a network of wearable sensors or devices on the human body that collects physiological signals. Our study proposes that human locomotion could be considered as a network of well-connected nodes. While hypothesizing that accelerometer data can model this BSN, we collected accelerometer signals from six body areas from ten healthy participants performing a cognitive task. Machine learning based on genetic programming was used to produce a collection of non-linear symbolic models of human locomotion. With implications in precision medicine, our primary finding was that our BSN models fit the data from the lower back's accelerometer and describe subject-specific data the best compared to all other models. Across subjects, models were less effective due to the diversity of human sizes. A BSN relationship between all six body nodes has been shown to describe the subject-specific data, which indicates that the network-medicine relationship between these nodes is essential in adequately describing human walking. Our gait analyses can be used for several clinical applications such as medical diagnostics as well as creating a baseline for healthy walking with and without a cognitive load.

A snake robot for locomotion in a pipe using trapezium-like travelling wave

Snake robots are a suitable solution for various types of applications, especially in rough terrain or hardly accessible areas such as, for example, pipes. This article deals with a snake robot moving in a pipe using a so-called trapezium-like travelling wave. In this paper, we present a mathematical model of locomotion of the snake robot in a pipe of rectangular cross-section. Subsequently, we designed a control algorithm using a trapezium-like travelling wave. Within the control algorithm we introduced the so-called motion matrix of a trapezium-like travelling wave that contains information about the vector of generalized variables at any point of the locomotion cycle. The paper also presents a simulation model in MATLAB R2019b interfacing with CoppeliaSim V4.0.0. Furthermore, in our research we have developed an experimental snake robot with the purpose to verify the derived mathematical model, control algorithm and simulation model. Experimental results show the influence of certain parameters of the trapezium-like travelling wave on locomotion properties, such as the travelled distance or the average speed of the snake robot passing through a pipe. In the final part of this paper, experimental results are discussed and key elements of the proposed control algorithm are highlighted.

Distributed Controllers for Human-Robot Locomotion: A Scalable Approach Based on Decomposition and Hybrid Zero Dynamics

This letter presents a formal foundation, based on decomposition, hybrid zero dynamics (HZD), and a scalable optimization, to develop distributed control algorithms for hybrid models of collaborative human-robot locomotion. The proposed approach considers a centralized controller and then decomposes the dynamics and feedback laws with a parameterization to synthesize local controllers. The Jacobian matrix of the Poincaré map with local controllers is studied and compared to that with centralized ones. An optimization problem is then set up to tune the parameters of the local controllers for asymptotic stability. The proposed approach can significantly reduce the number of controller parameters to be optimized for the synthesis of distributed controllers. The analytical results are numerically evaluated with simulations of a multi-domain hybrid model with 19 degrees of freedom for stable amputee locomotion with a powered knee-ankle prosthetic leg.

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review outlines the end-to-end process of methods that have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced-order models that capture essential walking behaviors to hybrid dynamical systems that encode the full-order continuous dynamics along with discrete foot-strike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiations on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is both agile and efficient.

The roles of ascending sensory signals and top-down central control in the entrainment of a locomotor CPG.

Previous authors have proposed two basic hypotheses about the factors that form the basis of locomotor rhythms in walking insects: sensory feedback only or sensory feedback together with rhythmic activity of small neural circuits called central pattern generators (CPGs). Here we focus on the latter. Following this concept, to generate functional outputs, locomotor control must feature both rhythm generation by CPGs at the level of individual joints and coordination of their rhythmic activities, so that all muscles are activated in an appropriate pattern. This work provides an in-depth analysis of an aspect of this coordination process based on an existing network model of stick insect locomotion. Specifically, we consider how the control system for a single joint in the stick insect leg may produce rhythmic output when subjected to ascending sensory signals from other joints in the leg. In this work, the core rhythm generating CPG component of the joint under study is represented by a classical half-center oscillator constrained by a basic set of experimental observations. While the dynamical features of this CPG, including phase transitions by escape and release, are well understood, we provide novel insights about how these transition mechanisms yield entrainment to the incoming sensory signal, how entrainment can be lost under variation of signal strength and period or other perturbations, how entrainment can be restored by modulation of tonic top-down drive levels, and how these factors impact the duty cycle of the motor output.

Creation of accurate 3D models of harbor porpoises (Phocoena phocoena) using 3D photogrammetry

AbstractCreating accurate 3D models of marine mammals is valuable for assessment of body condition, computational fluids dynamics models of locomotion, and for education. However, the methods for creating 3D models are not well‐developed. We used photography and video to create 3D photogrammetry models of harbor porpoises (Phocoena phocoena).We accessed one live adult female (155.5 cm total length), and two dead animals, one juvenile (110 cm total length) and one calf (88 cm total length). We accessed the two dead individuals through a stranding network in Germany, and the live individual through the Fjord and Baelt research center in Denmark. For all porpoises, we used still photographs from hand‐held cameras, drone video, and synchronized GoPro videos to create 3D photogrammetric models. We used Blender software, and other 3D reconstruction software, to recreate the 3D body meshes, and confirmed the accuracy of each of the 3D body meshes by comparing digital measures on the 3D models to original measures taken on the specimens. We also provide a colored, animated version of the live harbor porpoise for educational purposes. These open‐access 3D models can be used to develop methods to study body morphometrics and condition, and to study bioenergetics and locomotion costs.

Multi-material 3D printing of caterpillar-inspired soft crawling robots with the pneumatically bellow-type body and anisotropic friction feet

Due to large shape-changing ability and high adaptability, soft crawling robots become a promising candidate in applications with unpredictable terrain and complex environments. However, designing and fabricating of soft crawling robots with hybrid soft and rigid components are still elusive. Here, we present a novel caterpillar inspired pneumatically-driven soft crawling robot, which can be directly 3D printed with multiple materials and without complex assembling process. To mimic the biological structure and morphological locomotion of caterpillars, we design the soft crawling robot with a pneumatically driven bellow-type body, 12 anisotropic frictional feet, and two end caps, and introduce a passive synergy locomotion model between the crawling robot’s body and feet. By selecting different cross-section shape of the feet, we characterize the moving performance of soft crawling robots. Finally, we integrate a pneumatic closed-loop control system to drive the soft crawling robots with a periodic gait and demonstrate their motion capability in a curve plastic tube.