Dynamic Motion Research Articles

OR-LIM: Observability-aware robust LiDAR-inertial-mapping under high dynamic sensor motion

Light Detection And Ranging (LiDAR) technology has provided an impactful way to capture 3D data. However, consistent mapping in sensing-degenerated and perceptually-limited scenes (e.g. multi-story buildings) or under high dynamic sensor motion (e.g. rotating platform) remains a significant challenge. In this paper, we present OR-LIM, a novel observability-aware LiDAR-inertial-mapping system. Essentially, it combines a robust real-time LiDAR-inertial-odometry (LIO) module with an efficient surfel-map-smoothing (SMS) module that seamlessly optimizes the sensor poses and scene geometry at the same time. To improve robustness, the planar surfels are hierarchically generated and grown from point cloud maps to provide reliable correspondences for fixed-lag optimization. Moreover, the normals of surfels are analyzed for the observability evaluation of each frame. To maintain global consistency, a factor graph is utilized integrating the information from IMU propagation, LIO as well as the SMS. The system is extensively tested on the datasets collected by a low-cost multi-beam LiDAR (MBL) mounted on a rotating platform. The experiments with various settings of sensor motion, conducted on complex multi-story buildings and large-scale outdoor scenes, demonstrate the superior performance of our system over multiple state-of-the-art methods. The improvement of point accuracy reaches 3.39–13.6 % with an average 8.71 % outdoor and correspondingly 1.89–15.88 % with 9.09 % indoor, with reference to the collected Terrestrial Laser Scanning (TLS) map.

Research on the Performance and Control Strategy of Electro-Hydraulic Servo System for Selective Hole Digging Tree Planter

Compared to agricultural environments, afforestation sites are more complex, often presenting issues such as undulating and uneven terrain. These conditions lead to instability in hole digging depth and plant spacing during continuous movement, and the hole shape may not meet expectations. Additionally, the hydraulic system exhibits slow response speed and long steady-state time, affecting the quality of sapling planting. To address these issues, this paper designs an intelligent planting control system for intermittent hole digging under continuous dynamic movement, based on a large tree planter. The focus is on studying the dynamic accuracy of the hole digging cylinder to resolve the instability of plant spacing and planting depth in actual planting processes. Firstly, a motion trajectory model of the intermittent hole digging mechanism is established to obtain the relationship between the displacement trajectory of the rotating cutter and the displacements of the floating cylinder and the hole digging cylinder. Secondly, a mathematical model of the electro-hydraulic servo system is established to control the dynamic accuracy of the hole digging operation. Finally, a Simulink simulation model of the system is established to analyze the performance indicators of the hydraulic system during operation using step and sinusoidal excitation signals. The test results show that the displacement of the hydraulic piston rod can ensure a linear extension trend within the range of 0 to 0.4 m, and the extension distance of the hole digging cylinder in the planting system is 0 to 0.35 m, ensuring linear change within this stroke. When the system’s extension command is 1 V, the actual output is 0.6 m, with a relative error of less than 10% compared to the simulation value, indicating that the control strategy can effectively improve the dynamic performance of the system. When the hydraulic system is in a steady-state extension state at 50 to 58.6 s, the relative error with the simulation value is 7.3%, meeting the “double ten indicators” requirement. The research results clearly verify the superior performance of the proposed intelligent control system, and the proposed control strategy has great potential in practical applications, promising to improve afforestation quality by stabilizing planting spacing and planting depth.

A dual wave structure triboelectric sensor for heart rate and exercise monitoring

Recently, research on wearable devices for physiological exercise monitoring has garnered significant attention. Here, we propose a dual wave-structured triboelectric nanogenerator (DW-TENG) integrated with a cotton cloth, developed for smart running applications. The DW-TENG sensor leverages a flexible wave triboelectric layer composed of polydimethylsiloxane and silicone, with a copper electrode layer between them for sensing. This structure allows for customizable pressure sensitivity by adjusting the silicone hardness. Experimental results show that the DW-TENG achieves a sensitivity of 0.4 V kPa−1, with response and recovery times of 75 and 90 ms, respectively. The sensor effectively measures heart rate changes during various physical activities, including walking, running, and jumping. Electrical performance tests reveal that the DW-TENG’s output is significantly influenced by the silicone hardness, operational frequency, and microstructure height. The DW-TENG sensor demonstrates high durability and stability, maintaining consistent voltage output over 40 000 cycles. This research highlights the potential of the DW-TENG in multifunctional physiological and physical activity monitoring, providing real-time data on respiratory patterns, heart rate, and movement dynamics, thus enhancing athletic training, performance assessment, and health monitoring.

Low-Reynolds-number droplet motion in shear flow micro-confined by a rough substrate

A three-dimensional spectral boundary element method has been employed to compute for the dynamics of the droplet motion driven by shear flow near a single solid substrate with a rough surface. The droplet size is comparable with the surface features of the substrate. This is a problem that has barely been explored but with applications in biomedical research and heat management. This work numerically investigated the influences of surface roughness features, such as the roughness amplitude and wavelength, on the droplet deformation and velocities. We observe that a greater amplitude or wavelength leads to larger variations in droplet velocity perpendicular to the substrate. The droplet velocity along the substrate increases when the amplitude is reduced or when the wavelength increases. The effects of capillary number and viscosity ratios have also been studied. The droplet deformation and its velocity increases as we increase the capillary number, while the viscosity ratio shows a non-monotonic influence on the droplet behavior. The predicted droplet behaviors, including deformation, velocities, and trajectories, can provide physical insight, help to understand the droplet behavior in microfluidic devices without a perfectly smooth surface, and contribute in the design and operation of those devices.

Unsupervised Learning Bioreactor Regimes

Efficient operation of bioreactors is pivotal for the success of biomanufacturing. Traditional Computational Fluid Dynamics (CFD) simulations, while detailed, often suffer from long computation times and complexity, making them impractical for real-time applications. This study introduces a novel multivariate unsupervised learning algorithm for clustering bioreactors into coherent regions based on CFD-generated and real-world data. The resulting clusters can be used to determine regimes inside a reactor, or can work as an initial step for compartment models. Our method employs a custom k-means clustering algorithm that not only ensures spatial continuity within clusters but also optimizes the number of compartments based on clustering scores. This optimization process focuses on defining compartments clearly while retaining maximum information from the continuous body, as demonstrated by a Pareto front analysis. The efficacy and adaptability of this approach were validated through two case studies: a 202 m³ Rushton impeller bioreactor and an 840 m³ airlift reactor. The results underscore the benefits of 3-D compartmentalization in capturing the complex dynamics of fluid motion and cellular activities. By establishing a robust method for scaling down experiments and enhancing bioreactor design, this study paves the way for more efficient industrial applications.

The bright side of the Moon: The historical journey of our tidally locked satellite

Abstract The paper discusses a major shift in the (Western) science of our Moon. It reconsiders well-known developments, as the Aristotelian concept of distinct celestial and terrestrial worlds in which the Moon was one of seven perfect planetary spheres gave way to our modern view of a very Earth-like body, even endowed at one stage with oceans and continents. It examines the impact of pre-telescopic and telescopic observations in the period 1560 to 1660, notably those of Galileo Galilei and William Gilbert. Its new perspective is to present the strong evidence that supported the idea of the Moon as a planet. In large part this was because it is now known that aspects of the Moon’s orbit are unusual compared with the multiplicity of “moons” in the Solar System. It argues that a major reason was Aristotle’s influential argument for the theoretical impossibility of lunar libration. It concludes with the extraordinary work of William Gilbert (1544-1603) who, it is argued, was the true discoverer of libration because Galileo, who is often credited with it, failed to grasp the necessary dynamics of lunar motion. Notwithstanding, both played crucial roles in the emerging conception of our Moon as “another Earth”. Human activity is now degrading both bodies.

Numerical simulation of particles distribution of environmental tobacco smoke (ETS) and its concentration in a closed environment

Humans are frequently exposed to various chemical hazards, with smoking being a significant source of indoor air pollution. This pollution is particularly pronounced in environments such as smoking rooms, conference halls, cafes, and coffee houses. This study focuses on analyzing the concentration, distribution, and behavior of emitted particles from both mainstream and sidestream smoke in a controlled smoking room environment. A critical aspect of the research is the consideration of the thermal plume generated by the smoker's body, particularly around the breathing zone, which plays a crucial role in the dispersion and inhalation of pollutants. To conduct this analysis, a computational fluid dynamics approach was employed, incorporating a displacement ventilation (DV) system integrated with a detailed surface mesh model of a standing manikin. A Lagrangian approach was utilized to track the particle paths, considering factors such as particle size, density, and initial velocity. This approach was complemented by an Eulerian method to simulate the complex airflow patterns within the smoking room, accounting for turbulent flow and temperature variations. The integration of these methods provides a comprehensive understanding of both the macroscopic and microscopic behaviors of smoke particles. The motion equations governing the particles incorporated several forces, including inertial drag force, viscous drag force, buoyancy force, and gravitational force. Additionally, the study examined the interaction between thermal plumes and smoke particles, particularly how temperature gradients around the body affect particle dispersion and concentration. The study meticulously evaluated the distribution and volume average of respirable suspended particles (RSPs) and nicotine by analyzing a plane opposite to the breathing zone of both heated and unheated manikins. It was observed that the thermal plume generated by the temperature gradient around the body could significantly alter the flow field of both sidestream and mainstream smoke between puff periods. The simulation results demonstrated that the thermal plume increased the concentration of RSPs in the breathing zone, highlighting a critical exposure pathway for smokers and nonsmokers alike. A significant increase of approximately 70% in the nicotine concentration is due to the thermal plume. The concentration of nicotine peaks at approximately 0.003 mg/m3 by the third second in smoker#1's (6 smokers' position) breathing zone. Specific configurations of the DV system showed varying efficiencies in reducing pollutant concentrations, emphasizing the need for targeted ventilation strategies. In a chamber with six smokers, researchers found that the time required for suspended particles to reach a cleaning ratio, considering the dynamics of particle movement due to smoking activity, was approximately 184 s per puff.

Interacting myosin head dynamics and their modification by 2′-deoxy-ADP

The contraction of striated muscle is driven by cycling myosin motor proteins embedded within the thick filaments of sarcomeres. In addition to cross-bridge cycling with actin, these myosin proteins can enter an inactive, sequestered state in which the globular S1 heads rest along the thick filament surface and are inhibited from performing motor activities. Structurally, this state is called the interacting heads motif (IHM) and is a critical conformational state of myosin that regulates muscle contractility and energy expenditure. Structural perturbation of the sequestered state can pathologically disrupt IHM structure and the mechanical performance of muscle tissue. Thus, the IHM state has become a target for therapeutic intervention. An ATP analog called 2′-deoxy-ATP (dATP) is a potent myosin activator that destabilizes the IHM. Here, we use molecular dynamics simulations to study the molecular mechanisms by which dATP modifies the structure and dynamics of myosin in a sequestered state. Simulations of the IHM state containing ADP.Pi in both nucleotide binding pockets revealed dynamic motions of the blocked head-free head interface, light chain binding domain, and S2 in this “inactive” state of myosin. Replacement of ADP.Pi by dADP.Pi triggered a series of structural changes that increased heterogeneity among residue contact pairs at the blocked head-free head interface and a 14% decrease in the interaction energy at the interface. Dynamic changes to this interface were accompanied by dynamics in the light chain binding region. A comparative analysis of these dynamics predicted new structural sites that may affect IHM stability.

Bundling instability of lophotrichous bacteria

We present a mathematical model of lophotrichous bacteria, motivated by Pseudomonas putida, which swim through fluid by rotating a cluster of multiple flagella extended from near one pole of the cell body. Although the flagella rotate individually, they are typically bundled together, enabling the bacterium to exhibit three primary modes of motility: push, pull, and wrapping. One key determinant of these modes is the coordination between motor torque and rotational direction of motors. The computational variations in this coordination reveal a wide spectrum of dynamical motion regimes, which are modulated by hydrodynamic interactions between flagellar filaments. These dynamic modes can be categorized into two groups based on the collective behavior of flagella, i.e., bundled and unbundled configurations. For some of these configurations, experimental examples from fluorescence microscopy recordings of swimming P. putida cells are also presented. Furthermore, we analyze the characteristics of stable bundles, such as push and pull, and investigate the dependence of swimming behaviors on the elastic properties of the flagella.

Exact optimization of inter-array dynamic cable networks for Floating Offshore Wind Farms

Optimization of inter-array dynamic cables for Floating Offshore Wind Farms (FOWFs) using three integer linear programs and a heuristic is presented. Design optimization of fixed-bottom offshore wind is a challenging research problem but the presence of dynamic components in FOWFs adds new complexity - as the Floating Offshore Wind Turbine (FOWT), the support structure including the station-keeping system, and the floating power cables all experience dynamic movement in reaction to wind, wave and even current forcing. In this study, dynamic modelling for the response of this system is first carried out to assess the risk of potential mechanical interference between movable elements. Subsequently, safety zones constraints are defined in the optimization to ensure minimally safe conditions for operation of the combined FOWT/support-structure/cables system. Likewise, additional constraints including maximum thermal limits, tree topology without branching, and others are incorporated. The programs follow an incremental approach. Model 1 proposes a simple way to avoid mechanical interference, Model 2 adds variables modelling mooring lines anchoring, and Model 3 increases the degrees of freedom through addition of the positioning of the touchdown point where the dynamic and static sections meet at the seabed. The applicability is illustrated through realistic case studies for a reference FOWF in Europe. Results show that: (i) Modern branch-and-cut solvers are able to solve Model 2 getting the global optimum in seconds, and (ii) further cost refining can be obtained after wrapping Model 3 in the heuristic, using Model 2 as the initial design, decreasing the cost of this layout by around 1.5% in few hours through a nonrectilinear topology.

Optimal Location for Tower Crane and Dynamic Trailer Parking in High-Rise Modular Building Construction Project

Optimization of tower crane positioning is essential in precast building construction to ensure that a crane is in the right position to offer the best value for placing precast elements. The first goal is the optimization of transportation distances made by tower cranes, which will address the issues of efficiency and cost. This is done in a way that provides for minimization of the distances that lie between the trailer parking where elements are parked, the tower crane, and the construction installation point. However, current research fails to address the dynamic movement efficiency of trailers, especially when handling multiple trailers and several models of tower cranes, making this scenario an optimization problem that is classified as NP-hard due to the likelihood of causing a combinatorial explosion. This work endeavors to present a new mathematical model that has been applied to the Genetic Algorithm (GA). The ideal demand-generated model is designed to solve the optimal model and position of tower cranes and the prospective positioning of trailers for parking. The feasibility and applicability of the method exploited in the study are also established through a project case study. When adopting the proposed planning model compared to the earlier planning scale, comparisons highlight a small yet significant saving of 6% in time and cost when lifting elements instead of providing them from the trailers by setting up a new on-site stockyard. In addition, a great deal of enhancement is also observed in the final solution aspects, where the developed GA has even reduced the operational time and cost by half a percent each. The results of this research offer best-practice approaches to the position analysis of tower cranes in precast building construction to bring scalability and cost optimization to bear on the construction business.

The effects of pressure on anticipatory postural adjustments during a jump shot in basketball

BackgroundAnticipatory postural adjustments (APAs) play an important role in feedforward control of dynamic movements, such as jump shot performance in basketball. It is known that jump shot performance declines under pressure from a defender (shot blocker). Research questionDoes pressure from a shot blocker affect the APAs of a jump shot in basketball? Is jump shot performance in basketball associated with APAs? MethodsFourteen healthy male university basketball players performed jump shots under pressure and non-pressure (free) conditions by a shot blocker. Using a force plate, the APAs were defined as occurring until the point of thrust (TH) phase, and ground reaction force (GRF) and center of pressure (COP) at that moment were assessed. To assess jump shot performance, the maximum GRF during the TH phase (THmax), jumping height, and success score of the shot (accuracy score: AS) were measured by using the vertical component of the force plate. Two-way ANOVA examined the effects of the phase and condition on APA duration. The effects of pressure from a shot blocker on each variable (subjective pressure intensity, AS, GRF, and COP) were analyzed using a pairwise t-test or Wilcoxon signed-rank tests. Relationships between changes in jump shot performance and GRF or COP variables were assessed via Spearman’s correlation analysis. Differences between the pressure and free conditions were denoted by p/f (pressure/free). ResultsThe APA duration was shorter under the pressure condition compared to the free condition. The THmax and jump height values were greater under the pressure condition relative to the free condition. Across conditions, changes in COP sway velocity of the APA phase were significantly and negatively correlated with AS. SignificanceThe results of this study suggest that pressure from a shot blocker shortens APA duration and decreases jump shot performance.

Characterization of Human Shoulder Joint Stiffness Across 3D Arm Postures and Its Sex Differences.

Understanding the characteristics of shoulder joint stiffness can offer insights into how the shoulder joint contributes to arm stability and assists in various arm postures and movements. This study aims to characterize posture-dependent shoulder stiffness in a three-dimensional (3D) space and investigate its potential sex differences. A multi-degree-of-freedom, parallel-actuated shoulder exoskeleton robot was used' to perturb the participant's shoulder joint and measure the resulting torque responses while participants relaxed their shoulder muscles. The group average results of 40 healthy individuals (20 males and 20 females) revealed that arm postures significantly affect shoulder stiffness, particularly in postures involving shoulder flexion/extension and horizontal flexion/extension. Shoulder stiffness consistently increased as the shoulder flexion angle decreased and the shoulder horizontal flexion/extension approached the limit of its range of motion. The comparative group results between males and females indicated that shoulder stiffness in males was greater than that in females across all 15 arm postures measured in this study. Even after normalizing the data by subject body mass, the female group showed significantly lower stiffness than the male group in 12 out of the 15 arm postures. The results highlight that 3D arm postures and sex significantly affect shoulder stiffness even under relaxed muscles. This study provides valuable foundations for future studies aimed at characterizing shoulder stiffness in the context of active muscles and dynamic movement tasks, evaluating changes in shoulder stiffness following neuromuscular injuries, and formulating rehabilitative training protocols for individuals suffering from shoulder problems.

Global motor dynamics - Invariant neural representations of motor behavior in distributed brain-wide recordings

Objective.Motor-related neural activity is more widespread than previously thought, as pervasive brain-wide neural correlates of motor behavior have been reported in various animal species. Brain-wide movement-related neural activity have been observed in individual brain areas in humans as well, but it is unknown to what extent global patterns exist.Approach.Here, we use a decoding approach to capture and characterize brain-wide neural correlates of movement. We recorded invasive electrophysiological data from stereotactic electroencephalographic electrodes implanted in eight epilepsy patients who performed both an executed and imagined grasping task. Combined, these electrodes cover the whole brain, including deeper structures such as the hippocampus, insula and basal ganglia. We extract a low-dimensional representation and classify movement from rest trials using a Riemannian decoder.Main results.We reveal global neural dynamics that are predictive across tasks and participants. Using an ablation analysis, we demonstrate that these dynamics remain remarkably stable under loss of information. Similarly, the dynamics remain stable across participants, as we were able to predict movement across participants using transfer learning.Significance.Our results show that decodable global motor-related neural dynamics exist within a low-dimensional space. The dynamics are predictive of movement, nearly brain-wide and present in all our participants. The results broaden the scope to brain-wide investigations, and may allow combining datasets of multiple participants with varying electrode locations or calibrationless neural decoder.

Vibration control of two portal frames type shear buildings through self-synchronous dynamics of two non-ideal sources indirectly coupled

The present paper proposes a new device where it is observed the self-synchronization between two unbalanced DC motors with a limited power supply when they are indirectly coupled. The vibrating system studied consists of two portal frames type shear buildings coupled, carrying each an unbalanced DC motor. The engines are supposed to rotate in the same direction and act on each as external excitation. The dynamics investigations are done with analytical and numerical methods to achieve this purpose. The synchronous solutions are derived and their stability conditions are also explored using the averaging method. The results of this analytical investigation are confirmed later by numerical simulations. The effects of some physical parameters on the self-synchronization of DC motors are presented. The impact of the nonlinear coupling between the floors on the DC motors dynamics is also explored. The Sommerfeld effect appearing in the system is reduced by taking into account the damping coming from the environment and the coupling between the portal frame. It is observed that in-phase synchronization of the non-ideal sources assures a low amplitude of vibration in the different floors compared to opposite-phase synchronization.

Using an integrated motor imagery and physical training intervention after knee injury: an interim analysis of the MOTIFS randomised controlled trial

ObjectivesPhysical function is often a main focus of knee injury rehabilitation, but recent recommendations include increasing attention to psychological factors. We have developed the MOTor Imagery to Facilitate Sensorimotor re-learning...

A High‐Precision Dynamic Movement Recognition Algorithm Using Multimodal Biological Signals for Human–Machine Interaction

Accurate recognition of human dynamic movement is essential for seamless human–machine interaction (HMI) across various domains. However, most of the existing methods are single‐modal movement recognition, which has inherent limitations, such as limited feature representation and instability to noise, which will affect its practical performance. To address these limitations, this article proposes a novel fusion approach that can integrate two biological signals, including electromyography (EMG) and bioelectrical impedance (BI). The fusion method combines EMG for capturing dynamic movement features and BI for discerning key postures representing discrete points within dynamic movements. In this method, the identification of key postures and their temporal sequences provide a guiding framework for the selection and weighted correction of probability prediction matrices in EMG‐based dynamic recognition. To verify the effectiveness of the method, six dynamic upper limb movements and nine key postures are defined, and a Universal Robot that can follow movements is employed for experimental validation. Experimental results demonstrate that the recognition accuracy of the dynamic movement reaches 96.2%, representing an improvement of nearly 10% compared with single‐modal signal. This study illustrates the potential of multimodal fusion of EMG and BI in movement recognition, with broad prospects for application in HMI fields.

Analysis of plantar pressure of midsole prepared by 3d printed biomimetic structures with different densities

AbstractThis study investigates the impact of 3D printed midsoles with biomimetic structures of varying densities on plantar pressure during static and dynamic motions. The midsoles were designed with three densities of Tyson polygon (TS) structures: 1TS, 2TS, and 3TS. Plantar pressure tests were conducted on midsoles during static and dynamic motions such as walking, running, and jumping. The data were analyzed based on hypotheses related to samples, motions, and 10 plantar pressure zones. As results, for static motion, all midsoles improved pressure distribution and reduced peak pressure compared to barefoot conditions, with 1TS being the most effective. During dynamic motions, 1TS and 2TS effectively distributed plantar pressure in the midfoot and heel areas, while 3TS provided better support and stability during high-intensity activities like jumping. Statistical analysis revealed that 1TS offered comfort and flexibility but lacked support, 2TS balanced support and cushioning, and 3TS provided superior support and stability but reduced elasticity during jumps. In dynamic motions, 1TS excelled in walking, and 2TS performed best in high-intensity activities such as running and jumping. In the meta areas (M2 and M3), 1TS reduced pressure by over 30% during walking and nearly 40% during running, while 3TS showed similar reductions during jumping, with BF showing higher pressures compared to running. Thus, this study highlights the effectiveness of 1TS and 2TS in reducing pressure in the meta and midfoot areas, emphasizing the importance of selecting the right midsole density for optimal comfort and performance across different activities.

Transferable Deep Learning Models for Accurate Ankle Joint Moment Estimation during Gait Using Electromyography

The joint moment is a key measurement in locomotion analysis. Transferable prediction across different subjects is advantageous for calibration-free, practical clinical applications. However, even for similar gait motions, intersubject variance presents a significant challenge in maintaining reliable prediction performance. The optimal deep learning models for ankle moment prediction during dynamic gait motions remain underexplored for both intrasubject and intersubject usage. This study evaluates the feasibility of different deep-learning models for estimating ankle moments using sEMG data to find an optimal intrasubject model against the inverse dynamic approach. We verified and compared the performance of 1302 intrasubject models per subject on 597 steps from seven subjects using various architectures and feature sets. The best-performing intrasubject models were recurrent convolutional neural networks trained using signal energy features. They were then transferred to realize intersubject ankle moment estimation.

Modeling and motion analysis of flexible legged robots using the finite particle method

Robotics with flexible legs have attracted significant attention. Engineers often design and analyze the motion of legged robots from kinematic and biomimetic perspective. However, the influence of flexibility of the feet on robot locomotion is often not given sufficient considerations, which is also very crucial to the motion posture of the flexible legged robots, especially as the soft robots design becomes increasingly popular. The mainly difficulties lies in the traditional numerical methods in handling the dynamic motion analysis with both large rigid motion and large deformation. In this paper, the finite particle method (FPM) is used to simulate the motion and deformation coupled problems of the flexible six-legged robot. A shell-based particle model of a six-leg robot and the contact model between legs and ground are built. Without iterative and modification of the FPM analytical framework, structural nonlinearity is efficiently handled after eliminating rigid body motions by a fictitious reverse motion. The motion and deformation of a single leg with varying leg thickness, locomotion speed, and leg-to-ground friction coefficients were simulated. By analyzing the stress distribution in the leg and the number of contact points with the ground, the mechanical leg was optimized in design. Furthermore, the motion and deformation of the entire six-legged robot were simulated using the FPM. The numerical results' feasibility was validated through comparison with experimental data obtained from robot walking tests. The proposed method effectively simulates the motion and deformation of flexible robots, providing significant insights for the design of soft robots.