Robot Foot Research Articles

Robotic feet modeled after ungulates improve locomotion on soft wet grounds

Locomotion on soft yielding grounds is more complicated and energetically demanding than on hard ground. Wet soft ground (such as mud or snow) is a particularly difficult substance because it dissipates energy when stepping and resists extrusion of the foot. Sinkage in mud forces walkers to make higher steps, thus, to spend more energy. Yet wet yielding terrains are part of the habitat of numerous even-toed ungulates (large mammals with split hooves). We hypothesized that split hooves provide an advantage on wet grounds and investigated the behavior of moose legs on a test rig. We found that split hooves of a moose reduce suction force at extrusion but could not find conclusive evidence that the hoof reduces sinkage. We then continued by designing artificial feet equipped with split-hoof-inspired protuberances and testing them under different conditions. These bio-inspired feet demonstrate an anisotropic behavior enabling reduction of sinkage depth up to 46.3%, suction force by 47.6%, and energy cost of stepping on mud by up to 70.4%. Finally, we mounted these artificial feet on a Go1 quadruped robot moving in mud and observed 38.7% reduction of the mechanical cost of transport and 55.0% increase of speed. Those results help us understand the physics of mud locomotion of animals and design better robots moving on wet terrains. We did not find any disadvantages of the split-hooves-inspired design on hard ground, which suggests that redesigning the feet of quadruped robots improves their overall versatility and efficiency on natural terrains.

Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model

One of the major problems in robotics research has been developing an actuator system for extremely dynamic-legged robots. High torque density and the capacity to control dynamic physical interactions are two design requirements for high-speed locomotion that are challenging for conventional actuators used in manufacturing applications to meet. To address this system and apply the desired control to reach the best stability position, the robot's foot was simulated with the Van der Pol equations, applied the required control, and studied that application. This work describes the actions of a new novel control mechanism known as the Integral Resonant Negative Derivative Feedback (IRNDF) controller, which reduces the vibration response of a double Van der Pol oscillator subjected to external excitations. This unique controller combines integral resonant control (IRC) and negative derivative feedback (NDF) controllers to provide a new controller effect for double Van der Pol oscillators. The multiple scale perturbation technique (MSPT) has been applied to solve the controlled system analytically. The MATLAB and MAPLE programs have been used to complete and clarify all of the numerical talks. The frequency response curves have been used to study the impact that altering the parameter values had on the amplitude. The controlled system vibration amplitude is governed by frequency-response equations (FREs), which have been constructed. In the vibration system, the IRC, NDF, and IRNDF controllers were compared to see which one was the best. Numerical results show that the unique IRNDF controller is the best at reducing oscillations and decreasing amplitude values. The effects of the effective parameters on the controlled system have been identified. The frequency-response equation that was derived has been used to plot the various response curves for the framework that show the stable and unstable zones when the controller is off and on. Lastly, excellent agreement between the derived numerical findings and the analytical ones was observed. Lastly, utilizing time histories and response curves to compare analytical and numerical solutions was fascinating and significant.

A Motion Planner Based on Mask-D3QN of Quadruped Robot Motion for Steam Generator.

Crawling robots are the focus of intelligent inspection research, and the main feature of this type of robot is the flexibility of in-plane attitude adjustment. The crawling robot HIT_Spibot is a new type of steam generator heat transfer tube inspection robot with a unique mobility capability different from traditional quadrupedal robots. This paper introduces a hierarchical motion planning approach for HIT_Spibot, aiming to achieve efficient and agile maneuverability. The proposed method integrates three distinct planners to handle complex motion tasks: a nonlinear optimization-based base motion planner, a TOPSIS-based base orientation planner, and a Mask-D3QN (MD3QN) algorithm-based gait motion planner. Initially, the robot's base and foot workspace were delineated through envelope analysis, followed by trajectory computation using Larangian methods. Subsequently, the TOPSIS algorithm was employed to establish an evaluation framework conducive to foundational turning planning. Finally, the MD3QN algorithm trained foot-points to facilitate robot movement along predefined paths. Experimental results demonstrated the method's adaptability across diverse tube structures, showcasing robust performance even in environments with random obstacles. Compared to the D3QN algorithm, MD3QN achieved a 100% success rate, enhanced average overall scores by 6.27%, reduced average stride lengths by 39.04%, and attained a stability rate of 58.02%. These results not only validate the effectiveness and practicality of the method but also showcase the significant potential of HIT_Spibot in the field of industrial inspection.

Optimizing PID control for enhanced stability of a 16‐DOF biped robot during ditch crossing

AbstractThe current research article discusses the design of a proportional–integral–derivative (PID) controller to obtain the optimal gait planning algorithm for a 16‐degrees‐of‐freedom biped robot while crossing the ditch. The gait planning algorithm integrates an initial posture, position, and desired trajectories of the robot's wrist, hip, and foot. A cubic polynomial trajectory is assigned for wrist, hip, and foot trajectories to generate the motion. The foot and wrist joint angles of the biped robot along the polynomial trajectory are obtained by using the inverse kinematics approach. Moreover, the dynamic balance margin was estimated by using the concept of the zero‐moment point. To enhance the smooth motion of the gait planner and reduce the error between two consecutive joint angles, the authors designed a PID controller for each joint of the biped robot. To design a PID controller, the dynamics of the biped robot are essential, and it was obtained using the Lagrange–Euler formulation. The gains, that is, KP, KD, and KI of the PID controller are tuned with nontraditional optimization algorithms, such as particle swarm optimization (PSO), differential evolution (DE), and compared with modified chaotic invasive weed optimization (MCIWO) algorithms. The result indicates that the MCIWO‐PID controller generates more dynamically balanced gaits when compared with the DE and PSO‐PID controllers.

Research on Foot Contact State Detection Technology of Wheel-Legged Robot.

The accurate perception of external environment information through the robot foot is crucial for the mobile robot to evaluate its ability to traverse terrain. Adequate foot-end contact signals can provide robust support for robot motion control and decision-making processes. The shape and uncertain rotation of the wheel-legged robot foot end represent a significant challenge to sensing the robot foot-end contact state, which current foot-end sensing schemes cannot solve. This paper presents a sensing method for the tire stress field of wheel-legged robots. A finite element analysis was conducted to study the deformation characteristics of the foot-end tire under force. Based on this analysis, a heuristic contact position estimator was designed that utilizes symmetrical deformation characteristics. Strain sensors, arranged in an array, extract the deformation information on the inner surface of the tire at a frequency of 200 Hz. The contact position estimator reduces the dimensionality of the data and fits the eigenvalues to the estimated contact position. Using support vector regression, the force estimator utilizes the estimated contact position and sensor signal to estimate the normal reaction force, designated as FZ. The sensing system is capable of detecting the contact position on the wheel circumference (with a root mean square error of 1.150°), as well as the normal force of 160 N on the Z axis (with a root mean square error of 6.04%). To validate the efficacy of the sensor detection method, a series of randomized and repeated experiments were conducted on a self-constructed test platform. This novel approach offers a promising avenue for perceiving contact states in wheel-legged robots.

DE-AFO: A Robotic Ankle Foot Orthosis for Children with Cerebral Palsy Powered by Dielectric Elastomer Artificial Muscle.

Conventional passive ankle foot orthoses (AFOs) have not seen substantial advances or functional improvements for decades, failing to meet the demands of many stakeholders, especially the pediatric population with neurological disorders. Our objective is to develop the first comfortable and unobtrusive powered AFO for children with cerebral palsy (CP), the DE-AFO. CP is the most diagnosed neuromotor disorder in the pediatric population. The standard of care for ankle control dysfunction associated with CP, however, is an unmechanized, bulky, and uncomfortable L-shaped conventional AFO. These passive orthoses constrain the ankle's motion and often cause muscle disuse atrophy, skin damage, and adverse neural adaptations. While powered orthoses could enhance natural ankle motion, their reliance on bulky, noisy, and rigid actuators like DC motors limits their acceptability. Our innovation, the DE-AFO, emerged from insights gathered during customer discovery interviews with 185 stakeholders within the AFO ecosystem as part of the NSF I-Corps program. The DE-AFO is a biomimetic robot that employs artificial muscles made from an electro-active polymer called dielectric elastomers (DEs) to assist ankle movements in the sagittal planes. It incorporates a gait phase detection controller to synchronize the artificial muscles with natural gait cycles, mimicking the function of natural ankle muscles. This device is the first of its kind to utilize lightweight, compact, soft, and silent artificial muscles that contract longitudinally, addressing traditional actuated AFOs' limitations by enhancing the orthosis's natural feel, comfort, and acceptability. In this paper, we outline our design approach and describe the three main components of the DE-AFO: the artificial muscle technology, the finite state machine (the gait phase detection system), and its mechanical structure. To verify the feasibility of our design, we theoretically calculated if DE-AFO can provide the necessary ankle moment assistance for children with CP-aligning with moments observed in typically developing children. To this end, we calculated the ankle moment deficit in a child with CP when compared with the normative moment of seven typically developing children. Our results demonstrated that the DE-AFO can provide meaningful ankle moment assistance, providing up to 69% and 100% of the required assistive force during the pre-swing phase and swing period of gait, respectively.

Bipedal robot center of pressure feedback simulation for center of mass learning

This research aims to create a walking bipedal robot with center of pressure feedback simulation for the center of mass learning, describe its feasibility for learning, describe students' motivation to learn, and describe students' science literacy after using it. The research method used ADDIE (analysis, design, development, implementation, and evaluation). The research data was obtained using a motivation scale questionnaire, science literacy scale, and feasibility scale. The research sample was 48 people; after the research obtained, the simulation of bipedal robot pressure center feedback for center of mass learning can be implemented with the principle of the robot's center of mass detected on the sole of the robot's foot equipped with a force sensitive resistor (FSR) sensor, the position of the center of mass is visible on the monitor screen as a center of mass learning, so that it can motivate students to learn and improve students' science literacy. This can be seen from the feasibility scale score, motivation scale, and science literacy scale of 4.133, 4.072, and 4.067 (scale 1 to 5), respectively, in the "good" category.

Kinematics Analysis and Gait Study of Bionic Turtle Crawling Mechanism.

Longer distance water delivery culverts pose obstacles such as deposited silt, stones, and dead trees. In this paper, a crawling robot is designed to mimic the joint structure of a turtle using bionic design principles. The mechanism and gait of the robot are analyzed. The kinematics model of the robot is established using the D-H method and analytical approach, while the dynamics model is established using Lagrange's method. Based on kinematics and dynamics analysis theory, compound cycloid and cubic polynomial motion trajectories for the robot foot are planned along with a crawling gait resembling that of a turtle's abdomen. Simulation experiments and scale prototype experiments confirm that when gait parameters are identical, the energy consumption of compound cycloid trajectory exceeds that of cubic polynomial foot trajectory. When planning these two types of foot trajectories, it was observed that energy consumption ratio decreases with increasing step length but increases with increasing step height.

A Quasi-Passive Robotic Ankle Foot Orthosis With Speed-Adaptive Stiffness

A Quasi-Passive Robotic Ankle Foot Orthosis With Speed-Adaptive Stiffness

Investigating the performance of soft robotic adaptive feet with longitudinal and transverse arches.

Biped robots usually adopt feet with a rigid structure that simplifies walking on flat grounds and yet hinders ground adaptation in unstructured environments, thus jeopardizing stability. We recently explored in the SoftFoot the idea of adapting a robotic foot to ground irregularities along the sagittal plane. Building on the previous results, we propose in this paper a novel robotic foot able to adapt both in the sagittal and frontal planes, similarly to the human foot. It features five parallel modules with intrinsic longitudinal adaptability that can be combined in many possible designs through optional rigid or elastic connections. By following a methodological design approach, we narrow down the design space to five candidate foot designs and implement them on a modular system. Prototypes are tested experimentally via controlled application of force, through a robotic arm, onto a sensorized plate endowed with different obstacles. Their performance is compared, using also a rigid foot and the previous SoftFoot as a baseline. Analysis of footprint stability shows that the introduction of the transverse arch, by elastically connecting the five parallel modules, is advantageous for obstacle negotiation, especially when obstacles are located under the forefoot. In addition to biped robots' locomotion, this finding might also benefit lower-limb prostheses design.

Analytical Model and Experimental Testing of the SoftFoot: An Adaptive Robot Foot for Walking Over Obstacles and Irregular Terrains

Analytical Model and Experimental Testing of the SoftFoot: An Adaptive Robot Foot for Walking Over Obstacles and Irregular Terrains

Преодоление шагающим роботом препятствий, характерных для равнины

An upper estimate of the maximum width of the forbidden zone for foot fulcrums, which a walking robot can overcome in static stability mode, is presented. Using the examples of six-legged and four-legged robot, it is shown that the obtained estimate can't be improved. For this purpose, the sequences of the robot's foot placement have been formed, ensuring the achievement of the estimation meaning. The results of computer modeling and video materials illustrating the process of overcoming an obstacle by a six-legged robot are presented.

Управление статически неустойчивым шагающим аппаратом при ограниченном трении в опоре

A non-trivial problem in the biped walking is the preservation of stability under external influences without slowing down velocity. A dynamic walking control algorithm with a hierarchical structure is proposed in the article. The lower control level is organized according to the principle of tracking drives and ensures the position of the robot`s body using all given possible coordinates. The problem of traffic stabilization is solved at the upper level. An ideal mechanism — a flat inverted mathematical pendulum is considered in the feedback circuit. Its equations are synchronized by the moment of the step ending. Particular attention is paid to the interaction of the robot foot with the support surface to determine the conditions for the absence of slippage. Proposed control approach makes it possible to control the current position of the robot`s structure in the space in different walking modes without slowing down velocity. Critically assessing the results and prospects of the research, we can conclude about their use-fulness in the development of artificial intelligence cooperation with humans, about possible applications in everyday life, a specific environment and industry. The proposed approach may be applicable to the control of the walking mechanisms of similar mobile robots.

Design of Humanoid Robot Foot to Absorb Ground Reaction Force by Mimicking Longitudinal Arch and Transverse Arch of Human Foot

Design of Humanoid Robot Foot to Absorb Ground Reaction Force by Mimicking Longitudinal Arch and Transverse Arch of Human Foot

Estimation of body segmental orientation for prosthetic gait using a nonlinear autoregressive neural network with exogenous inputs

Assessment of the prosthetic gait is an important clinical approach to evaluate the quality and functionality of the prescribed lower limb prosthesis as well as to monitor rehabilitation progresses following limb amputation. Limited access to quantitative assessment tools generally affects the repeatability and consistency of prosthetic gait assessments in clinical practice. The rapidly developing wearable technology industry provides an alternative to objectively quantify prosthetic gait in the unconstrained environment. This study employs a neural network-based model in estimating three-dimensional body segmental orientation of the lower limb amputees during gait. Using a wearable system with inertial sensors attached to the lower limb segments, thirteen individuals with lower limb amputation performed two-minute walk tests on a robotic foot and a passive foot. The proposed model replicates features of a complementary filter to estimate drift free three-dimensional orientation of the intact and prosthetic limbs. The results indicate minimal estimation biases and high correlation, validating the ability of the proposed model to reproduce the properties of a complementary filter while avoiding the drawbacks, most notably in the transverse plane due to gravitational acceleration and magnetic disturbance. Results of this study also demonstrates the capability of the well-trained model to accurately estimate segmental orientation, regardless of amputation level, in different types of locomotion task.

Parametric Design and Prototyping of a Low-Power Planar Biped Robot.

This study proposes a design approach and the development of a low-power planar biped robot named YU-Bibot. The kinematic structure of the robot consists of six independently driven axes, and it weighs approximately 20 kg. Based on biomimetics, the robot dimensions were selected as the average anthropomorphic dimensions of the human lower extremities. The optimization of the mechanical design and actuator selection of the robot was based on the results of parametric simulations. The natural human walking gait was mimicked as a walking pattern in these simulations. As a result of the optimization, a low power-to-weight ratio of 30 W/kg was obtained. The drive system of the robot joints consists of servo-controlled brushless DC motors with reduction gears and additional bevel gears at the knee and ankle joints. The robot features spring-supported knee and ankle joints that counteract the robot's weight and compensate for the backlash present in these joints. The robot is constrained to move only in the sagittal plane by using a lateral support structure. The robot's feet are equipped with low-cost, force-sensitive resistor (FSR)-type sensors for monitoring ground contact and zero-moment point (ZMP) criterion. The experimental results indicate that the proposed robot mechanism can follow the posture commands accurately and demonstrate locomotion at moderate stability. The proposed parametric natural gait simulation-based design approach and the resulting biped robot design with a low power/weight ratio are the main contributions of this study.

Evaluation of Robotic Ankle-Foot Orthosis with Different Actuators Using Simscape Multibody for Foot-Drop Patients

Gait cycle plays a major role in human locomotion. Patients with neuromuscular problems are unable to walk normally. Foot drop causes difficulty in lifting the front part of the foot and affects the dorsiflexion (DF) and plantar flexion (PF) motion of the foot. Patient with foot drop must use ankle braces to achieve a normal gait. The existing ankle-foot orthosis (AFO) has its own limitations, as it does not produce adequate PF motion. To overcome this scenario, a study was conducted to analyse the two-degrees-of-freedom (DOF) motion of a robotic ankle foot orthosis (RAFO) with a spring-based series elastic actuator (SEA) and scissor actuator. The objective of this paper is to evaluate the two DOF of RAFO with two different actuators using simscape multibody. The RAFO with actuators were designed using Solidworks, and simulation was carried out using simscape multibody, to analyse the 2-DOF motion. The dynamic motion analysis was carried out using block libraries, bodies, joints, constraints, revolute joints, sensors and a proportional integral (PI) controller. From the simulation results, the total range of motion (ROM) 40° (PF angle of –25° and DF angle of 15°) is achieved by the proposed RAFO with different actuators. Further, based on the results, the input power consumption of spring-based SEA was found to be less than the scissor actuator. Similarly, torque and output power generation of the scissor actuator was found to be greater than spring-based SEA to achieve the normal human ROM. Hence, the designer can choose a hybrid actuator for foot-drop-disorder applications.

Design of Flexible Feet for Legged Robots

Due to its unique body structure and movement mode, the legged robot has strong terrain adaptability and can move in many complex environments. However, the robot's feet will frequently contact with the ground during the movement, and will be subject to greater ground impact. The flexible foot structure can effectively reduce the ground impact. The leg and foot structures, and locomotor characteristics of cats and insects were analyzed based on bionic principles. Combined with the structural characteristics of the small-legged robot, the structure and function of the flexible foot end is analyzed.

Soft climbing robot with magnetic feet for multimodal locomotion

Inspection robots that can be used to inspect man-made structures have significant potential for industrial applications, but existing soft robots are not well suited for the exploration of complex metallic structures with many obstacles. This paper proposes a soft climbing robot well suited for such conditions as the robot uses feet with a controllable magnetic adhesion. It uses soft inflatable actuators to control this adhesion as well as the deformation of the body. The proposed robot consists of a robot body that can bend and lengthen, robot feet that can magnetically adhere to and detach from metallic surface, and rotational joints connecting each foot to the body to give the robot additional flexibility. It combines extensional soft actuators for the deformation of the body and contractile linear actuators for the robot feet, and the robot can produce complex deformations of the body that allow it to overcome a variety of scenarios. The capabilities of the proposed robot were verified through the implementation of three scenarios on metallic surfaces: crawling, climbing, and transitioning between surfaces. The robots could crawl or climb nearly interchangeably, could transition to and from horizontal surfaces to either upward or downward vertical surfaces.

Morphology-Changeable Soft Pads Facilitate Locomotion in Wet Conditions

Stable robot walking requires effective gait planning and control. The mechanical properties of contact between feet and ground are important factors in this process. In this paper, we propose and test a design for a robot foot that houses soft pads, which adapt to facilitate locomotion on wet and dry floors. The morphology of each soft pad distributed in the sole of the foot is changed from a thin elastic sheet to a spherical dome that protrudes from the sole with the use of compressed air to adapt the foot for walking. We constructed an analytical model to estimate how soft pad dome shape is effected by air pressure and associated properties regarding friction and forces when in contact with a dry or wet floor. The contribution of wet adhesion to enhance shear force among the floor and the soft pads was elaborated theoretically. We report results of practical experiments with a sole (35 mm×15 mm) housing 14 such soft pads (radius 1.5 mm) comparing walking in dry and wet conditions. Finally, we present a setup of a walking robot leg with the proposed foot and soft pad on flat ground. The results demonstrate that soft pad domes improved walking stability under wet conditions on flat ground whereas they made no noticeable difference under dry conditions. Changeable morphology of the soft pads (stiffness, radius of the domes), which is controlled by adjusting air pressure, contributed to adaptive walking. The results obtained here may inform attempts at morphological design of soft pads to facilitate locomotion of legged robots under various terrain conditions.