Compliant Legs Research Articles

Leg compliance is required to explain the ground reaction force patterns and speed ranges in different gaits.

Two simple models, vaulting over stiff legs and rebounding over compliant legs, are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running and that legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking. Here, we show that leg compliance is necessary to model walking and, in the process, identify the principles that underpin two important features of legged locomotion: First, at the same speed, step length, and stance duration, multiple gaits that differ in the number of leg contraction cycles are possible. Among them, humans and other animals choose a gait with M-shaped vertical ground reaction forces because it is energetically favored. Second, the transition from walking to running occurs because of the inability to redirect the vertical component of the velocity during the double stance phase. Additionally, we also examine the limits of double spring-loaded pendulum (DSLIP) as a quantitative model for locomotion, and conclude that DSLIP is limited as a model for walking. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.

Research Of Bio-Inspired Compliant Legged Robot Designs

Research Of Bio-Inspired Compliant Legged Robot Designs

Role of compliant mechanics and motor control in hopping - from human to robot

Compliant leg function found during bouncy gaits in humans and animals can be considered a role model for designing and controlling bioinspired robots and assistive devices. The human musculoskeletal design and control differ from distal to proximal joints in the leg. The specific mechanical properties of different leg parts could simplify motor control, e.g., by taking advantage of passive body dynamics. This control embodiment is complemented by neural reflex circuitries shaping human motor control. This study investigates the contribution of specific passive and active properties at different leg joint levels in human hopping at different hopping frequencies. We analyze the kinematics and kinetics of human leg joints to design and control a bioinspired hopping robot. In addition, this robot is used as a test rig to validate the identified concepts from human hopping. We found that the more distal the joint, the higher the possibility of benefit from passive compliant leg structures. A passive elastic element nicely describes the ankle joint function. In contrast, a more significant contribution to energy management using an active element (e.g., by feedback control) is predicted for the knee and hip joints. The ankle and knee joints are the key contributors to adjusting hopping frequency. Humans can speed up hopping by increasing ankle stiffness and tuning corresponding knee control parameters. We found that the force-modulated compliance (FMC) as an abstract reflex-based control beside a fixed spring can predict human knee torque-angle patterns at different frequencies. These developed bioinspired models for ankle and knee joints were applied to design and control the EPA-hopper-II robot. The experimental results support our biomechanical findings while indicating potential robot improvements. Based on the proposed model and the robot’s experimental results, passive compliant elements (e.g. tendons) have a larger capacity to contribute to the distal joint function compared to proximal joints. With the use of more compliant elements in the distal joint, a larger contribution to managing energy changes is observed in the upper joints.

Bioinspired Soft Spine Enables Small-Scale Robotic Rat to Conquer Challenging Environments.

For decades, it has been difficult for small-scale legged robots to conquer challenging environments. To solve this problem, we propose the introduction of a bioinspired soft spine into a small-scale legged robot. By capturing the motion mechanism of rat erector spinae muscles and vertebrae, we designed a cable-driven centrally symmetric soft spine under limited volume and integrated it into our previous robotic rat SQuRo. We called this newly updated robot SQuRo-S. Because of the coupling compliant spine bending and leg locomotion, the environmental adaptability of SQuRo-S significantly improved. We conducted a series of experiments on challenging environments to verify the performance of SQuRo-S. The results demonstrated that SQuRo-S crossed an obstacle of 1.07 body height, thereby outperforming most small-scale legged robots. Remarkably, SQuRo-S traversed a narrow space of 0.86 body width. To the best of our knowledge, SQuRo-S is the first quadruped robot of this scale that is capable of traversing a narrow space with a width smaller than its own width. Moreover, SQuRo-S demonstrated stable walking on mud-sand, pipes, and slopes (20°), and resisted strong external impact and repositioned itself in various body postures. This work provides a new paradigm for enhancing the flexibility and adaptability of small-scale legged robots with spine in challenging environments, and can be easily generalized to the design and development of legged robots with spine of different scales.

Compliant gait control method based on CVSLIP-FF model for biped robot walking over uneven terrain

Bipedal walking over uneven terrain remains a challenging task due to the environmental complexity and unavoidable landing impact. To realize the stable and robust walking of biped robots, this paper proposes a compliant gait control method, which focuses on walking compliance and conducts research on two levels. In the gait generation level, a Continuous-Variable Spring-Loaded Inverted Pendulum with Finite-sized Foot (CVSLIP-FF) model is provided with the consideration of the ankle joint and compliant spring-loaded leg. Then, a CVSLIP-FF based gait generation pattern with relevant walking strategies is provided to enhance the mobility of biped robots. In the joint control level, an ankle joint admittance control strategy is applied to achieve compliant robot-environment interaction. Experimental results indicate that compared with the traditional SLIP model, the proposed method performs better adaptability to uneven terrain with a 217.77% improvement, and enables biped robots to cope with slight unknown disturbance.

A Parallel Compliant Leg for energy efficient walking of exoskeleton–walker systems

Lower limb exoskeletons have garnered significant attention for their effectiveness in gait training for paraplegic patients. For patients with insufficient trunk or upper limb strength to maintain balance, employing an unpowered robotic walker with an exoskeleton for gait training is an effective approach. The energy efficiency of the actuation system is a pivotal consideration in the design of the exoskeleton–walker system due to its significant influence on the system’s durability and service efficiency. The main contribution of this paper is the development of a Parallel Compliant Leg (PCL) for the exoskeleton–walker system. The PCL consists of both powered legs of the exoskeleton and a passive flexible mechanism within the walker. This integration allows for the storage and release of energy during cyclic walking, resulting in reduced system energy consumption. To enhance energy efficiency, the support force optimization of the flexible mechanism is established. Based on this optimization, a design scheme and parameter optimization for the flexible mechanism are proposed. The effectiveness of the proposed flexible mechanism is verified through simulations on a robot simulation platform. Experimental results demonstrate a remarkable 67.6% reduction in system energy consumption achieved by the optimized mechanism.

A compliant leg design combining pantograph structure with leaf springs

AbstractWe proposed a compliant leg configuration that enhances the conventional pantograph design with leaf springs. The following facts characterize the proposed configuration: (1) Due to the use of the pantograph structure, the mass is centralized around the hip joint, reducing the lower leg inertia; (2) Leaf springs are chosen as elastic parts to increase energy efficiency and estimate foot-end contact forces. Compared with coil springs, leaf springs require no guide rails to deploy, and their stiffness can be easily adjusted through shape cutting. Analytical models are introduced to analyze the leg’s stiffness and estimate the contact forces only with the deflections of leaf springs. A one-leg robot based on the proposed design is built, and various experiments are conducted. Experiments regarding the stiffness calibration and the contact forces estimation showed an acceptable agreement with the analytical model. Experiments of dropping demonstrate the feasibility of the leg to perform spring-like behaviors. Experiments of periodic hopping demonstrate the feasibility of using spring deflections to detect touch-down events. For energy efficiency, it is also observed that the elastic leg has a 20% increment concerning the jumping height in the flight phase, compared with the one where leaf springs are replaced with rigid materials.

An online learning algorithm for adapting leg stiffness and stride angle for efficient quadruped robot trotting.

Animals adjust their leg stiffness and stride angle in response to changing ground conditions and gait parameters, resulting in improved stability and reduced energy consumption. This paper presents an online learning algorithm that attempts to mimic such animal behavior by maximizing energy efficiency on the fly or equivalently, minimizing the cost of transport of legged robots by adaptively changing the leg stiffness and stride angle while the robot is traversing on grounds with unknown characteristics. The algorithm employs an approximate stochastic gradient method to change the parameters in real-time, and has the following advantages: (1) the algorithm is computationally efficient and suitable for real-time operation; (2) it does not require training; (3) it is model-free, implying that precise modeling of the robot is not required for good performance; and (4) the algorithm is generally applicable and can be easily incorporated into a variety of legged robots with adaptable parameters and gaits beyond those implemented in this paper. Results of exhaustive performance assessment through numerical simulations and experiments on an under-actuated quadruped robot with compliant legs are included in the paper. The robot platform used a pneumatic piston in each leg as a variable, passive compliant element. Performance evaluation using simulations and experiments indicated that the algorithm was capable of converging to near-optimal values of the cost of transport for given operating conditions, terrain properties, and gait characteristics with no prior knowledge of the terrain and gait conditions. The simplicity of the algorithm and its demonstrably improved performance make the approach of this paper an excellent candidate for adaptively controlling tunable parameters of compliant, legged robots.

Power Efficient Design a Compliant Robotic Leg Based on Klann's Linkage

This article presents the analysis and optimization of a compliant robotic leg based on Klann's linkage. This leg is specifically designed to efficiently distribute its power requirement over its complete motion cycle, avoiding large peaks in the energy drawn from the battery. The structural compliance of the leg will be shown to be able to both provide a satisfactory walking motion and a timely energy boost to help with the gait. Klann's linkage is selected here as the basic kinematic structure of the leg to demonstrate the proposed methodology, namely to combine in a single structure both a complex trajectory generation and energy storage/release. This work is first aiming at proposing a thorough kinematic analysis of that mechanism using planar screw theory. The latter will be shown to be able to efficiently provide the velocity equations of the linkage as well as its force input–output relationship and singularity conditions. In a second part of this article, the previous kinetostatic model will be used to design and optimize a compliant version of the leg optimizing the power required for the robot to move. Finally, experiments will be shown to support the proposed approach.

Design of topology optimized compliant legs for bio-inspired quadruped robots

Robotic legs are an important component of the quadruped robot for achieving different motion gaits. Although the conventional rigid-link-based legs can generally perform robust motions, they still have the issues with poor sealing when operating in complex and liquid terrains. To cope with this problem, fully compliant legs with monolithic structure have been introduced in recent years to improve the system compactness and structural compliance of quadruped robots. In this article, we present a topology-optimization-based method to achieve efficient design of compliant robotic legs. In order to balance the structural stiffness and bending flexibility of the realized leg, a multi-objective optimization algorithm is utilized. A series of design cases are presented to illustrate the design principle and analytical procedure of the proposed method. In addition, experimental evaluation is also performed, and the results have demonstrated that, a quadruped robot with the optimized legs can successfully achieve stable and continuous straight-line walking motions.

Shock Absorption for Legged Locomotion through Magnetorheological Leg-Stiffness Control

The objective of this study was to evaluate the performance of a magnetorheological-fluid-based variable stiffness actuator leg under high impact forces through optimal tuning and control of stiffness and damping properties. To achieve this, drop testing experiments were conducted with the leg at various drop heights and payload masses. The results showed that while lower stiffness and higher damping can lead to lower impact forces and greater energy dissipation, respectively, optimal control can also protect the leg from deflecting beyond its functional range. Comparison with a rigid leg with higher damping showed a 57.5% reduction in impact force, while a more compliant leg with lower damping results in a 61.4% reduction. These findings demonstrate the importance of considering both stiffness and damping in the design of legged robots for high impact force resistance. This simultaneously highlights the efficacy of the proposed magnetorheological-fluid-based leg design for this purpose.

Directionally Compliant Legs Enabling Crevasse Traversal in Small Ground‐Based Robots

Small ground‐based robots show promise for locomotion on complex surfaces. A critical application area for such robots is movement over complex terrain and within constricted space such as narrow gaps in rubble. To contend with this terrain complexity, robots typically require high degree‐of‐freedom (DOF) limbs. However, for small robot platforms, this approach of high DOF legs is impractical due to actuator limitations. This presents an opportunity to design robots whose morphology enables the outsourcing of computational tasks to the robot body through the use of compliant elements (morphological computation). Herein, a novel robot appendage is developed that can passively compress in a programmed direction in response to environmental constrictions. A robot equipped with these appendages can enter narrow spaces down to 72% of the robot's sprawled body width as well as low ceilings down to 68% its freestanding height. The robot is able to step onto and over small terrain features ( hip height) and navigate various natural terrain types with ease. The results show that these compressible appendages enable versatile robot locomotion for robot exploration in previously unmapped environments.

Anchoring Mechanism for Capsule Endoscope: Mechanical Design, Fabrication and Experimental Evaluation.

Capsule endoscopes are widely used to diagnose gut-related problems, but they are passive in nature and cannot actively move inside the gut. This paper details the design process and development of an anchoring mechanism and actuation system to hold a capsule in place within the small intestine. The design centres around the mechanical structure of the anchor that makes use of compliant Sarrus linkage legs, which extend to make contact with the intestine, holding the capsule in place. Three variants with 2 legs, 3 legs and 4 legs of the anchoring mechanism were tested using a shape memory alloy spring actuator (5 mm × ϕ 3.4 mm). The experiments determine that all the variants can anchor at the target site and resist peristaltic forces of 346 mN. The proposed design is well suited for an intestine with a diameter of 19 mm. The proposed design allows the capsule endoscopes to anchor at the target site for a better and more thorough examination of the targeted region. The proposed anchoring mechanism has the potential to become a vital apparatus for clinicians to use with capsule endoscopes in the future.

Path Tracking and Connection Mechanism of a Reconfigurable, Foldable, Legged, and Miniature Robot

This work introduces the reconfigurable, foldable, legged, and miniature robot (REMIRO), a palm-size modular robot with compliant c-shaped legs. The robot’s body modules are made by folding acetate sheets. The legs connected to these modules are made of Polydimethylsiloxane (PDMS) using molding. The backbone modules are made of Thermoplastic polyurethane (TPU) using 3D printing. In this study, we propose a path tracking algorithm for our robot that enables our modules to move from a random initial location to the pose required to lock with another module. We also design and manufacture backbones with embedded permanent magnets to allow connection between modules. We also present a kinematic model of our robot utilizing c-shaped leg kinematics, predicting the forward differential kinematics of the robot, which is then used to test the path tracking algorithm. Our experiments show that the proposed path tracking algorithm moves our robot to the desired location with an average positioning error of 5mm and an average orientation error of 22°, which are small enough to permit docking between modules.

UPed: A Quadruped Robot Platform to Study Directional Leg Compliance

Abstract This paper presents UPed, a quadruped robot platform, for studying passive, directional, leg compliance in robots. This work was motivated by the benefits provided by passively and directionally compliant legs in humans and animals. UPed uses under-actuated legs based on the bent-knee model which is capable of changing the direction and magnitude of the leg compliance by adjusting the knee angle and distal leg stiffness. Pneumatic pistons were chosen as variable compliance elements, enabling the leg compliance to be adjusted during locomotion. The platform was validated experimentally by evaluating how the robot’s pitch rate and cost of transport changed with variations in leg compliance and knee angle. Results of these experiments indicated that significant performance improvements are possible by selecting appropriate values of compliance and knee angle. They also demonstrated a unique capability to explore adjustable directional compliance and other parameters in robot legs on a physical robotic system. UPed has the potential to facilitate significant performance improvements of legged robots by enabling additional in-depth studies on directional passive leg compliance.

Design and Dynamic Analysis of a Compliant Leg Configuration towards the Biped Robot’s Spring-Like Walking

Design and Dynamic Analysis of a Compliant Leg Configuration towards the Biped Robot’s Spring-Like Walking

A passive planar model with rolling contact and its application for bounding and pronking on a quadruped robot

Abstract The development and investigation of a quadruped robot's dynamic bounding and pronking gaits using a sagittal planar model that captures the robot's natural dynamics are presented. The proposed reduced-order model, termed the Two-rolling-leg (TRL) model, is a 3-DOF planar rigid-body model consisting of two half-circular compliant legs with pure rolling contact. Throughout the non-dimensional steps-to-fall and fixed-point analysis, the model with feasible intrinsic parameters can passively perform the periodic dynamic behavior of bounding and pronking, revealing a relationship between the body parameters and the preferred dynamic behaviors. Dynamic bounding and pronking on a quadruped robot were initiated by developing a model-based control strategy based on the searched periodic dynamic behaviors of the TRL model. The experimental results showed that the robot can initiate its dynamic bounding and pronking behaviors at various forward speeds merely by causing the motor to track a preset trajectory derived from the fixed-point motion of the TRL model using position control. The higher success rate of the robot in stable bounding than in pronking is in line with the results from the analysis of the model. This paper confirms that the dynamic multi-gait locomotion of a quadrupedal robot can be initiated by utilizing a reduced-order model for control guidance and that the body configuration plays an important role in determining the characteristics of the dynamic behaviors.

Crab-inspired compliant leg design method for adaptive locomotion of a multi-legged robot

Chinese mitten crab has unique limb structures composed of a hard exoskeleton and flexible muscles. They enable the crab to locomote adaptively and safely on various terrains. In this work, we investigated the limb structures, motion principle, and gaits of the crab using a high-speed camera and a press machine. Then, a novel compliant robot leg design method is proposed, inspired by the crab limb. The leg comprises six hard scleromeres and a flexible thin-wall spring steel sheet (FSSS) mimicking the exoskeleton and muscle. The scleromeres connected one by one with rotational joints are designed with slots. The front end of the FSSS is fixed on the scleromere close to the ground. The rear end crosses the slots and is mounted at the shaft of a linear actuator installed at the rear scleromere. The leg bends and stretches when the actuator pushes and pulls the FSSS, respectively. The kinematic modeling, rigid-flexible coupling dynamic simulations, and leg prototype tests are conducted, which verify the leg design approach. Thirdly, we put forward a multi-legged robot with eight compliant legs and design its gait using the gaits of the crab. Finally, the robot’s performance is evaluated, including the capabilities of walking on different terrains at adjustable speeds and body heights, traversing low channels, walking on slopes, and carrying loads. The results prove that the single-motor-actuated compliant legs and their dynamic coupling with the rigid robot body frame can enable them to have the ground clearance ability and realize the adaptive walking of the robot. The leg design methodology can be used to design multi-legged robots with the merits of compact, light, low mechanical complexity, high safety, and easy to control, for many applications, such as environmental monitoring, search and rescue.

Modeling Human-Induced Loads Through a Calibrated Bipedal Walking Model

In this paper is proposed a set of empirical equations for parameters and initial conditions of a damped bipedal model with compliant legs. The parameters of the bipedal model are estimated by fitting numerical and experimental walking forces. Sixteen volunteers are recruited to participate in experimental tests to walk on a prototype footbridge. The vertical ground reaction forces (GRFs) induced by pedestrians are recorded by force plates and the accelerations of the structure are recorded by accelerometers. Multiple simulations within certain ranges of input parameters are performed to identify the best matches between the model’s predictions and experimentally measured GRFs. Based on empirical data, regression equations are proposed as functions of pedestrian’s mass, height, and walking speed. To validate the proposed equations, the experimental tests are simulated, and the predicted structure dynamic responses are compared to measured vibrations on the footbridge. To generate a more realistic pedestrian loading, the gait speed of each step is randomized within a range to reproduce the step-by-step variations. The results of this study validate the suitability of a set of parameters selected for the bipedal model, for use in predicting loads induced by humans and estimating the vibration response of pedestrian structures.

Development of Walking Robot Using Compliance Mechanism

Walking robot is a trend in this 21st century as Industrial Revolution 4.0 which involved automation has become a hot topic. Unlike ordinary moving robots, walking robots that take humans and animals as references can move on unpaved surfaces. Compliance mechanism is a flexible mechanism that transfers input force into output force through plastic deformation of certain members in the structure. A compliant structure can be classified as a monolithic structure that deforms elastically without any joint or linkage between the members. Unlike motorised robot legs requiring an input motion in each joint and link, a single input force can operate a compliant leg. Therefore, this research aims to develop a 3D printed compliant leg. This project is challenging because there is no reference for the single-piece compliant leg development using Three-Dimensional(3D) printing technology. The application of Jansen Linkage in the development of the compliant leg also results in difficulties because there is no standard equation for the calculation of each member in the Jansen Linkage. Hence, the development of the Jansen Linkage using different dimensions will solve these problems by varying the difference occurring upon changing the dimension. We also make Finite Element Analysis (FEA) of the product. The thesis will be supported by the walking motion pattern, force vs time graph and FEA analysis results for the product.