Bounding Gait Research Articles

Limb and hip morphology of two African colobine monkeys and its relationship to the mechanics of leaping and bounding locomotion.

Although a bounding gait is practiced by a diversity of animals, the morphological characteristics, kinematics, and energetics associated with this locomotor form remain poorly understood. This study focuses on the locomotor anatomy of two species of African colobine monkeys (Piliocolobus badius, a leaper, and Colobus polykomos, a leaper-bounder) in an effort to assess if bounding should be considered a unique primate locomotor category or is better viewed as a behavior on a leaping continuum. A total of 53 femora, 28 humeri, and 45 ossa coxae from the two species provide comparative morphological data. Free-body models of bounding and leaping are presented to characterize loading conditions. Species differences in morphometric traits are evaluated via parametric and nonparametric tests (i.e., analysis of variance, resampling). C. polykomos exhibits traits that align more closely with putative leaping specializations when compared to P. badius (e.g., large femoral head, long femur, low femoral neck angle), while also possessing certain traits that are not (e.g., long femoral neck and reduced relative femoral robusticity). Consequently, C. polykomos likely experiences absolutely greater joint forces at the hip and higher bending at the femoral neck both when it leaps and bounds, given equivalent accelerations in bounding and leaping. Bounding is best described as a form of low-acceleration leaping. If bounding has lower acceleration requirements relative to leaping, C. polykomos achieves locomotor competence with less energy, relatively smaller bending moments, and reduced joint forces.

Research on high-speed bounding gait analysis and control of quadruped robot

In order to improve the performance of the quadruped robot, the impact of high-speed gait is an important target to measure the performance of the robot. This paper elaborates the research methods of high-speed gait movement of quadrupeds, and a multi-rigid-body dynamics modelling method is presented. According to the analysis of high-speed bounding gait, the dynamic modelling of quadruped motion system is calculated. The motion planning for a rigid-torso quadruped robot based on Poincare Map is presented, and the high-speed bounding gait motion control strategy is established. The simulation experiments have been carried out, and the results have demonstrated the effectiveness of the motion planning model and high-speed bounding method.

Accelerating Hybrid Systems Differential Dynamic Programming

Abstract This letter presents approaches that reduce the computational demand of including second-order dynamics sensitivity information into optimization algorithms for robots in contact with the environment. A full second-order differential dynamic programming (DDP) algorithm is presented where all the necessary dynamics partial derivatives are computed with the same complexity as DDP’s first-order counterpart, the iterative linear quadratic regulator (iLQR). Compared to linearized models used in iLQR, DDP more accurately represents the dynamics locally, but it is not often used since the second-order partials of the dynamics are tensorial and expensive to compute. This work illustrates how to avoid the need for computing the derivative tensor by instead leveraging reverse-mode accumulation of derivatives, extending previous work for unconstrained systems. We exploit the structure of the contact-constrained dynamics in this process. The performance of the proposed approaches is benchmarked with a simulated model of the MIT Mini Cheetah executing a bounding gait.

Effects of spinal structure on quadruped bounding gait

AbstractThis paper proposes a robot model with multiple spines and investigates its effects on the bounding gait of quadruped robot. Contrastive tests, carried out by adding an active driving joint (ADJ) and changing the number of passive driving joints, were divided between simulation and physical. The results reveal that the spinal structure (one ADJ and several passive driving joints) is closely related to the performance parameters. Increasing the number of passive driving joints can improve the velocity and energy efficiency. This structure may have significant guidance for designing a quadruped robot.

Motion Planning for a Bounding Quadruped Robot Using iLQG Based MPC

When tackling motion control problem of the quadruped bionic robot with traditional control method, it is more and more difficult to improve the control effect due to the uncertainty caused by the factors such as model mismatch, distortion, and interference. Therefore, the demand for utilizing advanced control method to realize the motion control for legged bionic robot is growing. Among various advanced control methods, the model prediction control (MPC) has low requirements on model accuracy, and the system has good robustness and stability, which provides a good prospect for solving the balance problem of dynamic robots. In this paper model predictive control is used to realize the bounding gait motion control for a quadruped bionic robot. The MPC planner automatically generates the foot end position and contact force trajectory of the robot, so that the robot can track the desired motion state. However, as the model of the quadruped bionic robot is nonlinear, the generated MPC algorithm may be difficult to meet the real-time requirements. In order to solve this problem, this paper uses the iLQG optimization algorithm in the design of a model prediction controller and adds heuristic-based reference input. The comparison between the simulation and the classical SQP algorithm shows that the MPC based on the iLQG optimization algorithm has good convergence and tracking effect for the quadruped robot running, and has fast real-time performance.

Hybrid Systems Differential Dynamic Programming for Whole-Body Motion Planning of Legged Robots

This letter presents a Differential Dynamic Programming (DDP) framework for trajectory optimization (TO) of hybrid systems with state-based switching. The proposed Hybrid Systems DDP (HS-DDP) approach is considered for application to whole-body motion planning with legged robots. Specifically, HS-DDP incorporates three algorithmic advances: an impact-aware DDP step addressing the impact event in legged locomotion, an Augmented Lagrangian (AL) method dealing with the switching constraint, and a Switching Time Optimization (STO) algorithm that optimizes switching times by leveraging the structure of DDP. Further, a Relaxed Barrier (ReB) method is used to manage inequality constraints and is integrated into HS-DDP for locomotion planning. The performance of the developed algorithms is benchmarked on a simulation model of the MIT Mini Cheetah executing a bounding gait. We demonstrate the effectiveness of AL and ReB for handling switching constraints, friction constraints, and torque limits. By comparing to previous solutions, we show that the STO algorithm achieves 2.3 times more reduction of total switching times, demonstrating the efficiency of our method.

Asymmetrical gait kinematics of free-ranging callitrichine primates in response to changes in substrate diameter and orientation.

Arboreal environments present considerable biomechanical challenges for animals moving and foraging among substrates varying in diameter, orientation and compliance. Most studies of quadrupedal gait kinematics in primates and other arboreal mammals have focused on symmetrical walking gaits and the significance of diagonal sequence gaits. Considerably less research has examined asymmetrical gaits, despite their prevalence in small-bodied arboreal taxa. Here, we examined whether and how free-ranging callitrichine primates adjust asymmetrical gait kinematics to changes in substrate diameter and orientation, as well as how variation in gait kinematics affects substrate displacement. We used high-speed video to film free-ranging Saguinus tripartitus and Cebuella pygmaea inhabiting the Tiputini Biodiversity Station, Ecuador. We found that S. tripartitus used bounding and half-bounding gaits on larger substrates versus gallops and symmetrical gaits on smaller substrates, and also shifted several kinematic parameters consistent with attenuating forces transferred from the animal to the substrate. Similarly, C. pygmaea shifted from high-impact bounding gaits on larger substrates to using more half-bounding gaits on smaller substrates; however, kinematic adjustments to substrate diameter were not as profound as in S. tripartitus Both species adjusted gait kinematics to changes in substrate orientation; however, gait kinematics did not significantly affect empirical measures of substrate displacement in either species. Because of their small body size, claw-like nails and reduced grasping capabilities, callitrichines arguably represent extant biomechanical analogs for an early stage in primate evolution. As such, greater attention should be placed on understanding asymmetrical gait dynamics for insight into hypotheses concerning early primate locomotor evolution. .

P.543 Working memory of children: informatization of assessment task

This paper presents a control approach for bounding gait of quadruped robots by applying the concept of Virtual Constraints (VCs). A VC is a relative motion relation between two related joints imposed to the robots in terms of a specified gait, which can drive the robot to run with desired gait. To determine VCs for highly dynamic bounding gait, the limit cycle motions of the passive dynamic model of bounding gait are analyzed. The leg length and hip/shoulder angle trajectories corresponding to the limit cycles are parameterized by leg angles using 4 th-order polynomials. In order to track the calculated periodic motions, the polynomials are imposed on the robot as virtual motion constraints by a high-level state machine controller. A bounding speed feedback strategy is introduced to stabilize the robot running speed and enhance the stability. The control approach was applied to a newly designed lightweight bioinspired quadruped robot, AgiDog. The experimental results demonstrate that the robot can bound at a frequency up to 5 Hz and bound at a maximum speed of 1.2 m·s−1 in sagittal plane with a Froude number approximating to 1.

Study on effects of spinal joint for running quadruped robots

Most legged animals use their flexible body and supporting muscles to produce power for their locomotion, resulting in superior mobility and fast motions. In reality, an animal body consists of multiple bones and joints as well as legs having two or three segments with mass and inertia. In this paper, we study the bounding locomotion of a quadruped robot with a model closer to a real animal, i.e., a model that has one spinal joint, multiple two-segmented prismatic legs with masses and series elastic actuators, to obtain an insight into the robot’s dynamic behaviors. The models with passive mechanical properties are optimized with open-loop control to achieve the periodic bounding gait. The effects of spine flexibility in a segmented body are investigated on quadrupedal bounding gait by changing dynamic properties and hardware parameters. Comparisons of models reveal that body flexibility affects energy consumption and increases leg recirculation and stride length. The cost of transport of the articulated spine models is smaller than that of the rigid body one at low speed ($$ 0.45\sqrt{gl_0}$$). The stride length increases 25%. Furthermore, the study on location of spinal joint reveals that the asymmetric segmented body possesses bigger spine oscillation; up to 370% higher actuator force/torque in the rear leg but 36.1% smaller in the front leg; shorter stride period; and smaller cost of transport which helps the robot to run more efficiently. The study also shows that the asymmetric mass distribution of the body caused the torque/force increase at the rear leg, especially at hip joint, and the decrease at the front leg.

The effect of head movement on the bounding gait of a quadruped robot with an active spine

It is a common phenomenon in the movement of the quadruped mammals accompanied with head swings. Inspired by this, this article attempts to add head motion to the bounding gait of a quadruped robot. According to the theoretical analysis, there are two main functions of the head. First, the head can realize the active control of the center of mass position of the robot, which is of great significance to the stable motion of the robot. Second, the swing of the head plays a role in regulating the pitch angle of the torso and improves the coordination and stability of the motion. A simplified quadruped robot model with a head and spine joint is established and analyzed theoretically. The regularity of head movement in periodic bounding gait is summarized. Through simulation and experiment, we confirm the two roles of the head in the bounding gait of a quadruped robot.

Exploring Bipedal Hopping through Computational Evolution.

Bipedal hopping is an efficient form of locomotion, yet it remains relatively rare in the natural world. Previous research has suggested that the tail balances the angular momentum of the legs to produce steady state bipedal hopping. In this study, we employ a 3D physics simulation engine to optimize gaits for an animat whose control and morphological characteristics are subject to computational evolution, which emulates properties of natural evolution. Results indicate that the order of gene fixation during the evolutionary process influences whether a bipedal hopping or quadrupedal bounding gait emerges. Furthermore, we found that in the most effective bipedal hoppers the tail balances the angular momentum of the torso, rather than the legs as previously thought. Finally, there appears to be a specific range of tail masses, as a proportion of total body mass, wherein the most effective bipedal hoppers evolve.

Passive Dynamic Bounding Control using Symmetry Condition Control Laws

Legged locomotion is preferred over the wheeled locomotion as it can be used both for flat and rough terrains. Quadruped robots are preferred since they can offer better stability with considerable reliability. In recent years, passive dynamics has been used to obtain near zero-energy bounding gaits. Although theoretically such gaits consume no energy, in practice some additional energy is required to overcome losses. Existence and stability of such gaits have been thoroughly studied in literature for quadruped models with the assumption that the mass distribution and stiffness in the front and back legs are symmetric. Fixed points found using Poincare map indicate touchdown angle-liftoff angle symmetry between front and back legs. This property can be used to search for fixed points with ease. However, the range of initial conditions where the bounding gait is stable is highly limited. Control laws based on symmetry conditions observed are proposed in this paper to improve the stability region. One such control law based on body-fixed touchdown angles theoretically allows redesign of quadruped robot with physical cross coupling between legs to achieve inherent stability without leg actuation.

Turning strategies for the bounding quadruped robot with an active spine

Purpose This paper aims to study the turning strategies for the bounding quadruped robot with an active spine and explore the significant role of the spine in the turning locomotion. Design/methodology/approach Firstly, the bounding gait combining the pitch motion of the spine with the leg motion is presented. In this gait, the spine moves in phase with the front legs. All the joints of the legs and spine are controlled by cosine signals to simplify the control, and the initial position and oscillation amplitude of the joints can be tuned. To verify the effectiveness of the proposed gait, the spine joints are set with different initial positions and oscillation amplitudes, and the initial position and oscillation amplitude of the leg joints are tuned to make the virtual model do the best locomotion in terms of the speed and stability in the simulation. The control signals are also used to control a real robot called Transleg. Then, three different turning strategies are proposed, including driving the left and right legs with different strides, swaying the spine in the yaw direction and combining the above two methods. Finally, these strategies are tested on the real robot. Findings The stable bounding locomotion can be achieved using the proposed gait. With the spine motion, the speed of the bounding locomotion is increased; the turning radius is reduced; and the angular velocity is increased. Originality/value A simple and flexible planning of the bounding gait and three turning strategies for the bounding quadruped robot are proposed. The effectiveness of the proposed bounding gait, along with the beneficial effect of the spine motion in the yaw direction on the turning locomotion is demonstrated with the computer simulations and robot experiments. This will be instructive for the designing and actuating of the other quadruped robots.

On the Dynamic Similarity Between Bipeds and Quadrupeds: A Case Study on Bounding

In this letter, we identify passive dynamic bounding gaits of quadrupedal robots and investigate the dynamic similarities between these gaits and those of a bipedal model. For this purpose, we develop a passive dynamic bounding model of a quadruped with an extended main body. This model is based on the established SLIP model, yet has dynamic swing leg motions instead of a predefined angle of attack. We present a gait-identification framework that is based on a numerical continuation approach and that allows us to find all possible passive periodic motions that emerge from pronking and bounding in place. These gaits include forward pronking as well as forward bounding with gathered suspension, extended suspension, and with two suspensions. By conducting a parameter study on the body inertia, we can draw parallels between bipedal and quadrupedal gaits, and can also show how the structure of possible solutions changes with the main body inertia. In particular, we see sudden changes in the gait structure at certain critical values of the main body inertia. This letter shows connections between different types of quadrupedal gaits and may serve as a guideline in the design and control of gaits for energetically economical legged robots. It also sheds some light at the question why animals with different morphology use different gaits at the same Froude numbers.

Spontaneous gait transition to high-speed galloping by reconciliation between body support and propulsion

ABSTRACTQuadrupeds change their gait patterns in response to locomotion speed to achieve low cost of transport over a wide range of speeds. Understanding the underlying control mechanism is essential to establish a design principle for legged robots that can adaptively generate energy-efficient locomotion patterns. Even decerebrate cats exhibit spontaneous gait transition, suggesting that adaptive gait patterns are generated via decentralized control systems, i.e. central pattern generators and reflexes. Several studies address this issue; however, the essential control mechanism that enables spontaneous transition from low- to high-speed gait is still poorly understood. To address this issue, this work reconsiders the interlimb coordination mechanism by focusing on two fundamental roles of limbs: body support and propulsion. To verify the proposed model, 2D simulations and 3D hardware experiments were conducted. The results indicate that the proposed model enables the robot to spontaneously exhibit gait transition to high-speed galloping and to achieve faster and more energy-efficient locomotion than a bounding gait in 3D hardware experiments.

Benthic walking, bounding, and maneuvering in flatfishes (Pleuronectiformes: Pleuronectidae): New vertebrate gaits

Video-based observations of voluntary movements reveal that six species of pleuronectid flatfishes use sequential portions of long-based dorsal and anal fins as “feet” (hereafter, fin-feet) to move on the substrate. All six species used a gait that we term “walking,” which produced constant forward movement, and several of these species also used a second gait that we call “bounding” for intermittent movements over the substrate. We selected Pacific Sand Sole, Psettichthys melanostictus, and English Sole, Parophrys vetulus, for kinematic analyses of these two gaits. Psettichthys melanostictus consistently used walking for benthic locomotion; Parophrys vetulus primarily used a bounding gait. During forward walking, a fin ray swings up off the substrate, protracts and converges with neighboring fin rays to contribute to a fin-foot. The fin-foot pushes down on the substrate and rotates posteriorly by sequential recruitment of fin rays, a pattern known as a metachronal wave. As one fin-foot passes off the posterior end of the fin, a new fin-foot forms anteriorly. During bounding, undulations of the body and tail assist one or two waves of fin-feet, producing rapid but intermittent forward acceleration of the body. Flatfishes also use fin-feet to maneuver on the substrate. The Starry Flounder, Platichthys stellatus, performs near zero displacement rotation by running waves of fin-feet in opposing directions along the dorsal and anal fins. Although other teleosts use specialized pectoral fin rays for bottom walking (e.g., Sea Robins: Triglidae), the duplication of structures and patterns of movement in the median fins of flatfishes more closely resembles metachronal motions of millipede feet or the parapodia of polychaete worms. Sequential use of median fin rays in flatfishes resembles that of other teleosts that swim with elongate median fins, including Amiiformes, Gymnotiformes, and some Tetraodontiformes, but flatfishes offer a novel form of substrate locomotion based on dorsal and anal fins.

Subsea crab bounding gait of leg-paddle hybrid driven shoal crablike robot

This paper presents the design principles of a novel subsea propulsion pattern named as crab bounding gait for the shoal crablike robot and the gait experimental results. The concept of leg-paddle hybrid driven shoal crablike robot is developed for shoal environment; the robot moves on the seabed by employing six 3DOFs walking legs and swims by two 3DOFs swimming paddles. The proposed gait is derived by mimicking the movement mode of biological swimming crab when preying or being attacked underwater. Three aspects of gait planning, including gait process planning, kinematics modelling and trajectory planning, and subsea dynamics analyzing in back stance phase and flight phase by considering hydrodynamic factors such as water resistance and buoyancy, are discussed in this work. Experimental results of subsea crab bounding gait are presented and used to make a comparison with the bionic wave gait; the current and pitch angle of body centroid are monitored in real time. It is demonstrated that the average motion speed improves by 54%, and the total power consumption of crab bounding gait is 14.5 W, which enables that the total cost of transport (TCoT) decreases from 6.8 to 3.7 against bionic wave gait.

Comparing the Arboreal Gaits ofMuscardinus avellanariusandGlis glis(Gliridae, Rodentia): A First Quantitative Analysis

Body size may have a significant impact on arboreal locomotion, as small animals are more capable of navigating on smaller branches, acquire increased stability due to the lower position of the center of mass, and small substrates appear larger to them, compared to larger animals. To determine whether gaits are also affected by body size in relation to substrate size, we conducted a study on two sympatric arboreal glirid rodents of different size on simulated arboreal substrates. Our preliminary results showed that the smaller Muscardinus avellanarius used symmetrical walking gaits on the narrowest substrates (2 mm), moved significantly faster using asymmetrical bounding gaits with increased aerial phases on larger substrates, and regulated velocity via stride length. On the other hand, the larger Glis glis failed to move on 2 mm and 5 mm substrates, used asymmetrical gaits at lower velocities and decreased aerial phases on larger substrates, and regulated velocity mainly via stride frequency. We suggest that the observed differences in gait metrics may be related to body size and to the utilization of different microhabitats, reducing potential interspecific competition.

Virtual Constraint Based Control of Bounding Gait of Quadruped Robots

This paper presents a control approach for bounding gait of quadruped robots by applying the concept of Virtual Constraints (VCs). A VC is a relative motion relation between two related joints imposed to the robots in terms of a specified gait, which can drive the robot to run with desired gait. To determine VCs for highly dynamic bounding gait, the limit cycle motions of the passive dynamic model of bounding gait are analyzed. The leg length and hip/shoulder angle trajectories corresponding to the limit cycles are parameterized by leg angles using 4 th-order polynomials. In order to track the calculated periodic motions, the polynomials are imposed on the robot as virtual motion constraints by a high-level state machine controller. A bounding speed feedback strategy is introduced to stabilize the robot running speed and enhance the stability. The control approach was applied to a newly designed lightweight bioinspired quadruped robot, AgiDog. The experimental results demonstrate that the robot can bound at a frequency up to 5 Hz and bound at a maximum speed of 1.2 m·s−1 in sagittal plane with a Froude number approximating to 1.

Bio-inspired control strategy study for the quadruped robot with a segmented spine

PurposeThis study aims to establish a bio-inspired controller for realizing the bounding gait of a quadruped robot system presented in this paper.Design/methodology/approachThe bio-inspired controller is divided into three levels to mimic the biological patterns of animals. First, the high-level sub-controller is equivalent to the cerebellum, which could plan and control the motion of animals. Second, the effect of the middle-level sub-controller corresponds to the central nervous system. The central pattern generators in the spine generate the stable and cyclic signals as the fundamental rhythm for periodic motion of the leg and spine joints. Third, the low-level sub-controller is equal to the end effector, which adopts the simple proportional-derivative (PD) control to realize the specific motion trajectory of the legs and spine.FindingsCombined with the stability criterion presented previously and the delayed feedback control method, the bounding gait of the cheetah virtual prototype could be actuated and stabilized by the bio-inspired controller. Moreover, the bio-inspired controller is applied to realize the bounding gait of an SQBot, which is a quadruped robot with a spine joint. Meanwhile, the validity and practicability of the bio-inspired controller for the control of quadruped robot have been verified against different forward velocities.Originality/valueThe bio-inspired controller and bionic quadruped robot system are instructive for the designing and actuating of the real quadruped robot.