Running over unknown rough terrain with a one-legged planar robot

The ability to traverse unknown, rough terrain is an advantage that legged locomoters have over their wheeled counterparts. However, due to the complexity of multi-legged systems, research in legged robotics has not yet been able to reproduce the agility found in the animal kingdom. In an effort to reduce the complexity of the problem, researchers have developed single-legged models to gain insight into the fundamental dynamics of legged running. Inspired by studies of animal locomotion, researchers have proposed numerous control strategies to achieve stable, one-legged running over unknown, rough terrain. One such control strategy incorporates energy variations into the system during the stance phase by changing the force-free leg length as a sinusoidal function of time. In this research, a one-legged planar robot capable of implementing this and other state-of-the-art control strategies was designed and built. Both simulated and experimental results were used to determine and compare the stability of the proposed controllers as the robot was subjected to unknown drop and raised step perturbations equal to 25% of the nominal leg length. This study illustrates the relative advantages of utilizing a minimal-sensing, active energy removal control scheme to stabilize running over rough terrain.     

Running in the real world: adjusting leg stiffness for different surfaces.

A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal''s leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.     

Speed dependent phase shifts and gait changes in cockroaches running on substrates of different slipperiness

Background

Many legged animals change gaits when increasing speed. In insects, only one gait change has been documented so far, from slow walking to fast running, which is characterised by an alternating tripod. Studies on some fast-running insects suggested a further gait change at higher running speeds. Apart from speed, insect gaits and leg co-ordination have been shown to be influenced by substrate properties, but the detailed effects of speed and substrate on gait changes are still unclear. Here we investigate high-speed locomotion and gait changes of the cockroach Nauphoeta cinerea, on two substrates of different slipperiness.

Results

Analyses of leg co-ordination and body oscillations for straight and steady escape runs revealed that at high speeds, blaberid cockroaches changed from an alternating tripod to a rather metachronal gait, which to our knowledge, has not been described before for terrestrial arthropods. Despite low duty factors, this new gait is characterised by low vertical amplitudes of the centre of mass (COM), low vertical accelerations and presumably reduced total vertical peak forces. However, lateral amplitudes and accelerations were higher in the faster gait with reduced leg synchronisation than in the tripod gait with distinct leg synchronisation.

Conclusions

Temporally distributed leg force application as resulting from metachronal leg coordination at high running speeds may be particularly useful in animals with limited capabilities for elastic energy storage within the legs, as energy efficiency can be increased without the need for elasticity in the legs. It may also facilitate locomotion on slippery surfaces, which usually reduce leg force transmission to the ground. Moreover, increased temporal overlap of the stance phases of the legs likely improves locomotion control, which might result in a higher dynamic stability.

     

Crawling at High Speeds: Steady Level Locomotion in the Spider Cupiennius salei—Global Kinematics and Implications for Centre of Mass Dynamics

Spiders are an old yet very successful predatory group of arthropods. Their locomotor system differs from those of most other arthropods by the lack of extensor muscles in two major leg joints. Though specific functional characteristics can be expected regarding the locomotion dynamics of spiders, this aspect of movement physiology has been only scarcely examined so far.This study presents extensive analyses of a large dataset concerning global kinematics and the implications for dynamics of adult female specimens of the large Central American spider Cupiennius salei (Keyserling). The experiments covered the entire speed-range of straight runs at constant speeds. The analyses revealed specific characteristics of velocity dependent changes in the movements of the individual legs, as well as in the translational and rotational degrees of freedom of both the centre of mass and the body.In contrast to many other fast moving arthropods, C. salei avoid vertical fluctuations of their centre of mass during fast locomotion. Accordingly, aerial phases were not observed here. This behaviour is most likely a consequence of optimising energy expenditure with regard to the specific requirements of spiders'' leg anatomy. A strong synchronisation of two alternating sets of legs appears to play only a minor role in the locomotion of large spiders. Reduced frequency and low centre of mass amplitudes as well as low angular changes of the body axes, in turn, seems to be the result of relatively low leg coordination.     

Human hopping on damped surfaces: strategies for adjusting leg mechanics

Fast-moving legged animals bounce along the ground with spring-like legs and agilely traverse variable terrain. Previous research has shown that hopping and running humans maintain the same bouncing movement of the body's centre of mass on a range of elastic surfaces by adjusting their spring-like legs to exactly offset changes in surface stiffness. This study investigated human hopping on damped surfaces that dissipated up to 72% of the hopper's mechanical energy. On these surfaces, the legs did not act like pure springs. Leg muscles performed up to 24-fold more net work to replace the energy lost by the damped surface. However, considering the leg and surface together, the combination appeared to behave like a constant stiffness spring on all damped surfaces. By conserving the mechanics of the leg-surface combination regardless of surface damping, hoppers also conserved centre-of-mass motions. Thus, the normal bouncing movements of the centre of mass in hopping are not always a direct result of spring-like leg behaviour. Conserving the trajectory of the centre of mass by maintaining spring-like mechanics of the leg-surface combination may be an important control strategy for fast-legged locomotion on variable terrain.     

Effective leg stiffness in running

Leg stiffness is a common parameter used to characterize leg function during bouncing gaits, like running and hopping. In the literature, different methods to approximate leg stiffness based on kinetic and kinematic parameters are described. A challenging point in estimating leg stiffness is the definition of leg compression during contact. In this paper four methods (methods A–D) based on ground reaction forces (GRF) and one method (method E) relying on temporal parameters are described. Leg stiffness calculated by these five methods is compared with running patterns, predicted by the spring mass model.The best and simplest approximation of leg stiffness is method E. It requires only easily accessible parameters (contact time, flight time, resting leg length, body mass and the leg's touch down angle). Method D is of similar quality but additionally requires the time-dependent progression of the GRF. The other three methods show clear differences from the model predictions by over- or underestimating leg stiffness, especially at slow speeds.Leg stiffness is derived from a conceptual model of legged locomotion and does not exist without this model. Therefore, it is important to prove which experimental method is suited best for approximating the stiffness in a specific task. This will help to interpret the predictions of the conceptual model in comparison with experimental data.     

Does a crouched leg posture enhance running stability and robustness?

Humans and birds both walk and run bipedally on compliant legs. However, differences in leg architecture may result in species-specific leg control strategies as indicated by the observed gait patterns. In this work, control strategies for stable running are derived based on a conceptual model and compared with experimental data on running humans and pheasants (Phasianus colchicus). From a model perspective, running with compliant legs can be represented by the planar spring mass model and stabilized by applying swing leg control. Here, linear adaptations of the three leg parameters, leg angle, leg length and leg stiffness during late swing phase are assumed. Experimentally observed kinematic control parameters (leg rotation and leg length change) of human and avian running are compared, and interpreted within the context of this model, with specific focus on stability and robustness characteristics. The results suggest differences in stability characteristics and applied control strategies of human and avian running, which may relate to differences in leg posture (straight leg posture in humans, and crouched leg posture in birds). It has been suggested that crouched leg postures may improve stability. However, as the system of control strategies is overdetermined, our model findings suggest that a crouched leg posture does not necessarily enhance running stability. The model also predicts different leg stiffness adaptation rates for human and avian running, and suggests that a crouched avian leg posture, which is capable of both leg shortening and lengthening, allows for stable running without adjusting leg stiffness. In contrast, in straight-legged human running, the preparation of the ground contact seems to be more critical, requiring leg stiffness adjustment to remain stable. Finally, analysis of a simple robustness measure, the normalized maximum drop, suggests that the crouched leg posture may provide greater robustness to changes in terrain height.     

The influence of track compliance on running

A model of running is proposed in which the leg is represented as a rack-and-pinion element in series with a damped spring. The rack-and-pinion element emphasizes the role of descending commands, while the damped spring represents the dynamic properties of muscles and the position and the rate sensitivity of reflexes. This model is used to predict separately the effect of track compliance on step length and ground contact time. The predictions are compared with experiments in which athletes ran over tracks of controlled spring stiffness. A sharp spike in foot force up to 5 times body weight was found on hard surfaces, but this spike disappeared as the athletes ran on soft experimental tracks. Both ground contact time and step length increased on very compliant surfaces, leading to moderately reduced running speeds, but a range of track stiffness was discovered which actually enhances speed.     

Slit sense organs on the scorpion leg (Androctonus australis L., Buthidae)

As in other arthropods the exoskeleton of arachnids is subjected to loads generated by external stimuli and behavioral activities. Far from being mere by-products of various activities such loads act as signals for mechanoreceptors capable of detecting minute displacements caused by them in the cuticle. In arachnids the slit sense organs serve in this capacity. Spiders have the most elaborate system of slit sense organs. Our previous studies clearly pointed to a functional significance of their specific location and orientation, as well as degree and type of aggregation (isolated, grouped, compound or lyriform) on respective body parts. The present study extends our work to the slit sense organs of scorpions. It gives a detailed account of the topography of the organs on the walking legs. In general slits are less orderly arranged on the legs of scorpions than on those of spiders. In the scorpion they never aggregate to form lyriform organs. Instead there are groups at comparable locations forming much more irregular, but still specific patterns. Isolated slits are more numerous on the scorpion leg, but are also less regularly distrubuted there. A common feature of the majority of slits on both the spider and the scorpion leg is their position on the lateral surfaces and their orientation roughly parallel to the long axis of the leg.     

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.     

Control of a Quadruped Robot with Bionic Springy Legs in Trotting Gait

Legged robots have better performance on discontinuous terrain than that of wheeled robots. However, the dynamic trotting and balance control of a quadruped robot is still a challenging problem, especially when the robot has multi-joint legs. This paper presents a three-dimensional model of a quadruped robot which has 6 Degrees of Freedom （DOF） on torso and 5 DOF on each leg. On the basis of the Spring-Loaded Inverted Pendulum （SLIP） model, body control algorithm is discussed in the first place to figure out how legs work in 3D trotting. Then, motivated by the principle of joint function separation and introducing certain biological characteristics, two joint coordination approaches are developed to produce the trot and provide balance. The robot reaches the highest speed of 2.0 m.s-1, and keeps balance under 250 Kg.m.s-1 lateral disturbance in the simulations. The effectiveness of these approaches is also verified on a prototype robot which runs to 0.83 m.s-1 on the treadmill, The simulations and experiments show that legged robots have good biological properties, such as the ground reaction force, and spring-like leg behavior.     

Velocity Control of a Bounding Quadruped via Energy Control and Vestibular Reflexes

In this paper a bio-inspired approach of velocity control for a quadruped robot running with a bounding gait on compliant legs is set up. The dynamic properties ofa sagittal plane model of the robot are investigated. By analyzing the stable fixed points based on Poincare map, we find that the energy change of the system is the main source for forward velocity adjustment. Based on the analysis of the dynamics model of the robot, a new simple linear running controller is proposed using the energy control idea, which requires minimal task level feedback and only controls both the leg torque and ending impact angle. On the other hand, the functions of mammalian vestibular reflexes are discussed, and a reflex map between forward velocity and the pitch movement is built through statistical regression analysis. Finally, a velocity controller based on energy control and vestibular reflexes is built, which has the same structure as the mammalian nervous mechanism for body posture control. The new con- troller allows the robot to run autonomously without any other auxiliary equipment and exhibits good speed adjustment capa- bility. A series simulations and experiments were set to show the good movement agility, and the feasibility and validity of the robot system.     

Regulation of step frequency in transtibial amputee endurance athletes using a running-specific prosthesis

Running specific prostheses (RSP) are designed to replicate the spring-like behaviour of the human leg during running, by incorporating a real physical spring in the prosthesis. Leg stiffness is an important parameter in running as it is strongly related to step frequency and running economy. To be able to select a prosthesis that contributes to the required leg stiffness of the athlete, it needs to be known to what extent the behaviour of the prosthetic leg during running is dominated by the stiffness of the prosthesis or whether it can be regulated by adaptations of the residual joints. The aim of this study was to investigate whether and how athletes with an RSP could regulate leg stiffness during distance running at different step frequencies.Seven endurance runners with an unilateral transtibial amputation performed five running trials on a treadmill at a fixed speed, while different step frequencies were imposed (preferred step frequency (PSF) and −15%, −7.5%, +7.5% and +15% of PSF). Among others, step time, ground contact time, flight time, leg stiffness and joint kinetics were measured for both legs.In the intact leg, increasing step frequency was accompanied by a decrease in both contact and flight time, while in the prosthetic leg contact time remained constant and only flight time decreased. In accordance, leg stiffness increased in the intact leg, but not in the prosthetic leg. Although a substantial contribution of the residual leg to total leg stiffness was observed, this contribution did not change considerably with changing step frequency.Amputee athletes do not seem to be able to alter prosthetic leg stiffness to regulate step frequency during running. This invariant behaviour indicates that RSP stiffness has a large effect on total leg stiffness and therefore can have an important influence on running performance. Nevertheless, since prosthetic leg stiffness was considerably lower than stiffness of the RSP, compliance of the residual leg should not be ignored when selecting RSP stiffness.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Effects of altered stride frequency and contact time on leg-spring behavior in human running

Many studies have demonstrated that contact time is a key factor affecting both the energetics and mechanics of running. The purpose of the present study was to further explore the relationships between contact time (t(c)), step frequency (f) and leg stiffness (k(leg)) in human running. Since f is a compound parameter, depending on both contact and aerial time, the specific goal of this study was to independently vary f and t(c) and to investigate their respective effects on spring-mass characteristics during running, seeking to determine if the changes in k(leg) observed when running at different f are mainly due to inherent changes in t(c). We compared three types of constant 3.33 m s(-1) running conditions in 10 male subjects: normal running at the subject's freely chosen f, running with decreased and increased f, and decreased and increased t(c) at the imposed freely chosen f. The data from the varied f trials showed that the variation of t(c) was strongly correlated to that of k(leg) (r(2)=0.90), and the variation of f was also significantly correlated to that of k(leg) (r(2)=0.47). Further, changes in t(c) obtained in various t(c) conditions were significantly correlated to changes in k(leg) (r(2)=0.96). These results confirm that leg stiffness was significantly influenced by step frequency variations during constant speed running, as earlier demonstrated, but our more novel finding is that compared to step frequency, the effect of contact time variations appears to be a stronger and more direct determinant of k(leg). Indeed, 90-96% of the variance in k(leg) can be explained by contact time, whether this latter parameter is directly controlled, or indirectly controlled through its close relationship with step frequency. In conclusion, from the comparison of two experimental procedures, i.e. imposing various step frequency conditions vs. asking subjects to intentionally vary contact time at their freely chosen step frequency, it appears that changes in leg stiffness are mainly related to changes in contact time, rather than to those in step frequency. Step frequency appears to be an indirect factor influencing leg stiffness, through its effect on contact time, which could be considered a major determinant of this spring-mass characteristic of human running.     

Bio-Inspired Controller for a Robot Cheetah with a Neural Mechanism Controlling Leg Muscles

The realization of a high-speed running robot is one of the most challenging problems in developing legged robots.The excellent performance of cheetahs provides inspiration for the control and mechanical design of such robots.This paper presents a three-dimensional model of a cheetah that predicts the locomotory behaviors of a running cheetah.Applying biological knowledge of the neural mechanism,we control the muscle flexion and extension during the stance phase,and control the positions of the joints in the flight phase via a PD controller to minimize complexity.The proposed control strategy is shown to achieve similar locomotion of a real cheetah.The simulation realizes good biological properties,such as the leg retraction,ground reaction force,and spring-like leg behavior.The stable bounding results show the promise of the controller in high-speed locomotion.The model can reach 2.7 m·s- 1 as the highest speed,and can accelerate from 0 to 1.5 m·s -1 in one stride cycle.A mechanical structure based on this simulation is designed to demonstrate the control approach,and the most recently developed hindlimb controlled by the proposed controller is presented in swinging-leg experiments and jump-force experiments.     

Robust and efficient walking with spring-like legs

The development of bipedal walking robots is inspired by human walking. A way of implementing walking could be performed by mimicking human leg dynamics. A fundamental model, representing human leg dynamics during walking and running, is the bipedal spring-mass model which is the basis for this paper. The aim of this study is the identification of leg parameters leading to a compromise between robustness and energy efficiency in walking. It is found that, compared to asymmetric walking, symmetric walking with flatter angles of attack reveals such a compromise. With increasing leg stiffness, energy efficiency increases continuously. However, robustness is the maximum at moderate leg stiffness and decreases slightly with increasing stiffness. Hence, an adjustable leg compliance would be preferred, which is adaptable to the environment. If the ground is even, a high leg stiffness leads to energy efficient walking. However, if external perturbations are expected, e.g. when the robot walks on uneven terrain, the leg should be softer and the angle of attack flatter. In the case of underactuated robots with constant physical springs, the leg stiffness should be larger than k = 14 in order to use the most robust gait. Soft legs, however, lack in both robustness and efficiency.     

Runners adjust leg stiffness for their first step on a new running surface.

Human runners adjust the stiffness of their stance leg to accommodate surface stiffness during steady state running. This adjustment allows runners to maintain similar center of mass movement (e.g., ground contact time and stride frequency) regardless of surface stiffness. When runners encounter abrupt transitions in the running surface, they must either make a rapid adjustment or allow the change in the surface stiffness to disrupt their running mechanics. Our goal was to determine how quickly runners adjust leg stiffness when they encounter an abrupt but expected change in surface stiffness that they have encountered previously. Six human subjects ran at 3 m s(-1) on a rubber track with two types of rubber surfaces: a compliant "soft" surface (ksurf = 21.3 kN m(-1) and a non-compliant "hard" surface (ksurf = 533 kN m(-1). We found that runners completely adjusted leg stiffness for their first step on the new surface after the transition. For example, runners decreased leg stiffness by 29% between the last step on the soft surface and the first step on the hard surface (from 10.7 kN m(-1) to 7.6 kN m(-1), respectively). As a result, the vertical displacement of the center of mass during stance ( approximately 7 cm) did not change at the transition despite a reduction in surface compression from 6 cm to less than 0.25 cm. By rapidly adjusting leg stiffness, each runner made a smooth transition between surfaces so that the path of the center of mass was unaffected by the change in surface stiffness.     

A Bio-Inspired Biped Water Running Robot Incorporating the Watt-I Planar Linkage Mechanism

In this paper, a biped water running robot is developed by mimicking the water-running pattern of basilisk lizards. The dynamic mechanism of the robot was studied based on Watt-I planar linkages, and the movement trajectory of the double bar Assur Group was deduced to simulate the water-running foot trajectories of the basilisk lizard. A Central Pattern Generator （CPG）-based fuzzy control method was proposed to control the robot for realizing balance control and gait adjustment. The effectiveness of the proposed control method was verified on the prototype of a water running robot （weight： 320 g）. When the biped robot is running on water, the average force generated by the propulsion mechanism is 1.3 N, and the robot body tilt angle is 5~. The experiment results show that the propulsion mechanism is effective in realizing the basilisk lizards-like water running patterns, and the CPG-based fuzzy control method is effective in keeping the balance of the robot.     

Task-Level Strategies for Human Sagittal-Plane Running Maneuvers Are Consistent with Robotic Control Policies

The strategies that humans use to control unsteady locomotion are not well understood. A “spring-mass” template comprised of a point mass bouncing on a sprung leg can approximate both center of mass movements and ground reaction forces during running in humans and other animals. Legged robots that operate as bouncing, “spring-mass” systems can maintain stable motion using relatively simple, distributed feedback rules. We tested whether the changes to sagittal-plane movements during five running tasks involving active changes to running height, speed, and orientation were consistent with the rules used by bouncing robots to maintain stability. Changes to running height were associated with changes to leg force but not stance duration. To change speed, humans primarily used a “pogo stick” strategy, where speed changes were associated with adjustments to fore-aft foot placement, and not a “unicycle” strategy involving systematic changes to stance leg hip moment. However, hip moments were related to changes to body orientation and angular speed. Hip moments could be described with first order proportional-derivative relationship to trunk pitch. Overall, the task-level strategies used for body control in humans were consistent with the strategies employed by bouncing robots. Identification of these behavioral strategies could lead to a better understanding of the sensorimotor mechanisms that allow for effective unsteady locomotion.