Trunk pitch oscillations for energy trade-offs in bipedal running birds and robots

Skipping without and with hurdles in bipedal macaque: global mechanics

Macaques trained to perform bipedally used running gaits across a wide range of speeds. At higher speeds they preferred unilateral skipping (galloping). The same asymmetric stepping pattern was used while hurdling across two low obstacles placed at the distance of a stride within our experimental track. In bipedal macaques during skipping, we expected a differential use of the trailing and leading legs. The present study investigated global properties of the effective and virtual leg, the location of the virtual pivot point (VPP), and the energetics of the center of mass (CoM), with the aim of clarifying the differential leg operation during skipping in bipedal macaques. When skipping, macaques displayed minor double support and aerial phases during one stride. Asymmetric leg use was indicated by differences in leg kinematics. Axial damping and tangential leg work did not influence the indifferent peak ground reaction forces and impulses, but resulted in a lift of the CoM during contact of the leading leg. The aerial phase was largely due to the use of the double support. Hurdling amplified the differential leg operation. Here, higher ground reaction forces combined with increased double support provided the vertical impulse to overcome the hurdles. Following CoM dynamics during a stride, skipping and hurdling represented bouncing gaits. The elevation of the VPP of bipedal macaques resembled that of human walking and running in the trailing and leading phases, respectively. Because of anatomical restrictions, macaque unilateral skipping differs from that of humans, and may represent an intermediate gait between grounded and aerial running.

Effects of running skill and speed on limb coordination during submaximal and maximal sprinting

In locomotion, the relative phasing of the limbs changes with speed and provides valuable insight to neuromuscular control of gait. At present, it is unknown if individuals trained in sprinting coordinate their limbs differently than runners from other athletic backgrounds. Therefore, we aimed to characterize the effects of speed and skill on lower limb coordination. Twenty-five physically active (PA) and fifteen track and field (TF) athletes performed 40 m running trials at self-selected speeds, from jogging to maximal sprinting. We measured lower limb kinematics during steady-speed running, and quantified coordination using continuous relative phase (CRP) methods for interlimb pairs (Thigh-Thigh, Shank-Shank) and intralimb pairs (Shank-Thigh). Regression techniques showed between-group differences in scaling of coordination with speed during the stance phase, such that coordination was significantly more antiphase during jogging and running speeds in TF. During flight the scaling between groups was similar, but there were persistent and significant differences in coordination across all speeds. Comparing only the maximal speed trials, we found interlimb coordination was significantly more antiphase for TF in both stance and flight. In all cases, Shank-Shank coordination showed the largest between-group differences. Our results demonstrate the importance of interlimb coordination at maximal sprint speed, particularly during the flight phase and between shank segments. Between-group differences in coordination at slower speeds suggest a selective tuning of coordination in trained runners. We speculate differences in limb coordination are due to acquired motor patterns from optimizing forward velocity and its mechanical determinants, which differ particularly during flight/swing and between shank segments.

Walking like a robot: do the ground reaction forces still intersect near one point when humans imitate a humanoid robot?

Bipedal walking while keeping the upper body upright is a complex task. One strategy to cope with this task is to direct the ground reaction forces toward a point above the centre of mass of the whole body, called virtual pivot point (VPP). This behaviour could be observed in various experimental studies for human and animal walking, but not for the humanoid robot LOLA. The question arose whether humans still show a VPP when walking like LOLA. For this purpose, ten participants imitated LOLA in speed, posture, and mass distribution (LOLA-like walking). It could be found that humans do not differ from LOLA in spatio-temporal parameters for the LOLA-like walking, in contrast to upright walking with preferred speed. Eight of the participants show a VPP in all conditions (R2 > 0.90 ± 0.09), while two participants had no VPP for LOLA-like walking (R2 < 0.52). In the latter case, the horizontal ground reaction forces are not balanced around zero in the single support phase, which is presumably the key variable for the absence of the VPP.

'Virtual pivot point' in human walking: Always experimentally observed but simulations suggest it may not be necessary for stability

The intersection of ground reaction forces near a point above the center of mass has been observed in computer simulation models and human walking experiments. Observed so ubiquitously, the intersection point (IP) is commonly assumed to provide postural stability for bipedal walking. In this study, we challenge this assumption by questioning if walking without an IP is possible. Deriving gaits with a neuromuscular reflex model through multi-stage optimization, we found stable walking patterns that show no signs of the IP-typical intersection of ground reaction forces. The non-IP gaits found are stable and successfully rejected step-down perturbations, which indicates that an IP is not necessary for locomotion robustness or postural stability. A collision-based analysis shows that non-IP gaits feature center of mass (CoM) dynamics with vectors of the CoM velocity and ground reaction force increasingly opposing each other, indicating an increased mechanical cost of transport. Although our computer simulation results have yet to be confirmed through experimental studies, they already indicate that the role of the IP in postural stability should be further investigated. Moreover, our observations on the CoM dynamics and gait efficiency suggest that the IP may have an alternative or additional function that should be considered.

Hill-type, bioinspired actuation delivers energy economy in DC motors

Electromagnetic motors convert stored energy to mechanical work through a linear force-velocity (FV) relationship. In biological systems, however, muscle actuation is characterized by the hyperbolic FV mechanisms of the Hill muscle-in which a parameterαcharacterizes the degree of nonlinearity. Previous work has shown that bioinspiration in human-engineered systems can contribute favorable mechanical attributes-such as energy efficiency, self-stability, and flexibility, among others. In this study, we first construct an easily amendable, bioinspired electromagnetic motor which produces FV curves that mimic the Hill model of muscle with a high degree of accuracy. A proportional-integral-differential (PID) controller converges the characteristically linear FV relationship of a DC motor to nonlinear Hill-type force outputs. The bioinspired electric motor does a fixed amount of work by lifting a 147.5 g mass, and we record the translational velocity of the mass and the nonlinear applied force of the motor. Under optimized gain coefficients in the PID, the bioinspired motor achieves agreement ofR2>0.99with the Hill muscle model. Studies have shown that designing biologically inspired actuators produce comparatively energy efficient systems. We investigate the energy economy of actuating our motor with nonlinear, Hill-type forces in direct comparison with conventional linear FV actuation techniques. We find that the bioinspired motor delivers energy economy with respect to energy consumption and conversion: the nonlinear, Hill-type DC motor reduces the energetic cost of actuation when delivering a fixed amount of mechanical work.

Analysis and control of a running spring-mass model with a trunk based on virtual pendulum concept

The spring-loaded inverted pendulum model has been one of the most studied conceptual models in the locomotion community. Even though it can adequately explain the center of mass trajectories of numerous legged animals, it remains insufficient in template-based control of complex robot platforms, being unable to capture additional dynamic characteristics of locomotion exhibited in additional degrees of freedom such as trunk pitch oscillations. In fact, analysis of trunk behavior during locomotion has been one of the motivations behind studying the virtual pivot point (VPP) concept, with biological inspiration and basis for both natural and synthetic systems with non-negligible trunk dynamics. This study first presents a comprehensive analysis of the VPP concept for planar running behaviors, followed by a systematic study of the existence and characteristics of periodic solutions. In particular, we investigate how periodic solutions depend on model control parameters and compare them based on stability and energetic cost. We then develop a feedback controller that can stabilize system dynamics around its periodic solutions and evaluate performance as compared to a previously introduced controller from the literature. We demonstrate the effectiveness of both controllers and find that the proposed control scheme creates larger basins of attraction with minor degradation in convergence speed. In conclusion, this study shows that the VPP concept, in conjunction with the proposed controller, could be beneficial in designing and controlling legged robots capable of running with non-trivial upper body dynamics. Our systematic analysis of periodic solutions arising from the use of the VPP concept is also an important step towards a more formal basis for comparisons of the VPP concept with bio-locomotion.

BirdBot achieves energy-efficient gait with minimal control using avian-inspired leg clutching

Designers of legged robots are challenged with creating mechanisms that allow energy-efficient locomotion with robust and minimalistic control. Sources of high energy costs in legged robots include the rapid loading and high forces required to support the robot's mass during stance and the rapid cycling of the leg's state between stance and swing phases. Here, we demonstrate an avian-inspired robot leg design, BirdBot, that challenges the reliance on rapid feedback control for joint coordination and replaces active control with intrinsic, mechanical coupling, reminiscent of a self-engaging and disengaging clutch. A spring tendon network rapidly switches the leg's slack segments into a loadable state at touchdown, distributes load among joints, enables rapid disengagement at toe-off through elastically stored energy, and coordinates swing leg flexion. A bistable joint mediates the spring tendon network's disengagement at the end of stance, powered by stance phase leg angle progression. We show reduced knee-flexing torque to a 10th of what is required for a nonclutching, parallel-elastic leg design with the same kinematics, whereas spring-based compliance extends the leg in stance phase. These mechanisms enable bipedal locomotion with four robot actuators under feedforward control, with high energy efficiency. The robot offers a physical model demonstration of an avian-inspired, multiarticular elastic coupling mechanism that can achieve self-stable, robust, and economic legged locomotion with simple control and no sensory feedback. The proposed design is scalable, allowing the design of large legged robots. BirdBot demonstrates a mechanism for self-engaging and disengaging parallel elastic legs that are contact-triggered by the foot's own lever-arm action.

A model-based strategy for quadruped running with differentiated fore- and hind-leg morphologies

This article introduces a model-based strategy for a quadruped robot with differentiated fore- and hind-leg ground reaction force patterns to generate animal-like running behavior. The proposed model comprises a rigid body and two eccentric spring-loaded inverted pendulum (eSLIP) legs with dampers. The eSLIP model extends the traditional SLIP model by adding a bar to offset the spring direction. The proposed two-leg eSLIP (TL-eSLIP) model's fore- and hind legs were designed to have the same offset magnitude but in opposite offset directions, producing different braking and thrusting force patterns. The TL-eSLIP model's reference leg trajectories were designed based on the fixed-point motion of the eSLIP model. Additionally, the legs were clock torque-controlled to modulate leg motion and stabilize the model to follow its natural dynamics. The model's equations for motion were derived, and the model's dynamic behavior was simulated and analyzed. The simulation results indicate that the model with leg offsets and in either trotting or pronking has differentiated leg force patterns, and it is more stable and has larger basins of attraction than the model without leg offsets. A quadruped robot was built for experimental validation. The experimental results demonstrate that the robot with differentiated legs ran with differentiated ground reaction force patterns and ran more stably than another robot with the same leg morphology.

Virtual Point Control for Step-Down Perturbations and Downhill Slopes in Bipedal Running

Bipedal running is a difficult task to realize in robots, since the trunk is underactuated and control is limited by intermittent ground contacts. Stabilizing the trunk becomes even more challenging if the terrain is uneven and causes perturbations. One bio-inspired method to achieve postural stability is the virtual point (VP) control, which is able to generate natural motion. However, so far it has only been studied for level running. In this work, we investigate whether the VP control method can accommodate single step-down perturbations and downhill terrains. We provide guidelines on the model and controller parameterizations for handling varying terrain conditions. Next, we show that the VP method is able to stabilize single step-down perturbations up to 40 cm, and downhill grades up to 20-40° corresponding to running speeds of 2-5 ms-1. Our results show that the VP approach leads to asymmetrically bounded ground reaction forces for downhill running, unlike the commonly-used symmetric friction cone constraints. Overall, VP control is a promising candidate for terrain-adaptive running control of bipedal robots.

Postural stability in human running with step-down perturbations: an experimental and numerical study

Postural stability is one of the most crucial elements in bipedal locomotion. Bipeds are dynamically unstable and need to maintain their trunk upright against the rotations induced by the ground reaction forces (GRFs), especially when running. Gait studies report that the GRF vectors focus around a virtual point above the centre of mass (VPA), while the trunk moves forward in pitch axis during the stance phase of human running. However, a recent simulation study suggests that a virtual point below the centre of mass (VPB) might be present in human running, because a VPA yields backward trunk rotation during the stance phase. In this work, we perform a gait analysis to investigate the existence and location of the VP in human running at 5 m s-1, and support our findings numerically using the spring-loaded inverted pendulum model with a trunk. We extend our analysis to include perturbations in terrain height (visible and camouflaged), and investigate the response of the VP mechanism to step-down perturbations both experimentally and numerically. Our experimental results show that the human running gait displays a VPB of ≈-30 cm and a forward trunk motion during the stance phase. The camouflaged step-down perturbations affect the location of the VPB. Our simulation results suggest that the VPB is able to encounter the step-down perturbations and bring the system back to its initial equilibrium state.

A little damping goes a long way: a simulation study of how damping influences task-level stability in running

It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: instead of observing whether trajectories converge towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of 'stable' or 'unstable'. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open source.

Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of physical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring- damper is engaged between touch-down and mid-stance, and its damper auto-decouples from mid-stance to takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability, and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms: a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting the damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion.