Juergen Rummel

Stable Running with Segmented Legs

Spring-like leg behavior is found in both humans and animals when running. In a spring-mass model, running proves to be self-stable in terms of external perturbations or variations in leg properties (for example, landing angle). However, biological limbs are not made of springs, rather, they consist of segments where spring-like behavior can be localized at the joint level. Here, we use a two-segment leg model to investigate the effects of leg compliance originating from the joint level on running stability. Owing to leg geometry a non-linear relationship between leg force and leg compression is found. In contrast to the linear leg spring, the segmented leg is capable of reducing the minimum speed for self-stable running from 3.5 m s-1 in the spring-mass model to 1.5 m s-1 for almost straight joint configurations, which is below the preferred transition speed from human walking to running (≈2 m s-1). At moderate speeds the tolerated range of landing angle is largely increased (17° at 5 m s-1) compare with the linear leg spring model (2°). However, for fast running an increase in joint stiffness is required to compensate for the mechanical disadvantage of larger leg compression. This could be achieved through the use of non-linear springs to enhance joint stiffness in fast running.

Upright human gait did not provide a major mechanical challenge for our ancestors.

Habitual bipedalism is considered as a major breakthrough in human evolution and is the defining feature of hominins. Upright posture is presumably less stable than quadrupedal posture, but when using external support, for example, toddlers assisted by their parents, postural stability becomes less critical. In this study, we show that humans seem to mimic such external support by creating a virtual pivot point (VPP) above their centre of mass. A highly reduced conceptual walking model based on this assumption reveals that such virtual support is sufficient for achieving and maintaining postural stability. The VPP is experimentally observed in walking humans and dogs and in running chickens, suggesting that it might be a convenient emergent behaviour of gait mechanics and not an intentional locomotion behaviour. Hence, it is likely that even the first hominis may have already applied the VPP, a mechanism that would have facilitated the development of habitual bipedalism.

Swing leg control in human running

Humans can run within a wide range of speeds without thinking about stabilizing strategies. The leg properties seem to be adjusted automatically without need for sensory feedback. In this work, the dynamics of human running are represented by the planar spring mass model. Within this framework, for higher speeds, running patterns can be stable without control strategies. Here, potential strategies that provide stability over a broader range of running patterns are considered and these theoretical predictions are compared to human running data. Periodic running solutions are identified and analyzed with respect to their stability. The control strategies are assumed as linear adaptations of the leg parameters-leg angle, leg stiffness and leg length-during the swing phase. To evaluate the applied control strategies regarding their influence on landing behavior, two parameters are introduced: the velocity of the foot relative to the ground (ground speed matching) and the foots angle of approach. The results show that periodic running solutions can be stabilized and that control strategies, which guarantee running stability, are redundant. For any swing leg kinematics (adaptation of the leg angle and the leg length), running stability can be achieved by adapting the leg stiffness in anticipation of the ground contact.

Bipedal Walking and Running with Compliant Legs

Passive dynamics plays an important role in legged locomotion of the biological systems. The use of passive dynamics provides a number of advantages in legged locomotion such as energy efficiency, self-stabilization against disturbances, and generating gait patterns and behavioral diversity. Inspired from the theoretical and experimental studies in biomechanics, this paper presents a novel bipedal locomotion model for walking and running behavior which uses compliant legs. This model consists of three-segment legs, two servomotors, and four passive joints that are constrained by eight tension springs. The self-organization of two gait patterns (walking and running) is demonstrated in simulation and in a real-world robot. The analysis of joint kinematics and ground reaction force explains how a minimalistic control architecture can exploit the particular leg design for generating different gait patterns. Moreover, it is shown how the proposed model can be extended for controlling locomotion velocity and gait patterns with the simplest control architecture.

Stable and robust walking with compliant legs

Bipedal walking could be implemented into a robot by mimicking spring-like leg behaviour. The fundamental model, describing human-like leg function in walking is the bipedal spring-mass model which was investigated in this study. We identified several types of walking patterns, e.g. symmetric and asymmetric walking, that accounts for high variability of gait. The aim of this study is the identification of a stiffness range which allows for stable walking with comparatively large robustness against perturbations. Walking with compliant legs was tested with the bipedal PogoWalker, demonstrating advantages of the underlying leg mechanics, i.e. walking without the necessity of precise leg adjustments, and acceptable impact forces.

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.

Toward a human-like biped robot with compliant legs

Conventional models of bipedal walking generally assume rigid body structures, while elastic material properties seem to play an essential role in nature. On the basis of a novel theoretical model of bipedal walking, this paper investigates a model of biped robot which makes use of minimum control and elastic passive joints inspired from the structures of biological systems. The model is evaluated in simulation and a physical robotic platform by analyzing the kinematics and ground reaction force. The experimental results show that, with a proper leg design of passive dynamics and elasticity, an attractor state of human-like walking gait patterns can be achieved through extremely simple control without sensory feedback. The detailed analysis also explains how the dynamic human-like gait can contribute to adaptive biped walking.

Running and Walking with Compliant Legs

It has long been the dream to build robots which could walk and run with ease. To date, the stance phase of walking robots has been characterized by the use of either straight, rigid legs, as is the case of passive walkers, or by the use of articulated, kinematically-driven legs. In contrast, the design of most hopping or running robots is based on compliant legs which exhibit quite natural behavior during locomotion.

Advanced Swing Leg Control for Stable Locomotion

Locomotion can be described as a subsequent series of stance and flight phases. In both phases the leg properties can be adapted. Here we consider spring-mass running with a linear adaptation of two leg parameters, leg angle and leg stiffness, during swing phase. The region of stability is characterized by the basin of attraction with sufficient reduction of a given perturbation within one step.

Enlarging regions of stable running with segmented legs

In human and animal running spring-like leg behavior is found, and similar concepts have been demonstrated by various robotic systems in the past. In general, a spring-mass model provides self-stabilizing characteristics against external perturbations originated in leg-ground interactions and motor control. Although most of these systems made use of linear spring-like legs. The question addressed in this paper is the influence of leg segmentation (i.e. the use of rotational joint and two limb-segments) to the self-stability of running, as it appears to be a common design principle in nature. This paper shows that, with the leg segmentation, the system is able to perform self-stable running behavior in significantly broader ranges of running speed and control parameters (e.g. control of angle of attack at touchdown, and adjustment of spring stiffness) by exploiting a nonlinear relationship between leg force and leg compression. The concept is investigated by using a two- segment leg model and a robotic platform, which demonstrate the plausibility in the real world.