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Running and Walking with Compliant Legs

Authors:
Andre Seyfarth at Technical University of Darmstadt
Andre Seyfarth
Hartmut Geyer at Carnegie Mellon University
Hartmut Geyer
Reinhard Blickhan at Friedrich Schiller University Jena
Reinhard Blickhan
Susanne Lipfert
Susanne Lipfert
Susanne Lipfert
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Abstract and Figures

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.
Leg function is divided into global and internal leg function. Global leg function describes the leg control based on a given an internal leg function. The internal leg function addresses issues of design and control of a segmented leg itself. To identify control strategies we analyze the mechanical stability of select leg designs at different levels of leg function.
Leg function is divided into global and internal leg function. Global leg function describes the leg control based on a given an internal leg function. The internal leg function addresses issues of design and control of a segmented leg itself. To identify control strategies we analyze the mechanical stability of select leg designs at different levels of leg function.
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Three-segment model with equal segment lengths (L1=L2=L3) and two joint springs of same stiffness and same nominal angles (A). At a certain amount of leg compression (B) symmetric bending of both joints becomes unstable. Depending on infinitely small perturbation either one or the other joints starts to extend at further leg compression (C). The other joint is flexing rapidly at the same time.
Three-segment model with equal segment lengths (L1=L2=L3) and two joint springs of same stiffness and same nominal angles (A). At a certain amount of leg compression (B) symmetric bending of both joints becomes unstable. Depending on infinitely small perturbation either one or the other joints starts to extend at further leg compression (C). The other joint is flexing rapidly at the same time.
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Five strategies to avoid instability in an elastic three-segment leg: (A) nonlinear joint springs, (B) asymmetric leg segmentation and leg joint configuration, (C) biarticular elastic structures, (D) joint constraints, e.g. heel contact, and (E) operation in a bow configuration.
Five strategies to avoid instability in an elastic three-segment leg: (A) nonlinear joint springs, (B) asymmetric leg segmentation and leg joint configuration, (C) biarticular elastic structures, (D) joint constraints, e.g. heel contact, and (E) operation in a bow configuration.
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(A) Two-segment leg model with one extensor muscle and proprioceptive feedback. The activity of the -motoneuron driving the extensor muscle (STIM) was assumed to be the sum of a central command STIM0 and a contribution of the reflex loop based on different sensory signals (muscle length, muscle velocity or muscle force). Muscle stimulation STIM with and without sensory feedback for stable hopping on place was calculated. (B) The best hopping performance based on sensory feedback was achieved with positive force feedback and a constant signal STIM0. Here, spring-like leg behavior could be found. (C) The muscle-reflex dynamics was robust with respect to environmental changes like hopping on a dissipative substrate (sand).
(A) Two-segment leg model with one extensor muscle and proprioceptive feedback. The activity of the -motoneuron driving the extensor muscle (STIM) was assumed to be the sum of a central command STIM0 and a contribution of the reflex loop based on different sensory signals (muscle length, muscle velocity or muscle force). Muscle stimulation STIM with and without sensory feedback for stable hopping on place was calculated. (B) The best hopping performance based on sensory feedback was achieved with positive force feedback and a constant signal STIM0. Here, spring-like leg behavior could be found. (C) The muscle-reflex dynamics was robust with respect to environmental changes like hopping on a dissipative substrate (sand).
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Spring-mass running. (A) For certain combinations of leg stiffness k and angle of attack α 0 a cyclic movement of the centre of mass can be found. (B) Dif- ferent angles of attack can result in stable running patterns (here α 0 =67, 68 with
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Spring-mass running. (A) For certain combinations of leg stiffness k and angle of attack α 0 a cyclic movement of the centre of mass can be found. (B) Dif- ferent angles of attack can result in stable running patterns (here α 0 =67, 68 with
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... Visual inspection of simulations using the spring-mass model show the vertical CoM displacement and vertical GRFs were consistently overestimated compared to experimental running data (Bullimore andBurn 2007, Lipfert et al 2012); suggesting the springmass model is not as good at modelling running as the literature might imply. Presumably, to improve the agreement between the simulations and experimental data, a number of two-segment (Rummel and Seyfarth 2008, Phan et al) and three-segment (Seyfarth et al 2001, Seyfarth et al 2006, Qiao et al 2017 lower limb models have been developed. ...
... Lim and Park (2018) also showed that the addition of an off-centred curvy foot connected to the leg by a compliant segment qualitatively improved agreement with empirical data of both walking a running compared to the original spring mass model. On the other hand, the three-segment models showed that having a small foot relative to the shank allows for large knee extensions, and a small foot relative to the thigh requires a lower ankle joint stiffness than knee joint stiffness (Seyfarth et al 2001, Seyfarth et al 2006. These results are characteristic of a human leg configuration, suggesting such a model could improve prediction of the kinematic and kinetic characteristics of running. ...
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... Recent articles on quadrupedal and bipedal walking and running (Lee et al., 2011(Lee et al., , 2013Nauwelaerts et al., 2015;O'Neill and Schmitt, 2012), along with theoretical models by Geyer et al. (2006) and Seyfarth et al. (2006), have led to the development of a more nuanced model of a SLIP and the idea that pendular periods and collisional periods are both important to consider in evaluating potential costs of locomotion (Lee et al., 2011;O'Neill and Schmitt, 2012) rather than treating those as discreet and mutually exclusive. In SLIP models, a continuum between an infinitely stiff or infinitely compliant spring element can be used to represent a full range of gaits, from inverted pendulum-like walking, through pogo-stick-like running, to the highly compliant 'stealthy' gaits. ...
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... However, in wearable robotics, the required torques are rarely perfectly linear with respect to the output angle over the entire operating range of motion. The joint stiffness profiles required for walking, for example, exhibit low stiffness at low joint flexion and high stiffness at high joint flexion (Seyfarth et al., 2006). A closer match between the spring characteristic and the required torque can be achieved by means of nonlinear transmissions. ...
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... Legged robots have been developed with varying abilities to perform human-like locomotion (Collins et al., 2005;Torricelli et al., 2016;Kim and Wensing, 2017). For example, robots have been developed with comparable efficiency to human walking (Collins et al., 2005;McGeer, 1990) and an ability to generate a variety of movement tasks, such as walking and running (Seyfarth et al., 2006;Kwon and Park, 2003;Jones and Hurst, 2012). ...
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Article
  • Feb 2021
  • J BIOMECH
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... In the context of locomotion, robotic systems used biarticular structures with compliant properties of muscles or tendons [124,[130][131][132][133][134][135]. Such designs are inspired by biological bodies [136,137]. Both of these qualities, biarticular arrangement and inherent compliant properties, can be considered tools for control embodiment. ...
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... For this reason, several researchers have implemented springs in hopping robots [194,129,93,16]. Based on the notion that the knee joint needs to stiffen as it is flexed more in order to ensure stable hopping [201,186], the stiffness of the knee actuator is often nonlinear in compliant designs [220]. The ability to vary stiffness is also an important feature, because the stiffness of the leg determines the hopping frequency [65] and varying stiffness allows us to adapt to the surface stiffness [69]. ...
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Yay katsayısı sürekli değiştirilebilen seri elastik aktüatör tasarımı ve imalatı
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Toward a Human-like Biped Robot with Compliant Legs.
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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 investigate a simple model for biped robots which makes use of minimum control and elastic passive joints inspired from the structures of biological systems. The model is eval- uated in simulation and a physical robotic platform with respect to the kinemat- ics and the ground reaction force. The experimental results show that the behavior of this simple locomotion model shows a considerable similarity to that of human walking.
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Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure
Article
Full-text available
  • Dec 1977
  • Am J Physiol
The work done during each step to lift and to reaccelerate (in the forward direction) and center of mass has been measured during locomotion in bipeds (rhea and turkey), quadrupeds (dogs, stump-tailed macaques, and ram), and hoppers (kangaroo and springhare). Walking, in all animals (as in man), involves an alternate transfer between gravitational-potential energy and kinetic energy within each stride (as takes place in a pendulum). This transfer is greatest at intermediate walking speeds and can account for up to 70% of the total energy changes taking place within a stride, leaving only 30% to be supplied by muscles. No kinetic-gravitational energy transfer takes place during running, hopping, and trotting, but energy is conserved by another mechanism: an elastic "bounce" of the body. Galloping animals utilize a combination of these two energy-conserving mechanisms. During running, trotting, hopping, and galloping, 1) the power per unit weight required to maintain the forward speed of the center of mass is almost the same in all the species studied; 2) the power per unit weight required to lift the center of mass is almost independent of speed; and 3) the sum of these two powers is almost a linear function of speed.
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The Spring Mass Model for Running and Hopping
Article
  • Feb 1989
  • J BIOMECH
A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.
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