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Engineering
Control and Systems Engineering

Intelligence by mechanics

Profile image of R. BlickhanR. Blickhan

2007, … of the Royal …

https://doi.org/10.1098/RSTA.2006.1911
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Abstract

Research on the biomechanics of animal and human locomotion provides insight into basic principles of locomotion and respective implications for construction and control. Nearly elastic operation of the leg is necessary to reproduce the basic dynamics in walking and running. Elastic leg operation can be modelled with a spring-mass model. This model can be used as a template with respect to both gaits in the construction and control of legged machines. With respect to the segmented leg, the humanoid arrangement saves energy and ensures structural stability. With the quasi-elastic operation the leg inherits the property of self-stability, i.e. the ability to stabilize a system in the presence of disturbances without sensing the disturbance or its direct effects. Self-stability can be conserved in the presence of musculature with its crucial damping property. To ensure secure foothold visco-elastic suspended muscles serve as shock absorbers. Experiments with technically implemented leg models, which explore some of these principles, are promising.

Key takeaways
sparkles

AI

  1. Quasi-elastic leg operation is essential for dynamic locomotion and self-stability in both animals and legged machines.
  2. Spring-mass models effectively describe walking and running dynamics, aiding in the construction of legged systems.
  3. Self-stability reduces control demands, allowing legged robots to navigate disturbances without direct sensing.
  4. Segmentation in humanoid robots enhances energy efficiency and structural stability during locomotion.
  5. Experimental findings show that compliant, muscle-like actuators improve shock absorption and response to unexpected loads.
Figures (8)
Figure 1. The spring-mass model for walking (a, c) and running (0, d) during a single contact from apex to apex. (a, b) Path of the centre of gravity (dashed lines) and springy legs in contact (black right leg, grey left leg). In walking, the leg extends during midstance and almost approaches its initial unloaded length (thin line). (c, d) In walking the typical camel-back pattern of the ground reaction force is obtained. The walk depicted represents a rather dynamical stable mode (comp. Geyer et al. 2006).
Figure 1. The spring-mass model for walking (a, c) and running (0, d) during a single contact from apex to apex. (a, b) Path of the centre of gravity (dashed lines) and springy legs in contact (black right leg, grey left leg). In walking, the leg extends during midstance and almost approaches its initial unloaded length (thin line). (c, d) In walking the typical camel-back pattern of the ground reaction force is obtained. The walk depicted represents a rather dynamical stable mode (comp. Geyer et al. 2006).
Figure 2. While walking (bright) and running (dark) at different speeds (from above: 0.25, 0.75 and 1.25 mean transition speed), vertical stiffness as the average slope of the characteristics of the vertical force depending on the vertical centre of mass displacement represents a rather conservative property and is independent of the selected gait. Differences are observed with respect to energy occurring in discrete steps. The measurements are obtained for an individual running on an instrumented treadmill (ADAL 3D, Tecmachine) in the Locomotion Lab at Jena.
Figure 2. While walking (bright) and running (dark) at different speeds (from above: 0.25, 0.75 and 1.25 mean transition speed), vertical stiffness as the average slope of the characteristics of the vertical force depending on the vertical centre of mass displacement represents a rather conservative property and is independent of the selected gait. Differences are observed with respect to energy occurring in discrete steps. The measurements are obtained for an individual running on an instrumented treadmill (ADAL 3D, Tecmachine) in the Locomotion Lab at Jena.
By placing the foot with its heels and shifting the point of pressure towards the toes, the foot acts like the rim of a wheel. Owing to the eccentric positioning of the ankle joint and the action of the M. tibialis anterior, its placement helps to bend the knee in the first quarter of stance. It starts to extent until reaching midstance, where the stiff inverted pendulum situation is approached. With the progression of the centre of gravity the knee again starts to bend, i.e. the protraction of the thigh starts already during the last third of the stance phase (Seyfarth 2005). During the last quarter of the stance phase, the heel is lifted off the ground owing to ankle extension (Saunders et al. 1953). At midstance, in walking, ankle and knee operate in a push-pull situation. In contrast, during running both joints are working in phase, the coupling between the movement of the ankle joint and the knee joint is increasing. At the preferred transition speed, the hip moves in both gaits in a close to sinusoidal pattern with a short interruption of leg retraction owing to landing impact (figure 3). During running, the role of the foot as a rim diminishes, whereas its role as spring segment increases. Qimilar roles mav he attributed to the joints and ceomente of all Jeo of
By placing the foot with its heels and shifting the point of pressure towards the toes, the foot acts like the rim of a wheel. Owing to the eccentric positioning of the ankle joint and the action of the M. tibialis anterior, its placement helps to bend the knee in the first quarter of stance. It starts to extent until reaching midstance, where the stiff inverted pendulum situation is approached. With the progression of the centre of gravity the knee again starts to bend, i.e. the protraction of the thigh starts already during the last third of the stance phase (Seyfarth 2005). During the last quarter of the stance phase, the heel is lifted off the ground owing to ankle extension (Saunders et al. 1953). At midstance, in walking, ankle and knee operate in a push-pull situation. In contrast, during running both joints are working in phase, the coupling between the movement of the ankle joint and the knee joint is increasing. At the preferred transition speed, the hip moves in both gaits in a close to sinusoidal pattern with a short interruption of leg retraction owing to landing impact (figure 3). During running, the role of the foot as a rim diminishes, whereas its role as spring segment increases. Qimilar roles mav he attributed to the joints and ceomente of all Jeo of
Figure 4. An effective foot with a length of 0.4 thigh length is optimum with respect to low energy leg shortening and helps to avoid structural instability. (a) As compared with the three-segment equivalents of a two-segment leg, the aligned configuration with a short foot has a higher effective mechanical advantage. (b) When compressing a symmetrically configured leg with elastic joints a structural instability is observed. (c) A short foot helps to move the point of bifurcation out of the working range of the leg.
Figure 4. An effective foot with a length of 0.4 thigh length is optimum with respect to low energy leg shortening and helps to avoid structural instability. (a) As compared with the three-segment equivalents of a two-segment leg, the aligned configuration with a short foot has a higher effective mechanical advantage. (b) When compressing a symmetrically configured leg with elastic joints a structural instability is observed. (c) A short foot helps to move the point of bifurcation out of the working range of the leg.
Figure 5. The spring-mass model amortizes a step without altering stiffness or the angle of attack at touchdown. Owing to the step, the flight phase is shortened and the system takes off at a steeper angle, recovering in the next step. The vertical as well as the horizontal components of the ground reaction force are diminished after the step. (a) Dashed line, path of the centre of gravity; open circles, apex; shaded sector after second contact: change in take-off angle. (b) Dashed line, body weight (after Blickhan et al. 2003).
Figure 5. The spring-mass model amortizes a step without altering stiffness or the angle of attack at touchdown. Owing to the step, the flight phase is shortened and the system takes off at a steeper angle, recovering in the next step. The vertical as well as the horizontal components of the ground reaction force are diminished after the step. (a) Dashed line, path of the centre of gravity; open circles, apex; shaded sector after second contact: change in take-off angle. (b) Dashed line, body weight (after Blickhan et al. 2003).
Figure 6. Leg compression (a, b) and ground reaction force (c, d) while running up steps of different height (0m, solid line; 0.1 m, dashed line; 0.15 m, dotted line) embedded into a rough ground. (a, c) Experiments; (b, d) simulation with a two-segment extensor model without elasticity. The experiment (a, c) reveals that initial condition is changing with respect to initial velocity (step height), adapted leg length and initial angle of attack of the leg. Compression during contact remains the same, whereas force reduces with step size. Correspondingly, leg stiffness is decreasing. The simple model runner does not match all figures but displays similar tendencies under roughly corresponding initial conditions (initial leg lengths in sequence of the step height: 0.95, 0.9, 0.85 m; angle of attack: 71, 67 and 63°; mass=60 kg; vertical touchdown velocity = —0.7 ms‘; horizontal touchdown velocity =4.5 ms‘).
Figure 6. Leg compression (a, b) and ground reaction force (c, d) while running up steps of different height (0m, solid line; 0.1 m, dashed line; 0.15 m, dotted line) embedded into a rough ground. (a, c) Experiments; (b, d) simulation with a two-segment extensor model without elasticity. The experiment (a, c) reveals that initial condition is changing with respect to initial velocity (step height), adapted leg length and initial angle of attack of the leg. Compression during contact remains the same, whereas force reduces with step size. Correspondingly, leg stiffness is decreasing. The simple model runner does not match all figures but displays similar tendencies under roughly corresponding initial conditions (initial leg lengths in sequence of the step height: 0.95, 0.9, 0.85 m; angle of attack: 71, 67 and 63°; mass=60 kg; vertical touchdown velocity = —0.7 ms‘; horizontal touchdown velocity =4.5 ms‘).
Figure 7. (a) Visco-elastically suspended muscle masses at thigh and shank. (b) Line: acceleration measured at the surface of the shank, note the delayed damped oscillation; dashed line: acceleration of the tibia relying on surface marker kinematics at the ankle joint (after Giinther et al. 2003).
Figure 7. (a) Visco-elastically suspended muscle masses at thigh and shank. (b) Line: acceleration measured at the surface of the shank, note the delayed damped oscillation; dashed line: acceleration of the tibia relying on surface marker kinematics at the ankle joint (after Giinther et al. 2003).
Figure 8. Examples of elastic legged robots (Locomotion Laboratory Jena). In all cases, locomotion was found without sensory feedback by merely introducing oscillatory fore-aft movements at the hip. (a) Pogo stick runner; (b) two-segment runner; (c) biped with elastic three-segment. legs. Based on the mono- and biarticular elastic coupling, stable walking with human-like knee and ankle joint kinematics (similar to figure 26) is found.
Figure 8. Examples of elastic legged robots (Locomotion Laboratory Jena). In all cases, locomotion was found without sensory feedback by merely introducing oscillatory fore-aft movements at the hip. (a) Pogo stick runner; (b) two-segment runner; (c) biped with elastic three-segment. legs. Based on the mono- and biarticular elastic coupling, stable walking with human-like knee and ankle joint kinematics (similar to figure 26) is found.

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