The Virtual Pendulum Concept

Ground Reaction Forces for Stabilising the Body

The locomotion of humans is typically a bipedal gait while the centre of mass is located close to the hip. Therefore, the human body can be defined as an inverted pendulum. From a technical point of view, the stabilisation of an inverted pendulum is a challenging control. When we take a closer look at the human body, we find the centre of mass above the hip joint. This, however, makes the system more complicated because it is quasi a doubled inverted pendulum, even more difficulty to stabilise.

At the Lauflabor Locomotion Lab in Jena, a concept was created, how the upper body of a human could be stabilised during the bipedal locomotion. The basic idea is to generate a leg force acting on the ground (ground reaction force) that is aligned to a virtual point above hip and centre of mass. In this way, the inverted pendulum becomes a virtual pendulum. Investigations with a spring-mass model upgraded with a rigid body demonstrated that stability in walking and running can be achieved.

Does the concept of the virtual pendulum exist in humans? If true, is it a unique feature of humans who move on two legs in contrast to many other animals?

Experiments with human subjects walking and running on an equipped treadmill revealed that the ground reaction forces intersect the body axis above the centre of mass. The force intersects more or less at an area than on an exact point. The intersections are almost always above the centre of mass. A noticeable exception is identified during the short time when the foot hits the ground. Here, the impact forces point more toward the centre of mass. This could have the effect that during the impact no torque would be applied at the body. An undesired rotation and an inefficient counteraction can be avoided before the real elastic ground contact is performed.

Ground reaction forces in running chickens and walking dogs.

Animals have a more elastic ground contact and here the similar ground reaction force can be observed. As well as in humans, the ground reaction force intersects a vertical line above the centre of mass and transforms the inverted pendulum of the animals into a stable virtual pendulum. In running chickens, who move bipedal like humans, the virtual intersection area is very prominent. Experiments with walking dogs showed that the concept of the virtual pendulum still exists but there is no single point where the force intersects the vertical line. The intersections are large above the centre of mass and the range is much wider. Thanks to the four leg, the dog can use for locomotion and stabilisation, the control of upper body motion can be performed in a very relaxed manner.

In conclusion, we can assume that a concept of a virtual pendulum for stabilising the upper body already existed before the human ancestors erected and learned to move on two legs. It is not a unique feature, however, walking on two legs was probably a main advantage to use the free hands for creative activities.


Featured Paper

H.M. Maus, S.W. Lipfert, M. Gross, J. Rummel, A. Seyfarth.
Upright human gait did not provide a major mechanical challenge for our ancestors.
Nature Communications, 1(6): 70, 2010.
DOI: 10.1038/ncomms1073