## The Gap between Walking and Running

### The Gait that closes the Gap

The mostly used gaits of human locomotion are walking and running. In walking the important characteristics are that always one or both legs have ground contact, and the center of mass is lifted during a single leg stance phase. In running exist true flight phases and the center off mass reaches a minimum during stance phase. In order to change from one gait to another, an abrupt switching is observed. Maybe, there exists no smooth transition over many steps. The bipedal spring-mass model can reproduce both gaits, but there were significant differences in velocity, respectively system energy observed. However, the observations had a limited view because the simulation results were reduced to self-stable gait solutions. A more general investigation on model predictions should focus on periodic gait solutions and could propose additional strategies for stabilizing the identified gait patterns.

In order to investigate periodic gait patterns for analyzing walking and running, a common platform for gait simulations is required. As mentioned, the bipedal spring-mass model is able to show both gaits and using the methodology of Poincaré maps, periodic solutions can be identified. For applying Poincaré maps, the definition of start and stop conditions is necessary, which should exist in both gaits similarly. A useful start and stop event was established in the Locomotion Lab Jena, namely the instant of Vertical Leg Orientation (VLO). The issue regarding VLO is explained in another article.

Does there still exist a gap between walking and running when focussing on periodic gait solutions?

Classification of the gaits. R: running, W2,W3: walking, GR: grounded running.

Previously, it was known that walking operates at low velocities only. When increasing the energy respectivley the energy, the body will lift off at some time. Due to that reason, the following investigation will be focussed on gaits at low velocities. Analyses on running revealed that it is easy to find running at low speeds. It is depends mainly on the setting of the leg’s angle of attack $\alpha_0$, allowing for running or not. With our novel map for gait solutions, the systems variables at the instant of VLO are shown. Here, we focus on symmetric gait patterns, which means that the first half of the stance phase is symmetrically identical to the second half. The system state is then reduced to a single, independent variable, i.e. the height of the center of mass $y_0$ at the event of VLO. In the figure, two system parameters, i.e. the leg’s angle of attack $\alpha_0$ and the system energy (thick lines) were varied.

The simulation results for typical walking (green area, W2) reveal a height of the center of mass at midstance $y_0$ always above the height at touch down $y_{TD}$. The difference between them can be very small. In contrast, the center of mass is always lowered in running (blue area, R) with $y_0 < y_{TD}$. There is another difference regarding the angle of attack $\alpha_0$ found simulations with the same system energy. In conclusion, the gap between walking and running clearly exists.

Is there a chance to reduce the gap between the typical gaits of walking and running?

Inside the model simulations exists one condition, not explained so far. It is implied that the center of mass moves downward at the event of leg’s touch down. It feels like curious when a leg with a fixed angle at touch down would approaching the ground from a lower level. From now we reject this thought and allowing the center of mass to move upward when the leg is touching the ground. What happens with the leg? In fact, the simulated leg is not defined when it does not have ground contact. We assume of course that the leg will lengthen or rotating before hitting the ground.

With this modified assumption, the center of mass is lifted during touch down, we can identify a novel gait (orange area), which connects both, walking and running. In this gait, we observe that the center off mass is clearly lowered during single leg stance phase as usual in running. However, there exists a distinct double support phase, typical for walking.

The gait called Grounded Running. Motion of the center of mass and the ground reaction forces with distinct double support phases of the legs.

With the spring-mass model, a novel gait is identified, that could be classified as a running gait where $y_0 < y_{TD}$ although there is always ground contact respectively no flight phase exists. Based on simulations, this is a new gait, but it is already observed in locomotion of birds and is called Grounded Running. The simulations have shown, that grounded running exists for low velocities only. In contrast, the same simulation study revealed that walking can be faster than assumed.

#### Featured Paper

J. Rummel, Y. Blum, A. Seyfarth.
From walking to running.
Autonome Mobile Systeme 2009, R. Dillmann, J. Beyerer, C. Stiller, J.M. Zöllner, T. Gindele (Eds.) Springer: 89-96, 2009.
DOI: 10.1007/978-3-642-10284-4_12
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## Gait Mapping with Vertical Leg Orientation

### A general system state for gait model simulations

In walking and running, the motion of the centre of mass can be understood as a kind of oscillation, however, this oscillation is sometimes hardly comparable with a sinus function. For investigations of gaits, a special kind of mapping, so called Poincaré maps are used. In Poincaré maps a comparison between the systems state at the beginning and at the end of an oscillation is conducted which removes the time from the dataset. In the case, the systems state variables are equal, a periodic motion is revealed. Poincaré originally used the period duration for fixing start and end events (in order to analyse the motion of planets). When simulating gaits with legged models, the period duration is not known prior the simulation start.

In gait simulations, the scientists apply physical system states to define start and end event of a simulation while two conditions are very popular in the biomechanics field, i.e. the touch down of a leg and the apex of the centre of mass. The touch down event is often used for simulating Passive Dynamic Walkers with rigid legs. In models with compliant legs, the apex is mostly used to describe start and end of a gait cycle. When the touch down event is used, the conditions of the counter leg need to be fixed a priori. Is the counter leg at the ground? Does it lift off at the same moment or does it swing without ground contact?

Similar a priori definitions are required when using the apex. Is the leg lifted at the instant of apex, the gait of running is selected.  In the walking gait, the active leg must have ground contact during apex. By definition, the apex is the highest point of the centre of mass during locomotion. However, the stop condition of a simulation is identified when one maximum is reached. That could be one maximum of possibly several peaks. In some simulations with a walking model, there were truly more than one maximum identified. Hence, the apex ore the maximum is not necessarily a unique event in walking and the apex return map is incomplete or maybe incorrect.

The instant of Vertical Leg Orientaion (VLO) with a simulated walking model.

At the Locomotion Lab in Jena another system state event for Poincaré maps was established, which allows to investigate both gaits, walking and running, with the same simulation and mapping. This event is called Vertical Leg Orientation (VLO). The definition is, that the active leg has ground contact and is oriented vertically or the hip joint is vertically above the foot point. While the active leg is on the ground, the counter leg is lifted. This system state exists in both gaits equally.

Well defined motion events for Poincaré maps ensure for a reduction of independent system variables in order to simplify the analysis. The system variables of the spring-mass model are the positions $x$ and $y$ of the centre of mass, which is located at the hip, and the velocities $v_x$ and $v_y$ of the centre of mass. At the instant of Vertical Leg Orientation, the system state can be reduced to two independent variables, i.e. the height $y$ and the angle of the velocity $\theta = \arctan(v_y/v_x)$.

Parameter map where symmetric walking patterns were found.

The novel method for gait analysis using VLO was applied for walking simulations first. There is a clear distinction between symmetric and asymmetric gait patterns. In symmetric walking, the velocity angle $\theta$ is always zero, which means, the first half of the stance phase is symmetrically identical to the second half. In asymmetric walking patterns is $\theta \neq 0$. Asymmetric walking patterns are not worse than symmetric patterns as there exist also self-stable solutions. A surprising finding is that in symmetric walking solutions, the centre of mass $y$ is always lifted at the event of VLO compared to the height at touch down $y_{TD}$.

Why is the novel event for Poincaré maps called VLO instead of “mid-stance”? The term mid-stance is already used in scientific literature but addresses various conditions. Mid-stance is for instance the time based centre of the stance phase, a period of time during the stance phase, or the event when the ground reaction force is perpendicular to the ground. In order to clearly define the event of vertical orientation and differentiate from a less explicit term, the name of Vertical Leg Orientation was established.

Simulation results on Walking and Running combined in a single map using VLO will be presented in another article.

#### Featured Paper

J. Rummel, Y. Blum, H.M. Maus, C. Rode, A. Seyfarth.
Stable and robust walking with compliant legs.
IEEE International Conference on Robotics and Automation, May 3-8, Anchorage, Alaska: 5250-5255, 2010.
DOI: 10.1109/ROBOT.2010.5509500
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