In the area of walking habits, some important studies have been conducted. Hel- bing & Molnar [35] described factors that affect people during walking as a com- bination of attractive and repulsive forces. According to their explanation, these hidden forces drive people to walk from a starting point to the destination in a safe manner avoiding collisions with static and dynamic obstacles in the pathway. For example, when people walk from a location to a destination, they are affected by an "attractive force" created by the destination: people try to move closer to their destination after each step. Or take another example, during the walk, people try to keep themselves far away from obstacles in the pathway in order to avoid collision, i.e. they are influenced by the "repulsive force" from obstacles.
However, in the case of a group of people walking together, each individual in the group can be seen as a moving obstacle to other members. If one person simply considers the others as obstacles, everyone tends to move apart according to the effect of repulsive force, and therefore a group cannot be formed. Xu et al. [47] improved Helbing & Molnar’s model with a new factor called “bonding force”. When a group of people are walking together, every person in the group always
tries to keep themselves within a short distance from the group, i.e. they don’t want to move too far from their group. In contrast to the definition of repulsive force, the bonding force is defined to be exponential in the opposite direction. Figure 2-5
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Figure 2-5: Hidden Forces affect to pairs in walking
illustrates the hidden forces that affect pairs in walking. 𝑖 and 𝑗 are two members of a pair, they are walking to their destination 𝐷. There is a static obstacle 𝑂 located near their pathway. Both the members 𝑖 and 𝑗 are influenced by the attractive forces 𝐴𝐹𝐷 from the destination, the repulsive forces 𝑅𝐹𝑂 from the obstacle and
𝑅𝐹𝑃 from their partner - because their partners themselves are obstacles, and the
bonding forces 𝐴𝐹𝐵. During the walk, they also prefer the side-by-side walking
formation rather than one follows the other.
Around the same period, Costa et al. [20] observed that when people walk in pairs, they normally move in side-by-side spatial formation rather than in other spatial formations, unless the environment is strictly crowded or the pathway is too narrow. In other words, two members in a pair normally try to walk abreast their partners, rather than with one walking ahead, and the other following (the leader- follower mode). Moussaid et al. [21] had similar observations about side-by-side
walking formation of pairs when they studied human walking behaviors.
The human walking habits can also be represented as physical formulas. Ac- cording to Helbing & Molnar’s study [35], people normally prefer to keep a stable velocity 𝑀𝑣 at which they feel most comfortable. During a walk, if an event occurs
and it affects to the walking velocity of a person, then when the event is over, he will quickly return to his preferred walking velocity. According to two related studies of Helbing et al. and Ralston [27, 34], people generally try to minimize their ac- celeration 𝑀𝑤 on each step, i.e. they prefer to keep walking at a constant velocity
rather than continuously changing their walking velocity. The observations of Hel- bing, Montello and then Morales et al. [12, 27, 28] revealed that humans prefer to walk in a straight line toward their destinations 𝐷 rather than changing directions often.
I found some other studies, which are highly relevant to navigation of wheelchairs. Morales et al. [26, 59] commented that when using a wheelchair, wheelchair users tend to move like they themselves walk. The situations illustrated in Figure 2-6 are two examples. In Figure 2-6 a), there is an obstacle 𝑂 in the middle of a pathway.
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b) Figure 2-6: Moving habits of wheelchair usersThe wheelchair user 𝑖 tends to choose the wider pathway 𝐴 to move instead of choosing the narrow one 𝐵 although he needs some more movements to pass the obstacle, because plan 𝐴 makes him feel more comfortable than plan 𝐵. In Fig- ure 2-6 b), the moving plan 𝐵 has a shorter path to pass the corner, whereas the plan 𝐴 takes a longer detour. However, wheelchair users tend to choose the plan 𝐴to maximize their view, i.e. their comfort, during the movements.
In addition, in [25], Morales et al. commented that both wheelchair users and surrounding people prefer to maintain their “personal space” and “social distance” as well. As they move they try to maximize the distance from themselves to sur- rounding people and obstacles. Other studies, for example [10, 12, 23, 43–45, 60], also observed that when humans interact with mobile robots in general and robotic wheelchairs in particular, they expect the robots to react in ways that humans do. In other words, people expect mobile robots to obey the same rules that are ac- ceptable to humans, including social distance, walking habits, etc.
To summarize, a common finding of human walking habits and social spatial formation is that, when people stand, walk, or chat, they normally obey some hid- den rules regarding social and personal factors including the distances between people in their group and bystanders, the distances between one person and ob- stacles in the environment, and factors related to their habits. When these rules are obeyed, people normally feel more comfortable, i.e. their comfort needs are better satisfied. Moreover, those rules are also expected to be implemented on mobile robots in general and on robotic wheelchairs in particular, i.e. both the wheelchair users and surrounding people feel more comfortable if the robotic wheelchairs are able to move in ways humans naturally do.