ESFM parameters learning

The first part of the experiments is dedicated to the study of the ESFM parameters that governs human motion. We consider three kinds of interaction forces: person-to-person, person-obstacle and person-robot. The first and the second interactions have been studied in previous papers like [Helbing and Molnar,1995;Zanlungo et al.,2011]. However, the person-robot interaction parameters were not directly obtained in any previous work, thereby, in this section we present the results obtained for the parameters ρrp= {arp, arp, λrp, drp}.

As discussed in Sec.4.3.1, we have divided the parameter estimation in two different parts, analyzing 80 trajectories described by 20 different volunteers between 20 and 54 years old. During the first part, we optimize (4.8) the intrinsic parameter of the ESFM{k} describing the expected human trajectories under no external constrains. The experiment setting is as follows: the volunteers are told to walk towards a goal in a scene free of obstacles. A total of 4 different initial orientations are recorded in order to obtain more diverse trajectories.

The second part of the ESFM parameter learning was done under the influence of the Tibi robot. We optimize the parameters of the force interaction model ρrp= {arp, brp, λrp, drp} under

the presence of a moving robot, asserting that it is the only external force altering the outcome of trajectory described by the person. The volunteers walk towards a given goal in a free obstacle scenario. Simultaneously, the teleoperated Tibi robot approaches the walking pedestrian and interacts with him/her. We observe and track their trajectories and process them in order to obtain the remaining ESFM parameters.

Interaction k [s−1] a [m/s−1] b [m] d [m] λ

Per-Per [Luber et al.,2010] 2 1.25 0.1 0.2 0.5

Per-Per [Zanlungo et al.,2011] 4.9 10 0.34 0.16 1

Robot-to-Person 2.3 2.66 0.79 0.4 0.59

(our approach) (± 0.37) (± 4.51) (± 0.21) (± 0.25) (± 0.36)

Table 4.1: Parameters of the SFM calculated in different works and our calculations for the robot-to-person interaction considered in the ESFM

Table4.1shows the parameters learned after applying the minimization process (see Sec.4.3.1), using genetic algorithms, to all database trajectories. Each parameter includes a standard devi- ation obtained after estimating the parameters for each trajectory independently. Furthermore, in this table it can be seen the parameters proposed byLuber et al.[2010] and Zanlungo et al. [2011] are referred to the person-to-person SFM. The standard deviations of some parameters are high, because people behave differently when they interact with robots. Motivated to solve this problem, we have proposed the behavior-based estimation of the ESFM parameters for a more accurate prediction.

4.6.2 Behavior clustering

The second part of the experiments, performed in the FME, consisted of one robot and one person as obstacles, where a set of volunteers performed experiments in a controlled scene. The objective was to obtain data to calculate the behavior classes, as explained in Sec.4.4.1. Over 40 volunteers were recorded during a full day of experiments. Men and women, ranging from 20 to 56 years old participated as volunteers and some of them had not any experience in robotics. In Fig.4.8is depicted a real example of an experiment, as observed by the robot GUI.

Figure 4.8: Behavior clustering experiment. On the Left the volunteer walks and interacts with the interacting obstacle while trying to reach the goal (lilac cylinder). On the Right takes place the second interaction with the robotic platform, that is teleoperated in order to provide interaction.

The experiment setting is simple: the volunteers are told to naturally walk towards a very visible destination (a huge lilac cylinder), while approaching their destination, a dynamic obsta- cle crosses his/her path. Two dynamic obstacles are used during the experiments, a person and the Dabo robot. During the experiment, it is very important not to interact with both obstacles at the same time, but the volunteers were not told anything regarding this condition.

Once obtained and processed the trajectories, the parameters ρk= {k, ak, bk, λk, dk} can be

calculated by simply applying the procedure described in Sec.4.4.1. For plotting purposes, we have reduced the dimensionality of the SFM parameters ρ to the parameters{a, b} , as depicted in Fig. 4.9. A PCA analysis reveals that the two principal eigenvectors, were almost a linear combination of{a, b} exclusively and their respective eigenvalues concentrated more than 99% of the “energy”.

The results in Fig.4.9clearly show three basic behaviors. The Aware behavior in blue{k = 2.3, a = 4.78, b = 6.22, λ = 0.56, d = 0.20}, which is high both in a and b and represents all those trajectories of people extremely cautious, that exceed in consideration towards the other target. This behavior was clearly visible when some volunteers seemed to be afraid of the robot.

4.6 Experiments 49 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 1 2 3 4 5 6 7 8 Clustering behaviors A [m/s2] B [m] Aware Behavior Balanced Behavior Unaware Behavior

Figure 4.9: Cluster of behaviors. A projection of the most representative parameters{a, b} in order to illustrate in a graphic the three basic behaviors detected.

ing to all those people that virtually ignored their obstacles and went to their destinations no matter what. This behavior is not atypical and it may happen often in daily life.

And finally in red we can observe the Balanced behavior {k = 2.3, a = 3.05, b = 2.91, λ = 0.56, d = 0.20}. This cluster describes all those behaviors that are not Aware or Unaware behaviors, and hence, it is a mixture of a great variety of behaviors.

The separability of clusters is not really significant, but this classification answers most of the questions arisen regarding the interaction of moving targets in a scene. It is not important the nature of the target, but the consideration of the person towards the target. An implication of this paradigm of interaction modeling is that it is no longer reciprocal, that is, an Unaware pedestrian may inflict great social-force stress to other pedestrians, but in response he or she gets almost no social-force feedback since the force exerted by other people to the Unaware pedestrian is much more smaller. On the contrary, an Aware pedestrian may suffer more social stress on a typically social environment. All those considerations greatly affect the deployment of social robots, being the first, the Unaware target a threaten to the integrity of the robot, and the Aware pedestrian would suffer a high social stress in the presence of a robot which should act accordingly to reduce that impact. For these reasons it is of vital importance to detect those behaviors if we want to deploy social robots on urban or social environments and being accepted by humans and facilitate their daily life and not in the contrary.

In Fig.4.10is depicted a function of the social-force module| ˆfint_obs| for each set of parameters with respect to the distance to target. Additionally, we can observe the obtained social-force parameters for each ρk that resulted in the minimization of (4.13). We can appreciate that the

1 2 3 4 5 6 7 8 9 0 0.5 1 1.5 2 2.5 3 3.5

Social−force modules as a function of distance

distance to target [m] force module [m/s 2 ] Aware Balanced Unaware

Figure 4.10: Social-force modules clustered by behaviors. The expected force of interaction | ˆfint_obs| is plotted with respect to distance from interacting target and clustered into the three behaviors detected.

separation of the clusters is not so significant, despite the noisy conditions and the variability of humans.