## 4 Discussion
### Head Yaw Predicts the Geographical Turning Point at a Constant but Unknown Distance  
The paper [38] can be considered a pioneering study about geographical anticipation. In this case, anticipation was measured against the point defined by the intersection of the rectilinear part of the actual path that the subject described before and after the turn. Results show that Head Yaw started later and later as speed increased, from 3.8 s at 1.4 m/s to 0.44 s at 9.7 m/s. However, when it was plotted versus the distance from the corner, the waveforms aligned almost perfectly; thus, being the first work to support that the anticipation of Head Yaw to the turning point is constant in distance, not in time. Numerical results showed an anticipation of between 2 m and 9 m depending on the individual subject. However, these experiments were designed using a virtual reality environment that sometimes supposed very high velocities and were thus not representative of normal walking conditions. Later studies supported what has been called the \"spatial invariance\" hypothesis, which means that Head Yaw starts to vary at a constant distance to the turning point. However, reported anticipation distances did not allow to quantify it with precision. Head Yaw anticipation to the corner pivot was quantified in 0.3 m [27] and 1.1 m [31]. This anticipation was found to be invariant to the walking velocity [27] and to the turning angle (from 22\({}^{\circ}\) to 135\({}^{\circ}\)) [31]. Interestingly, this did not depend on the turn strategy, as there were no significant differences in results from experiments where users were told to walk along a trajectory painted on the floor from results from other experiments where users could freely negotiate the turn [31]. The work [17] reported a larger anticipation distance of 2.1 m. Similarly, in [30], authors reported anticipation to the turning point in the range of 2-4 m. These results,consistent for each work but greatly diverging between different references, might advance that the actual anticipation distance may depend on the type of turn and its environmental constraints. 5 Considerations about Turn Prediction Systems from Upper Body Kinematics in Human-Robot Interaction  
The previous analysis finds a direct application in human-robot interaction. It revealed that Head Yaw is the earliest variable affected by the turning maneuver with an adequate degree of reliability. As Head Yaw predicts anticipated trajectory heading, based in the correlation-based studies in Table 1, it can be used to elaborate advanced predictive models of the spatial occupancy of the subject for the \"goal-free motion prediction\" problem [3]. At the moment, quite simplistic models have been used for this purpose, mainly based on the projection of the current position of the subject using the current velocity and trajectory heading direction [1; 3]. Head Yaw/Trunk Roll can also be used to predict in time an upcoming turning maneuver (onset-based studies, Table 1), and therefore, can be used to predict the specific destination or walking direction when a finite number of possibilities are available (\"goal-based motion prediction\" problem [3]). From a safety point of view, robot motion planning in human robot collaboration that considers turn prediction from Head Yaw or Trunk Roll has to be used with caution. Head Yaw is the preferred behavior during turning [19]. However, head rotations are neither a necessary nor a sufficient component of steering control [39]. With regard to Trunk Roll, the reliability of the anticipation is lower, even though the anticipated detection of walking turns can be useful to increase comfort or perceived safety. An appropriate sensor-based dynamic robot motion planning [40] with improved proxemic behavior can be achieved by controlling the movement synchronization or the separation distance with the human. For a walking velocity of 1.6 m/s, an anticipation to the trajectory change around 200 ms may permit to forecast the position of the subject about 0.32 m ahead.