## 2 Materials and Methods
### Data Collection and Preprocessing  
Table 3 contains the collected mean and standard deviation (column 2) of time delays of onsets on Gaze Yaw (GY), Head Yaw (HY), Trunk Roll (TR) and Medio-Lateral COM (MLC) displacement from a reference event in a preparatory step. Different reference events were used in the analyzed  
\begin{table}
\begin{tabular}{c c c} \hline
**Ref.** & **Trials \(\times\) People/Age (mean \(\pm\) std)/Speed (m/s)** & **Turning Angle (\({}^{\circ}\)) or Turn Type** \\ \hline
[12] & \(6\times 5/28\pm 2.5/(0.69\pm 0.03;1.01\pm 0.03)\) & \\
[21] & \(2\times 6\)/-/- & 90 \\
[22] & \(3\times 6/33\pm 4/1.15\pm 0.15\) & 90 \\
[23] & \(5\times 6/22.5\pm 2.1/\)- & \(20,40,60\) \\
[24] & \(20\times 5/24.8\pm 4/\)- & \(-60,-30,30,60\) \\
[25] & \(20\times 5/19.7\pm 1.2/1.3\pm 0.2\) & \(30,60\) \\
[26] & \(10\times 7/24.8\pm 4/\)- & \(-60,-30,30,60\) \\
[16] & \(10\times 6/26.3\pm 2.9/1.3\pm 0.2\) & Obstacle \\
[27] & \(1\times 12/33\pm 3/(0.8\pm 0.07;1.2\pm 0.05,1.6\pm 0.06)\) & 90 \\
[28] & \(30\times 3/20.7\pm 2.9/1.30\pm 0.1\) & \(-40,40\) \\
[29] & \(27\times 10/29.9\pm\) -/- & Limacon, eight (normal and extended), \\  & & cloverleaf, free-left and right \\
[19] & \(13\times 6/22\) to \(33.5/1.08\) to \(1.29\) & \(-90,90\) \\
[20] & \(8\times 10/30\pm 5.2/\) & Eight, limacon \\
[30] & \(24\times 10/32.1\pm 11.9/\)- & \\
[31] & \(8\times 24/24\pm 2.5/(1.4\cdot 2)\) & 45, 180 \\
[17] & \(2\times 8/26.9\pm\) 6.4/1.4 & 90 \\ \hline \end{tabular}
\end{table}
Table 2: Experimental conditions used in the studies based on optical motion capture systems.  
studies. In [26], the contralateral toe-off of the step that preceded the turn was used for that purpose. Other studies were based on the right foot contact [23; 24; 25] or the heel contact that corresponded to the initiating turning step [28].  
References [12; 16; 21; 22; 30] did not provide precise quantitative results. Relevant findings from these works will be qualitatively considered in the discussion when appropriate.  
Other authors reported anticipation times directly between variables and the trajectory heading. In [29], authors reported an anticipation of 202 \(\pm\) 83 ms from Gaze Yaw to Head Yaw, 444 \(\pm\) 202 ms from Gaze Yaw to Trunk Yaw and 212 \(\pm\) 162 ms from Head Yaw to Trunk Yaw. In [19], Head Yaw was found to anticipate Trajectory Heading by 207 \(\pm\) 165 ms. In [20], Gaze Yaw and Head Yaw were found to anticipate Trajectory Heading by 557 \(\pm\) 160 ms and 264 \(\pm\) 134 ms respectively.  
Regarding the IMU-based studies, an anticipation of head, upper back and lower back orientation onsets to the actual turning time of 204 ms, \(-\)69 ms and 5 ms were reported in [10]. Anticipation of head turning with respect to pelvis turning was found to be of 528 \(\pm\) 385 ms in [32].  
With respect to geographical anticipation, [17] reported a time anticipation of Gaze Yaw, Head Yaw and Trunk Yaw onsets to the corner pivot of 500 \(\pm\) 300 ms, 800 \(\pm\) 200 ms and 1500 \(\pm\) 200 ms, respectively. From them, we estimated the corresponding anticipation in distance at 0.35 \(\pm\) 0.21 m, 0.57 \(\pm\) 0.14 m and 1.07 \(\pm\) 0.14 m. [27] reported an anticipation distance of Head Yaw onset to the corner pivot of 0.3 \(\pm\) 0.3 m. Other values regarding the anticipation to the corner pivot have been reported in [30; 31], however, they lacked precision and will be qualitatively considered in the discussion section when appropriate.