Team lifting is a complex and collective motor task that possesses both motor and cognitive components. We study the collective load carriage adaptation due to an additional accuracy constraint. Ten dyads performed a first condition in which they collectively transported a load (CC), and a second one in which they transported the same load while maintaining a ball in a target position on its top (PC). The recovery-rate, amplitude, and period of the center-of-mass of the whole system (dyad + table, CoMPACS) were computed. We analyzed the forces and moments exerted at each joint of the upper limbs of the subjects. We observed a decrease in the overall performance of the dyads when the Precision task was added, i.e., i) the velocity and amplitude of CoMPACS decreased by 1,7% and 5,8%, respectively, ii) inter-subject variability of the Moment-Cost-Function decreased by 95% and recovery rate decreased by 19,2% during PC. A kinetic synergy analysis showed that the subjects reorganized their coordinations in the PC. Our results demonstrate that adding a precision task affects the economy of collective load carriage. Notwithstanding, the joint moments at the upper-limbs are better balanced and co-vary more across the paired subjects during the precision task.

We recorded two conditions the first one were the subjects walked side by side at spontaneous speed while carrying a box (CC: Control Condition) and a second one were the individuals were instructed to transport the box, while performing an accuracy task consisting in keeping a ball in the center (PC:Pecision Condition).

Motion capture data were collected using thirteen infrareds (11 MX3 and 2 TS40) transmitter-receiver video cameras (Vicon©, Oxford metric’s, Oxford, United Kingdom) sampled at 200 Hz. Forty-two retro-reflective markers were placed on bony landmarks and on the navel of each subject ( according to Wu et al., 2002, 2005) R. Soc. open sci. and fourteen on the box. The ball used during the PC tests was reflective as well and was tracked by the Vicon© system. In order to record the gait pattern at constant speed (i.e. to exclude the acceleration and deceleration phases at the beginning and end of each trial) the volume calibrated by the Vicon© system (30 m3) was located in the middle of the 20m-long walkway crossed by the subjects. The reflective marks were tracked to define the kinematics of the Poly-Articulated Collective System (PACS) formed by the two individuals and the load they carry (22,23). The data were recorded on one gait cycle defined by the first heel strike of the first subject and the third heel strike of the second subject of the PACS to ensure a cycle of each subject. The 3D reconstruction was performed using Vicon Nexus 1.8.5© software. The two lateral handles used to transport the box were equipped with Sensix® force sensors sampled at 2000 Hz. A 4th order Butterworth filter and a 5 Hz and 10 Hz cut frequency have been applied to analyze the positions of the markers and the forces exerted on the box handles, respectively

The De Leva Anthropometric tables (24) was used to estimate the mass mi and the CoM of each segment i (CoMi) of the PACS and to compute its global CoM (CoMPACS) as follow: 𝑮𝑷𝑨𝑪𝑺 = 1 𝑚_{𝑃𝐴𝐶𝑆} ∑ 𝑚𝑖𝑮𝑖 𝑛=33 𝑖=1  with GPACS the 3D position of the CoMPACS in the frame R (the global coordinate system), m_PACS the mass of the PACS, n the number of PACS segments (i.e. 16 segments per volunteer plus one segment for the box) and Gi the 3D position of the CoMi in the frame R. The CoM of the box was determined at the intersection point of the vertical lines obtained by hanging it with a thread fixed at different positions. The material used for the box construction, i.e. wood and aluminium, was considered as not deformable. According to Holt et al., (2003), the amplitude (A = Zmax – Zmin, with Z the height of the CoMPACS, in meters,) and the period (peak to peak, in percent of the gait cycle) of the CoMPACS were also assessed. The forward kinetic (Wkf), as well as the vertical (Wv) and external work (Wext) of the CoMPACS were computed according to the method of Bastien et al. (2016). Then based on the external work, the percentage of energy recovered of the CoMPACS in the sagittal plane was computed (called recovery rate RR in Fumery et al., 2018a, 2018b). This parameter assess the amount of energy transferred between the potential and the kinetic energy (Eqn 2). 𝑅𝑅 = 100 𝑊kf+𝑊v−𝑊ext 𝑊kf+𝑊v (2) The closer the value of RR to 100%, the more consistent the locomotor pattern is with the inverted pendulum system (IPS) model of locomotion (26–28,13). In this study, the trajectory of CoMPACS and CoM of an inverted pendulum have been investigated.

Sensix force sensors recorded the forces and moments applied by each individual on the two box handles. Before the computation, the data of the sensors located by specific markers were transfer to the Galilean frame of the laboratory using rotation matrix. A cross correlation method has been applied in order to analyze the coordination between the forces produced by both subjects. To investigate whether the movement of the box results from an action-reaction strategy, we computed the time lag required for the position of the left side and right side of the box to be the same on the medio-lateral, antero-posterior and vertical axis in CC and PC. The coordination was assessed through the forces exerted on three directions (medio-lateral, antero-posterior and vertical axis). This results will reflect the level of coordination of two subjects during a collective transport In order to quantify muscular constraints produced at the upper limb, the Inverse Dynamic Method was used to estimate forces and moments at each joint of the upper limb. The Moment Cost Function was then computed (kg.m2 .s-2 , Costes et al., 2018) as follow : MCF = √𝑀𝐿_𝑤𝑡 2 + √𝑀𝑅_𝑤𝑡 2 + √𝑀𝐿_𝑒𝑙 2 + √𝑀𝑅_𝑒𝑙 2 + √𝑀𝐿_𝑠ℎ 2 + √𝑀𝑅_𝑠ℎ 2 + √𝑀𝑏𝑎𝑐𝑘 2 + √𝑀𝑛𝑒𝑐𝑘  Where ML_wt, MR_wt, ML_el, MR_el, ML_sh, MR_sh, Mback and Mneck are the mean values over a PACS gait cycle of the three-dimensional left and right wrist, left and right elbow, left and right shoulder, top of the back and neck moments, respectively. √M2 represents the Euclidian norm of M (i.e. √M2 = √∑ (𝑀𝑖) 3 2 𝑖=1 , with Mi the i-th component of the vector M). Then, the MCF values of each individual was summed to obtain the total moment cost function (Total MCF). This Total MCF allows to quantify the global effort produced at the upper-limbs of the PACS during one gait cycle. Finally, the MCF difference (∆ MCF) was computed as the difference between the two individuals to investigate whether the subjects produced the same effort in the upper limbs during the load transport.

We extracted the synergies by using a principal component analysis (PCA) applied to the wrist, elbow, shoulder, back, and neck joint moment on the right and left sides of the body. The PCA was used to reduce data dimensionality. It consisted in the eigen-decomposition of the co-variance matrix of the joint moment data (Matlab eig function). The joint moments data from one trial per condition were arranged in time × joint moment matrices. In this analysis we only used the y-component which is very close to the norm of the 3D joint moments, except that the y-component (medio-lateral) could be positive and negative. The joint moments were normalized by their amplitude and centered (mean removed) before application of the PCA. We called the eigenvectors extracted from the PCA, dynamic synergy vectors. We computed the VAF (Variance Accounted For) which corresponded to the cumulative sum of the eigenvalues, ordered from the greatest to the lowest value, normalized by the total variance computed as the sum of all eigenvalues. The synergy vectors retained were then rotated using a Varimax rotation method to improve interpretability. We first extracted the synergy vectors for each experimental condition and each participant separately. In this analysis the initial data matrices were constituted of all available time frames in line, concatenated from one trial per condition, and of eight columns corresponding to each joint moment, namely the right wrist, left wrist, right elbow, left elbow, right shoulder, left shoulder, back, and neck. Based on a previous study we extracted 3 synergies in this analysis. We then performed a second analysis to identify possible co-variations between the joint moments of the two participants in each pair. The columns of the initial matrices were thus constituted of the joint moments of the two loaded arms, i.e., the right wrist, elbow, and shoulder joint moments of participant #1, plus the left wrist, elbow and shoulder joint moments of participant #2. Based on a previous study we extracted 2 synergies in this analysis. We used Pearson’s r to order the different synergies similarly between the different subjects and conditions.

A performance score (Scorep) was assigned to each image of the videos captured by the Vicon© system (200 images/s). The score depended on the location of the ball in the target: 1 when the ball was inside the small circle, 0.5 when it was in-between the small and large circle and 0 when it was outside the large circle. The accuracy over the whole gait cycle was measured by an overall score (Scoreaccuracy), expressed in percentage, and calculated as follows: 𝐒𝐜𝐨𝐫𝐞𝐚𝐜𝐜𝐮𝐫𝐚𝐜𝐲 = ∑ 𝐒𝐜𝐨𝐫𝐞𝐩 ×𝟏𝟎𝟎 𝐭𝐠𝐚𝐢𝐭 𝐜𝐲𝐜𝐥𝐞 where tgait cycle represents the number of Vicon© images recorded along one gait cycle.

The head, shoulders and pelvis rotation angles were computed around the vertical axis of each individual in the two conditions. The angle was positive when the subjects turned towards the box they carried, otherwise it was negative. The distance between the forehead and the sternum (distance FOR-STE) was also computed in order to investigate the flexion of the cervical spine.

The data were analyzed with Matlab R2016b© and StatView 5.0© software. A paired t-test was used to compare the RRs, the amplitudes, the periods, the velocities of the vertical displacement of the CoMPACS, the head, shoulders and pelvis rotation angle and the length FOR-STE between the CC and PC condition. The significance threshold was set to 0.05. We computed with a cross-correlation method the time lag required for the position of the left side and right side of the box to be the same on the medio-lateral, antero-posterior and vertical axis in CC and PC. We used the average subspace angles to compare the subspaces spanned by the synergy vectors (Knyazev and Argentati, 2002). In order to decide whether the subspaces were more similar than expected by chance, the confidence interval (CI) of random comparisons was computed. For this analysis, we generated pairs of random subspaces constituted each of either 3 unit vectors of dimension 8 (individual PCA analysis) or 2 unit vectors of dimension 6 (conjoint PCA analysis) and computed the mean subspace angle between them. The unit vectors were built using normally distributed pseudo-random numbers (Matlab randn function). We performed 10000 simulations in order to determine the 95%-CI of the mean subspace angle between the pairs of random subspaces. The confidence interval was 39.5°–70.0° (55.0±7.6°) for the individual PCA analysis and 36.3°–79.1° (57.7±10.7°) for the conjoint analysis. We used Student tests for single mean to compare the subspaces angles to the lower bound CI with the assumption that similarity was higher than expected by chance when the angles were lower than the lower bound CI. VAFs were compared with an ANOVA with one repeated measure (control vs. precision conditions) and one factor (participant #1 vs. participant #2) when synergies were extracted separately for each subject. For the conjoint analysis, a paired Student t-test was used. Subspace angles were compared with t-tests for dependent samples (paired t-test) when comparing the control and precision conditions and t-test for independent samples when comparing the two participants. Adjustments for multiple comparisons were performed by Bonferroni’s method. Initial level of significance was set to p<0.05.