Figures and data in How individual vigor shapes human–human physical interaction

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5 figures, 2 tables and 1 additional file

Figures

Figure 1

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Hypothetical strategies to combine motor plans and experiment.

(A) Different hypotheses for coordination between a fast (F) and a slow (S) partner. The arrows represent the haptic communication flow triggering motor adaptations in the respective hypotheses. The *co-activity* strategy corresponding to independent motor plans, *leader–follower* here based on the faster partner’s individual motor plan, *weighted adaptation* generalizing the leader-follower hypothesis based on a weighting of their initial strategies in the task, and *interactive adaptation* where both partners dynamically adapt their original motor plan, possibly differently as illustrated by the solid and dashed arrows, due to the interaction with an uncertain partner. (B) Experiment to investigate vigor in individuals and in mechanically connected dyads. The two partners have to reach one of the targets ${A_{1}, . . ., A_{5}}$ on their individual monitor using wrist flexion/extension of the right arm. Their real-time wrist angles $q_{i}$ and $q_{j}$ are mapped to individual red cursors $c_{i}$ and $c_{j}$ . In the dyadic session, their hands are coupled through a virtual elastic band of either low (KL) or high (KH) stiffness. (C) Experimental protocol. The initial solo session consists of four blocks: one null-field block (NF) with exoskeletons’ motor off to estimate the individual vigor, two blocks with low (VL) or high (VH) resistive viscous load to vary the cost of movement (i.e. effort), and a null-field washout block (W). The subsequent dyadic session involves six blocks in coupled mode and a final block in null-field mode to analyze after-effects of the practice with mechanical connection. The KL and KH blocks, performed in random order, first allow participants to familiarize themselves with the interaction, and the KxVx blocks are to investigate all combinations of the connection stiffness and viscous load.

Figure 2 with 2 supplements

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Kinematics and vigor in the solo conditions.

(A) Trajectories of reaching movements of different amplitude averaged across the population in the first null-field block (NF1) of Figure 1C (shaded areas represent the standard deviations). (B) Resulting individual and averaged amplitude–duration relationships. (C) The vigor scores in the three solo conditions {NF1, VL, VH} are all correlated, indicating that vigor can be defined robustly across varied effort conditions.

Figure 2—figure supplement 1

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Effect of the viscous resistance on movement time and vigor.

(A) Movement time increases with VL and VH compared to NF1 and with VH compared to VL. Error bars represent standard errors. (B) The vigor scores of individuals in NF1 are spread as in previous studies. VL induces a global decrease in vigor scores compared to NF1, and VH induces a second reduction compared to VL.

Figure 2—figure supplement 2

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Minimum time–effort compromise in the VL and VH conditions.

We simulated the behavior of the average participant in the solo session using a minimum time–effort compromise (see Equation 6 in the main text). This compromise was derived by identifying the average participant’s cost of time through an inverse optimal control method applied to data from NF1 (see main text). For both conditions, the behavior of the average participants is compared to an optimal time–effort compromise strategy (dashed line with markers). (A) Predicted movement duration in the VL and VH conditions. (B) Average absolute error (AAE) in terms of movement duration, with error bars representing standard errors. (C) Predicted absolute work of the robot torque in the VL and VH conditions. (D) AAE in terms of absolute work, with error bars representing standard errors.

Figure 3 with 15 supplements

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Dyads’ kinematics, interaction torque, and dyadic vigor.

(A) Predicted trajectories and interaction torque of a dyad with independent motor plans for the faster and slower partners for $A_{5}$ in the KL condition. (B) Participant trajectories averaged across the population for KL and for the five targets (shaded areas represent the standard deviations). (C) Average absolute interaction torque with low (KL) and high (KH) connection stiffness. Error bars represent standard errors. (D) The average interaction efforts in KL and KH are independent of the difference in individual vigor between the partners of a dyad (here during the first null-field block). (E) Amplitude–duration relationships of each participant’s movements and average relationship across the population during the KL condition. (F) Effect of the two different viscous loads on movement duration, for the KL connection, averaged across all participants with error bars representing standard error. (G) Movement durations are not different between the fast and slow groups in the connected conditions (here KL). (H) Percentage of time saved by the fast and slow groups between NF1 and KL, and between VL and KLVL, where positive values indicate faster movements. (I) Correlations between the vigor scores obtained during the three KL connected conditions. Vigor scores were computed using the average movement duration between members of the dyad.

Figure 3—figure supplement 1

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Adaptation of interaction torque through trials in the connected session.

The trends are computed using the first connected block performed by the dyads. (A) First 10 trials of the largest amplitude in KL condition. The dashed line corresponds to the average behavior for the remaining trials toward this target. (B) First 10 trials KH condition, as allowed by the absence of differences between targets for this block. The dashed line corresponds to the average behavior during the rest of the KH block.

Figure 3—figure supplement 2

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Limited adaptation of movement duration through trials in the connected session.

The trends are computed using the first connected block performed by the dyads. Columns correspond to the five targets. (A) KL condition. (B) KH condition.

Figure 3—figure supplement 3

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Movement performance of the dyads.

Metrics include the time saved when compared to the solo session, the SPARC smoothness of velocity profiles, the dimensionless jerk, and the standard deviation of position during stabilization (after the movement). All performance metrics are computed separately for the low (KL) and high (KH) connection stiffness. The time saved when compared to the solo session is split between the faster and slower participant. (A) Passive conditions. (B) Low viscosity (VL) conditions. (C) High viscosity (VH) conditions.

Figure 3—figure supplement 4

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Complementary behavioral data of the dyadic session.

(A) Trajectories and velocity profiles averaged across the population for KH and for the five targets. (B) Individual and averaged amplitude–duration relationships during KH. (C) Absolute average interaction efforts in the presence of a viscous load, with error bars representing standard errors. (D) Correlation of the difference in solo vigor between partners and interaction efforts with a viscous load. (E) Effects of the viscous load movement duration with KH. Error bars represent standard errors. (F) Percentage of time saved by the fast and slow groups between NF1 and KH, positive values indicate faster movements during KH. (G) Percentage of time saved by the fast and slow groups between VH and KLVH. (H) Percentage of time saved by the fast and slow groups between VL and KHVL. (I) Percentage of time saved by the fast and slow groups between VH and KHVH. (J) Significant correlations of vigor scores between the three KH conditions. (K) Examples of correlations between the vigor scores obtained by the fast and slow group during NF1 and those obtained during KL and KH. Dyadic vigor is predicted by the vigor of the slow group (linear mixed model [LMM], see main text).

Figure 3—figure supplement 5

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Average interaction efforts throughout conditions and targets for dyad D1.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) Low stiffness and passive robot (KL). (B) Low stiffness and low viscous torque applied by the robot (KLVL). (C) Low stiffness and high viscous torque applied by the robot (KLVH). (D) High stiffness and passive robot (KH). (E) High stiffness and low viscous torque applied by the robot (KHVL). (F) High stiffness and high viscous torque applied by the robot (KHVH).

Figure 3—figure supplement 6

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Average interaction efforts throughout conditions and targets for dyad D2.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 7

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Average interaction efforts throughout conditions and targets for dyad D3.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 8

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Average interaction efforts throughout conditions and targets for dyad D4.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 9

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Average interaction efforts throughout conditions and targets for dyad D5.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 10

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Average interaction efforts throughout conditions and targets for dyad D6.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 11

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Average interaction efforts throughout conditions and targets for dyad D7.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 12

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Average interaction efforts throughout conditions and targets for dyad D8.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 13

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Average interaction efforts throughout conditions and targets for dyad D9.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 14

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Average interaction efforts throughout conditions and targets for dyad D10.

Efforts received by the more vigorous participant are represented with solid lines and those received by the less vigorous participant are represented with dashed-dotted lines. (A) KL. (B) KLVL. (C) KLVH. (D) KH. (E) KHVL. (F) KHVH.

Figure 3—figure supplement 15

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The fast and slow participants have similar movement durations when connected.

Figure 4 with 3 supplements

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Predictions of dyad movement duration obtained with the model arising from the *interactive adaptation* hypothesis.

(A) Illustration of predicted velocity profiles and measured averaged durations for movements toward $A_{5}$ in the KL condition. The solid and dashed-dotted blue lines represent, respectively, the average and samples of the distribution of the slow partner, with the average movement duration of the slow partners as a dashed-dotted blue vertical line. The solid green line illustrates the average velocity profile of the fast partners moving alone, with the green dashed-dotted vertical line the corresponding duration in the experiment. Finally, the solid black represents the velocity profile predicted by an *interactive adaptation* (IA), and the black dashed-dotted vertical line the average experimental duration of dyadic movements. (B) Comparison between predicted movement time and data for all the connected conditions.

Figure 4—figure supplement 1

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Evolution of optimal time predictions for the KL conditions.

The three treated conditions are KL, KLVL, and KLVH. The discretizations of variables spaces were $0.02 s$ for μ, $0.02 s$ for σ, and 2 for. $Q_{τ}$ . (A) Predicted optimal movement duration for two values of $σ \in {0.1, 0.3} s$ , and for ranges of average partner movement duration adapted to the condition. (B) Predicted optimal movement duration for two values of μ depending on the condition, and for $σ \in [0, 0.3] s$ .

Figure 4—figure supplement 2

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Evolution of optimal time predictions for the KH conditions.

The three treated conditions are KH, KHVL, and KHVH. The discretizations of variables spaces were $0.02 s$ for μ, $0.02 s$ for σ, and 2 for $Q_{τ}$ . (A) Predicted optimal movement duration for two values of $σ \in {0.1, 0.2} s$ , and for ranges of average partner movement duration adapted to the condition. (B) Predicted optimal movement duration for two values of μ depending on the condition, and for $σ \in [0, 0.3] s$ .

Figure 4—figure supplement 3

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Effect of varying the cost of time of the fast partner on predicted movement time.

Solid lines represent predicted times and dashed-dotted lines the absolute change of predicted time when varying $G (T_{k})$ with a change in [−30%, +30%], These results were obtained for $κ = 0.5 N m s / r a d$ and the same weighting and uncertainty as in the main paper.

Figure 5 with 1 supplement

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Kinematics and vigor before and after human–human interaction.

Data before (NF1) and after (NF2) the dyadic session are represented using dashed-dotted and solid lines, respectively. (A) Population average of the position and velocity for each target. (B) Averaged amplitude–duration relationships for the fast and slow partners in NF1 and NF2. (C) Time saved between NF1 and NF2 for the fast and slow partners and for each target. (D) Difference in vigor scores between NF1 and NF2, for the fast and slow partners. (E) Illustration of the fast and slow partners’ adaptations. When connected, the average vigor of the slow partners increases to match the one of the fast partners, while the fast partners’ group changes its internal ranking in vigor to match the ranking of the slow partners. These adaptations are retained for both groups in after-effects (AE).

Figure 5—figure supplement 1

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Effect of the connection on vigor and the affine amplitude–duration relationship.

(A) Distribution of vigor scores in NF1 and NF2. (B) Affine coefficient. Main effect of the condition ( $W = 0.34$ , $p < 10^{- 3}$ ), further confirmed by pairwise comparisons showing that coefficients in NF1 are significantly higher than in the other conditions (in the three cases: $p < 2 \cdot 10^{- 3}$ , Cohen’s $D > 1.09$ ). (C) Offset. Main effect of the condition ( $W = 0.15$ , $p = 0.03$ ), pairwise comparisons showed that offsets were lower in KH than in KL and NF2 (in both cases: $p < 0.03$ , Cohen’s $D > 0.55$ ).

Tables

Table 1

Ability of the different models to reproduce the main qualitative (top) and quantitative (bottom) experimental findings.

The interactive adaptation hypothesis is the only one among those tested that can reproduce all the main qualitative experimental findings. It also results in the lower median prediction errors for the low stiffness conditions and in the second lower median errors for the high stiffness movements, with a negligible $12 m s$ difference compared to the best predictions.

Characteristic	Co-activity	Leader–follower	Leader–follower	Weightedaverage	Interactiveadaptation
Characteristic	Co-activity	Fast lead	Slow lead	Weightedaverage	Interactiveadaptation
Bell-shaped and smooth velocity profile	No	Yes	Yes	Yes	Yes
Low h–h interaction force	No	Yes	Yes	Yes	Yes
Dyad faster than fast partner	No	No	No	No	Yes
Only slow partner impacts h–h vigor	Yes	No	Yes	No	Yes
Median error low stiffness ( $m s$ )	138.2	35	138.2	(35, 138.2)	28.7
Median error high stiffness ( $m s$ )	130.5	38	130.5	(38, 130.5)	50.8

Appendix 2—table 1

Summary of the vigor scores of participants through the experiment.

The vigor scores in the VH and VL conditions (with and without connection) were computed using the average movement durations collected in the corresponding condition without viscous resistance to better show the effects of changes in the dynamics. Vigor scores in the NF2 condition were computed using average durations from the NF1 conditions to highlight changes after exposure to the human–human connection.

		Solo			Dyads						AE
Dyad Id.	Subject Id.	NF1	VL	VH	High stiffness			Low stiffness			NF2
Dyad Id.	Subject Id.	NF1	VL	VH	KH	VL	VH	KL	VL	VH	NF2
D1	S1	1.4	1.34	1.19	1.44	0.86	0.68	1.32	0.93	0.72	1.42
D1	S2	1.47	1.12	1.04	1.44	0.86	0.68	1.32	0.93	0.72	1.6
D2	S3	1.37	1.15	1.17	1.21	0.82	0.64	1.17	0.79	0.64	1.11
D2	S4	1	0.78	0.64	1.21	0.82	0.64	1.17	0.79	0.64	1
D3	S5	0.75	0.66	0.42	0.84	0.69	0.59	0.97	0.75	0.54	1.18
D3	S6	1.58	1.19	0.94	0.84	0.69	0.59	0.97	0.75	0.54	1.05
D4	S7	0.8	0.67	0.61	0.94	0.64	0.56	0.87	0.64	0.57	0.99
D4	S8	0.91	0.84	0.8	0.94	0.64	0.56	0.87	0.64	0.57	1.29
D5	S9	0.91	0.82	0.81	1.1	0.7	0.55	1.06	0.75	0.61	1.17
D5	S10	1.05	1.16	0.54	1.1	0.7	0.55	1.06	0.75	0.61	1.6
D6	S11	1.74	1.28	1.02	1.32	0.85	0.72	1.38	0.92	0.76	1.87
D6	S12	1.41	1.11	0.92	1.32	0.85	0.72	1.38	0.92	0.76	1.75
D7	S13	1.02	0.7	0.56	0.94	0.59	0.43	1.06	0.64	0.47	1.18
D7	S14	0.89	0.64	0.52	0.94	0.59	0.43	1.06	0.64	0.47	1.06
D8	S15	1.11	1.01	0.82	1.03	0.61	0.57	1.1	0.7	0.57	1.21
D8	S16	0.95	0.98	0.75	1.03	0.61	0.57	1.1	0.7	0.57	1.35
D9	S17	0.86	0.83	0.79	0.79	0.66	0.61	0.83	0.67	0.6	0.83
D9	S18	0.74	0.8	0.93	0.79	0.66	0.61	0.83	0.67	0.6	1.05
D10	S19	1.01	0.73	0.65	0.8	0.56	0.49	0.68	0.53	0.59	1.01
D10	S20	0.61	0.71	0.56	0.8	0.56	0.49	0.68	0.53	0.59	1.1