Participants.

Twenty-one right-handed participants (8 women, 24 ± 6 yr of age) took part in the experiment. Five participants participated in the two-digit condition, five participated in the three-digit condition, five participated in the four-digit condition, and six participated in the five-digit condition. All participants had no history of neurological or motor deficits. The testing procedures were approved by the ethics committee of Bielefeld University, in accordance with the guidelines of the Declaration of Helsinki for research involving human participants. Informed written consent was obtained from all participants involved in the study.

Experimental setup.

The experimental device, referred to as the tactile object (TACO), records the position and the normal force exerted by each finger on its sensorized surface and facilitates participants freely choosing digit positions on the object for unconstrained grasping. The TACO has a cuboid shape (length, l = 170 mm; height, h = 85 mm; width, w = 55 mm). Four high-speed tactile sensor modules (Schurmann et al. 2011), subsequently named “Myrmex,” are mounted on two opposing faces of the cuboid. Each Myrmex module provides a 16 × 16 tactile array on an area of 80 × 80 mm² and has a sampling rate of up to 1.9 kHz and spatial resolution of 5 mm (one sensor element). The TACO consists of four Myrmex (1,024 tactels) modules mounted on both the front and back surface plane, two on the front and the other two on the back (Schurmann et al. 2012). The TACO allows us to simultaneously record the center of pressure and the normal force exerted by each digit. The device is calibrated using a force gauge with a force ranging from 0 to 25 N. During the calibration, we varied the cross-sectional area of the gauge tip from 10 to 50 mm² with a step of 20 mm² to account for differences in fingertip size between participants.

A mirrored screen occluded the participants’ hands and the TACO from sight, removing any visual feedback of their hand location and grasp. The mirror faced a computer monitor (21-in. CRT, SONY CPDG520, with a resolution of 1,280 × 1,024 pixels and refresh rate of 100 Hz) that we used to display the visual stimulus. The visual stimulus consisted of a rectangular cuboid, with the same dimensions of the TACO. Participants wore liquid-crystal shutter glasses (CrystalEyes) providing binocular disparity (Fig. 1A).

The TACO was attached to two PHANToM (SensAble Technologies) force-feedback devices to track its position and allow force/torque perturbations to be applied during the holding phase of the trial (Fig. 1B). The sampling rate of the PHANToM is 1 kHz, allowing a precise position match between the simulation and the TACO. The total mass of TACO is 0.470 kg. Because of the constraints of the two PHANToM devices, the TACO has five degrees of freedom: translation along the x, y, and z directions, and rotation along the yaw (α) and roll (β) axes (Fig. 2A).

In the control experiment, we replicated the task using the Shadow Dexterous Hand (Shadow Robot Company, London, UK), which is a humanoid robotic hand endowed with approximately the same kinematics and number of degrees of freedom as the human hand (Fig. 3A). The hand has 18 actively controlled degrees of freedom (DoF) plus 2 DoF for the wrist (abduction/adduction and flexion/extension). Movements of the Shadow Dexterous Hand closely resemble those of a regular human participant (Rothling et al. 2007). An antagonistic pair of McKibben-style pneumatic muscles actuates each joint in an inherently compliant fashion, thus mimicking human muscle properties. We employed a stiffness control of the artificial muscles. The stiffness was fixed during each grasping trial. The maximum normal force produced by each finger opposing the thumb during object perturbation was ~8 N. The Shadow Dexterous Hand was attached to a KUKA lightweight robot4+ “KUKA-LWR4+” as the end effector (Fig. 3B) to mimic the lifting movements of the TACO performed by human participants.

Procedures.

Participants sat on a chair with an adjustable height. Before the start of the grasping movement, participants’ forearms rested on a plank with the palm of the hand facing downward. Participants received an auditory “GO” signal, instructing them to grasp the TACO and to lift it to a target height of 100–150 mm. A simulated rectangular cuboid was displayed on the CRT via the mirror with the appropriate size and in the same location as the TACO. Upon lifting, the virtual representation of the TACO changed color to inform participants that the TACO had reached the desired target height. At that height, participants were asked to hold the TACO as still as possible, irrespective of any disturbance forces acting on the object. After having stabilized the TACO for ~20 s, participants received another auditory signal cueing them to place the TACO back on the table. In different experiments participants were instructed to grasp the TACO with two, three, four, or five fingers (thumb-index finger, thumb-index-middle fingers, thumb-index-middle-ring fingers, or all fingers of one hand). Fingers not involved in the task were extended and taped to a splint made of cardboard to prevent them from contacting the TACO. The finger placements on the TACO were self-chosen (grasping without constraints).

During the object holding phase, perturbation forces and torques were applied using the PHANToM force-feedback devices. We evaluated five force/torque conditions (perturbation type) and two periodical/aperiodical perturbations (perturbation frequency). In the F_y condition, a force of 2.4 N was applied along the vertical direction (downward; Fig. 2B). In the T_y and T_z conditions, torques of 0.25 N·m were applied around the y- or z-axis (Fig. 2C), causing respectively yaw and roll rotations around the TACO’s center of mass. Perturbation torques, T_y and T_z, were applied in clockwise (CW) and counterclockwise (CCW) directions. In one instance the applied force and torques were turned “on” and “off” periodically (perturbation frequency) and were thus “predictable” in terms of frequency and timing (Fig. 2D). In the other instance, the applied perturbation forces and torques occurred aperiodically. That is, the onset times for the perturbations “on” ranged at random between 1 and 3.5 s after the last offset of the perturbation and had a random duration between 0.6 and 1 s. They were thus “unpredictable” (Fig. 2E). The rationale of this experimental design was to test whether the grasping forces of the fingers would depend on the predictability of the perturbations and therefore adapt differently to the two temporal patterns of the perturbations. Overall, there were 5 × 2 = 10 conditions: 5 force perturbations types, F_y, ${\text{T}}_y^{\text{CCW}}$, ${\text{T}}_y^{\text{CW}}$, ${\text{T}}_z^{\text{CCW}}$, and ${\text{T}}_z^{\text{CW}}$, applied either periodically or aperiodically (the two perturbation frequencies, P and Ap). The order of conditions was randomly presented to the participants. Participants performed 10 trials per condition. Each trial lasted ~25 s from grasp onset to release. Before starting the experiment, participants were informed that during the holding phase the two PHANToM devices would apply periodic or aperiodic perturbations to the TACO and that the perturbation type would remain the same within each trial. Before the experiment, participants performed four trials with F_y perturbation applied periodically to familiarize themselves with the task. The total duration of the experiment was ~2 h per participant with a few minutes’ break at the halfway point. Participants were also allowed to take a short break and rest at the end of each trial whenever they wanted.

In the control experiment, we replicated the same task performed by human participants (5-fingers condition) using a robotic hand (Shadow Dexterous Hand) in combination with the TACO. The hand controller developed by Rothling et al. (2007) is based on two control variables: joint position and joint stiffness. Each joint is controlled by a pair of air pressure-controlled artificial muscles. Whereas the difference in pressure correlates with the joint position, the pressure sum correlates to the joint’s stiffness. The passive compliance of the muscles physically realizes an impedance control whose stiffness is adjustable. In this experiment, we chose a fixed stiffness of the grasping posture that allowed successful grasping and lifting of the TACO. The successful grasping posture of the robot hand was saved (referred to as “grasp” later in the text) and used during the whole experiment (the same posture across trials). Thus the hand had two states: release state, in which the hand was fully opened and there was “no grasp,” and grasp state, in which the “grasp” posture was applied and the TACO was grasped. The positions of the robotic finger during the “grasp” posture would result in complete closure of the hand if applied in free space. The presence of the object, however, prevents the fingers from complete closure and ensures grasp forces are applied passively due to the inherent compliance of the hand when the TACO is present (Rothling et al. 2007). After the GO signal, the Shadow Dexterous Hand grasp state was changed from “no grasp” to “grasp.” Once the hand successfully grasped the TACO (Fig. 3B), the experimenter lifted the TACO using KUKA-LWR4+. When the arm reached the intended height, the KUKA-LWR4+ was grounded to avoid any oscillations due to active control that could have altered the grasp performance. During the object hold phase, the PHANToM applied either ${\text{T}}_y^{\text{CCW}}$ or ${\text{T}}_y^{\text{CW}}$ perturbation (Fig. 2C) in a periodic or aperiodic fashion. We used only these two perturbations because of the low friction forces between the Shadow Dexterous Hand and the TACO. At the end of each trial, the KUKA-LWR4+ placed the TACO back on the table and the hand grasp state was set to “no grasp,” releasing the TACO. Each perturbation was repeated 16 times, giving a total of 64 trials.

Crucially, the robot hand was not programmed to actively control grasping forces of individual digits to counteract the disturbances. Instead, the stiffness was fixed during each grasping trial, and the passive compliance of the artificial muscles resembles the mechanical properties of the muscles of the human hand and forearm. Hence, the robotic hand provides a plausible model for a grasping strategy based on the control of the global hand stiffness, as suggested (Winges et al. 2007).

Data processing.

The normal forces (F) of the fingers and their positions, derived as the digit horizontal and vertical center of pressures (CoP_x and CoP_y), respectively, were read from of the TACO. We set the center of the TACO as the origin of the coordinate system (0, 0, 0). CoP_x and CoP_y were defined as the location of the global maximum of the activated region of tactels for each finger’s region in the output matrix. The output matrix was converted to Newtons using the lookup table generated during calibration. The calibration table was obtained with a resolution of ±0.2 N. Digit locations, normal forces, and TACO position were recorded and processed with a second-order Butterworth low-pass filter with 10-Hz cutoff frequency (Fig. 4). The CoP_x and CoP_y values used for further analysis were extracted during the holding phase.

The three-dimensional (3-D) position and the rotations around the yaw and roll axes of the TACO were tracked using the PHANToM devices. They were further used to compute the net torques generated by the participant (HT_y, HT_z) using Newton’s second law for rotation:

To satisfy a stable grasp of the TACO, the force produced by the thumb must be equal to the sum of opposing digit normal forces:

Statistical analysis.

First, we evaluated whether digit positions on the TACO were idiosyncratic, that is, whether there was a consistent pattern within each participant. To this end, we computed for each participant and condition the mean CoP_x and CoP_y of the different digits, averaged across trials and perturbation type. The averaged data are plotted in Fig. 5. These data were used to conduct a cluster analysis on the CoP_x and CoP_y of the fingers opposing the thumb in the three-, four-, and five-finger conditions. We did not include the thumb in the analysis because it contacted the opposite face of the TACO; i.e., it was projected on a different plane in the CoP space. We used k-means clustering: in the different conditions, we set the number of clusters to k = 2, 3, or 4 corresponding to the 2, 3, or 4 fingers opposing the thumb. The analysis aimed at investigating whether the initial placement of the different fingers was preserved within each participant and across perturbation type, that is, whether the hand posture was “idiosyncratic.” Furthermore, we ran two-way ANOVA on the mean CoPs (factors: digit and participant) to test whether hand posture was significantly different between participants. We tested the cluster mean CoP_x and CoP_y separately.

In each perturbation number and for each digit we computed the time to reach the maximum grip force (time to peak). If the maximum force were to occur approximately at the same time between different digits, it would suggest a parallel control of digits to stabilize the object. To test this hypothesis, we used a multivariable linear mixed models (LMM) analysis evaluating whether the time to peak varied systematically across different digits. The time to peak (measurement variable denoted by “y” in Eq. 6) was modeled as a linear combination of the experimental variables (referred to as the fixed-effect linear predictors, Xβ), the random variability between participants (the random-effect predictors, Zb), and the residual random error, ε (Bates et al. 2015).

The LMM equation has the following general form:

Next, we studied the effect of learning and adaptation to the perturbations in each trial. To this end, we evaluated whether the value of peak force (in N) and the error in hand net torque changed with the number of perturbations within a trial. We fit a polynomial LMM including the following fixed effect predictors: perturbation number (P1, P2, P3, P4, P5), digit (T and, depending on the condition, I, M, R, L), perturbation type (F_y, ${\text{T}}_y^{\text{CCW}}$, ${\text{T}}_y^{\text{CW}}$, ${\text{T}}_z^{\text{CCW}}$, and ${\text{T}}_z^{\text{CW}}$), and frequency (P, Ap). To account for nonlinear effect, we used a second-order polynomial of the form β₁P + β₂P² for fitting, where P is the perturbation number and β_{1,2} are the fixed-effect parameters. We evaluated the significance of the effect using the LR test.

To evaluate the contribution of each finger to the task, we studied the variation of normal force between the different fingers. We averaged data from each participant across the five perturbation numbers and across the periodic and aperiodic conditions. Within each trial, we subtracted the mean value of normal force of the index finger from the normal force of each other finger [F(diff) = F(M or R or L finger) – F(I finger)]. This aimed to compare the force change between fingers across different experimental conditions (3-, 4- and 5-digit grasp) that were collected on different participants (i.e., see Fig. 10). Using LMM, in torque perturbations we evaluated the modulation of actual normal force for digit and torque direction. We ran the analysis separately for each torque direction; therefore, it was not necessary to subtract the force value of the index finger as we did for the plot of Fig. 10. We applied the LR test to evaluate whether the difference in normal force between digits and torque direction was statistically significant. We did not include the two-digit condition in the analysis or in Fig. 10 because the thumb and the index digits share equally the total grip force.

We replicated the experiment using the robotic Shadow Dexterous Hand to evaluate whether the passive stiffness control of the robot would reproduce a similar pattern of forces as did the human participants. For the comparison, we computed the same measurements for the robotic hand as we did for human participants: the digit normal forces, the time to peak force, and the error in hand net torques. We modeled the data with the robotic hand using a simple linear model. The data from the robotic hand were not clustered like the human data, which include multiple participants. Hence, it was not necessary to use mixed models for this analysis.

Control experiment: robot hand.

We considered two alternative motor strategies: either participants controlled the stiffness of all fingers jointly (grasping synergy), or they modulated the force of each finger independently in response to the given external perturbation. The former motor strategy is more parsimonious because it reduces the degrees of freedom of the system and is in accordance with the synchronous response of the different fingers. We evaluated whether the synergistic motor control was compatible with the asymmetry in normal force between outer and inner fingers observed in torque perturbation. To this end, we replicated the same experimental paradigm using the robotic hand (Shadow Dexterous Hand) programmed with a synergic control of fingers’ stiffness. We tested conditions ${\text{T}}_y^{\text{CCW}}$ and ${\text{T}}_y^{\text{CW}}$ (5 digits; Fig. 11).

Because of the different friction coefficients between human and robot fingers, a larger normal force was required to obtain a stable grasp with the robot hand, which accounts for the larger reaction torque (Fig. 10). Errors in net hand torque, computed as the difference between the perturbation and the reaction torque, were smaller compared with those of human participants (Fig. 9) and were not significantly affected by perturbation type [${\chi }_{(1)}^2$ = 2.21, P = 0.14], perturbation frequency [χ²₍₁₎ = 0.02, P = 0.88], and perturbations number [${\chi }_{(4)}^2$ = 9.16, P = 0.06]. Figure 10, B and C (dark rhombus with dotted line), shows mean normal force of each robot’s finger, averaged across trials and the frequency condition (periodic and aperiodic). Similarly to findings in humans (gray lines), the index finger exerted a larger force relative to the other fingers in condition ${\text{T}}_y^{\text{CW}}$ and the little and ring fingers exerted a relatively larger force in ${\text{T}}_y^{\text{CCW}}$. Because of the larger torque, this difference was larger compared with that of the human hand. This is also illustrated in Fig. 11 (single trial), showing that during external perturbation with ${\text{T}}_y^{\text{CCW}}$, the reaction force was higher for the little and ring fingers. Due to the controller that we implemented, this difference in force among fingers can only be ascribed to mechanical factors such as the length of the lever arm. Time to peak was not significantly different between the fingers [LR test; T, I, M, R, L: ${\chi }_{(4)}^2$ = 0.23, P = 0.99] and between perturbation types (${\text{T}}_y^{\text{CW}}$, ${\text{T}}_y^{\text{CCW}}$: ${\chi }_{(1)}^2$ = 3.83, P = 0.05]. This was expected and indicates that digit times to peak force were synchronized between fingers.

In summary, the asymmetry in the normal force between fingers that we observed in human grasp can be qualitatively reproduced by the robotic hand, where the only controlled variable was the global hand stiffness. The hand-stiffening strategy successfully compensated the external torque regardless of the external perturbation frequency and type. The differences between the robot and human hand data were the larger torques and forces exerted by the robotic hand, the absence of a learning trend observed between the earliest perturbations (P1 and P2) vs. the rest of the perturbations, and the lack of difference between periodic and aperiodic conditions. The grasp controller employed in the robot hand did not actively control the grasping forces of the individual fingers to counteract disturbances. Therefore, the difference in force among fingers was due to their locations on the TACO. The larger the lever arm is, the higher is the reactive finger force opposing the external torque.

Summary of results.

In the current study, we evaluated the force response to external perturbations during multidigit grasping. The position of the fingers on the manipulandum was unconstrained, which is a methodological novelty with respect to previous studies. We found that the modulation of the force responses was almost synchronous across digits, in accordance with a synergistic control of the hand. Furthermore, participants were better able to stabilize the manipulandum in the periodic than aperiodic condition, thus suggesting a feedforward motor strategy when participants could predict the upcoming perturbations. This is consistent with previous studies showing that to reduce motor delays and to attain grasp stability, the CNS manifests feedforward properties based on an anticipatory control of force mediated by internal models (Budgeon et al. 2008; Johansson and Flanagan 2008). However, alternative mechanisms have been proposed, including controlling the muscle activation threshold, i.e., the muscle length at which motor neurons begin their recruitment (Latash et al. 2010; Pilon and Feldman 2006; Pilon et al. 2007). This feedforward, synergistic motor strategy was employed in the current experiment regardless of the type of external perturbation or the number of digits used in the grasping task. In a control experiment, we replicated the grasping task with a robotic hand that employed a simple stiffness controller, and we observed a force distribution that was qualitatively similar to that obtained from experiments with humans. The main difference between human and robot grasp was that human participants quickly adapted their grip force within the first few perturbations to successfully compensate for external perturbations.

Idiosyncratic hand posture.

Our experimental setup allowed participants to freely choose the placement of their fingers on the object while grasping. This revealed large variability between participants in the initial digit placement. Friedman and Flash (2007) also observed a large amount of variability in finger placement on common objects with the use of five-digit grasps. Although the task is stereotypical, initial digit position seems to be highly preserved across stimulus repetitions for individual participants. This has been confirmed by k-means clustering analysis and ANOVA and can be explained by idiosyncratic grasping strategies.

Control of grip force.

The time to peak normal force was nearly synchronous across all digits engaged in grasping within a single perturbation (Figs. 6 and 7 and Table 1), suggesting that digit normal forces were controlled as a unit within a single perturbation. Similarly, synchronous force changes were found when the fifth finger was added or removed during the hold phase of the grasping task (Budgeon et al. 2008) and during tripod grasps (Budgeon et al. 2008; Winges et al. 2007). In the current task, a change in reaction force was indistinguishable from a change in finger stiffness opposing the perturbation. For simplicity, we assumed that the change in reaction force measured with the apparatus was due to a change in finger stiffness (or pseudo-stiffness; see below), because the type of the force perturbation varied unpredictably from trial to trial. A motor strategy based on the control of hand stiffness would be in accordance with previous literature on hand grasping (Milner and Franklin 1998; Winges et al. 2007). We recognize, however, that because of possible changes in muscle length due to involuntary contractions and attenuation of reflex responses following repeated perturbations (Rothwell et al. 1986; Turpin et al. 2016), the term pseudo-stiffness would be more appropriate. Finally, it is important to remark that the aim of the experiment was to evaluate whether participants controlled different digits independently or in a synergistic fashion, and not whether they used a stiffness or force control. The hypothesis of a synergistic motor strategy was confirmed by the results of the control experiment with the Shadow Dexterous Hand, which employed a single controller for the whole hand without considering force modulation at each individual finger. Force profile was qualitatively similar between the robot and human participants.

Learning within a trial.

The feedforward stiffening strategy led to stable grasp that optimized the error in the hand net torque across perturbations, indicating that the hand-stiffening strategy was resistive to external perturbations (Hasan 2005). Previous studies showed that human adaptation to the perturbation is performed on a trial-to-trial basis by feeding the error of previous trial into the feedforward controller of the current trial (Lukos et al. 2013; Shadmehr et al. 2010). In our results, digit normal force increased from the first perturbation to subsequent ones with the result that the error in net hand torque dropped (Figs. 8 and 9). This suggests that digit normal forces are adapted across consecutive perturbations during the holding phase such that grip force (whole hand stiffening) is gradually increased from one perturbation to the next. Such a simple strategy seems sufficient to successfully counterbalance disturbances on the TACO and consequently to reduce the error in hand net torque caused by predictable and unpredictable perturbations. A similar observation was made with tripod grasps conducted in a study by Winges et al. (2007), in which they suggested that the neuromuscular control system compensated for predictable and unpredictable object mechanical properties by pursuing inherent global stiffness of the hand through co-contraction and modulation of hand muscle activity. The only difference between predictable and unpredictable conditions was the error in hand net torque that was reduced faster in the predictable condition compared with the unpredictable one, especially after the first perturbation (the interaction effect). This latter result can be explained by the work of Aimola et al. (2014) that showed the onset of muscle response took longer in the unpredictable than in the predictable condition. They suggest that precise prediction of the perturbation sequence improves muscle responses, thus shortening the latency of muscle activity in relation to the mechanical perturbation.

Concerning the normal forces of individual digits, we observed a relatively higher force response in the outer fingers. This effect can be explained solely as a mechanical consequence of the full hand stiffening and the outer fingers’ longer moment arm: the farther the finger from the center of the TACO, the higher the normal force in a torque perturbation. This result was confirmed in the control experiment using the Shadow Dexterous Hand, which employed a simple stiffness controller of the entire robotic hand. In this experiment we observed a similar force trend between digits position (outer vs. inner) for a five-digit grasp (Fig. 10).

The stiffening strategy was observed regardless of the external perturbations and the number of digits used in the task. Therefore, on the basis of our results, the modulation of digit normal forces may be a “configuration” rather than a “specialization” outcome (Wu et al. 2012; Zatsiorsky et al. 2002). In the domain of digit normal force, it has been reported that two force synergies (i.e., two principal components) accounted for more than 90% of the finger force variance in constrained and unconstrained grasping (Naceri et al. 2014; Zatsiorsky and Latash 2004). The robot hand has only the first synergy of full hand closure when its stiffness controller is engaged. This might suggest that the second synergy found in human studies is of mechanical, rather than neural, origin and is caused by the fingers’ moment arm and digit-object interaction forces caused by the external perturbation.

Despite the high variability in initial placement of digits and the number of digits used in the task, the synchronous digits stiffening strategy persisted throughout all conditions of the experiment and for all participants. A contribution from biomechanical constraints acting on finger muscles (Santello et al. 2013) could also account for the strategy adopted by participants. Different hand postures led to different grasp stiffness (Friedman and Flash 2007) and different grip force (Naceri et al. 2014), but each satisfied a stable grasp because of the canceling of the applied perturbation forces (equilibrium). It has been shown that arbitrary net force and/or torques produced by force closure of a robotic hand (SoftHand) satisfy a stable grasp in the absence of friction forces (Bicchi et al. 2011). In addition, the latter work showed that with one synergy in the kinematic domain, the robotic hand was able to grasp a large variety of daily objects. With this work, we have shown that one force synergy is sufficient to resist different types of external perturbations while achieving a stable grasp.

In conclusion, participants substantially varied in their initial placements of their fingers on the TACO. Once they grasped and lifted the object using the required grip, the magnitude of digit normal force corrective responses was controlled in a feedforward manner within single perturbations. However, hand net torque was optimized across perturbations by increasing the grip force in the perturbations following the first disturbance, which indicates that participants gradually adapted their feedforward whole hand stiffening across perturbations. The synchronous increase of digit normal forces was achieved by all digits regardless of the external perturbation and the number of digits involved in the task. This suggests that in a simple grasping and holding task, the CNS adopts a stiffening strategy that compensates for the task uncertainty associated with unpredictable external perturbations and with the variability in required grip force. This finding underscores the flexibility and independence of high-level motor processing from low-level motor execution by end effectors (Fu et al. 2011).