Myoelectric hand prostheses seek to restore the lost manipulation capabilities of individuals with a limb difference by using electromyographic (EMG) signals to estimate the user's motion intent to drive powered prosthetic devices. Closed-loop user-prosthesis interfaces, which combine EMG-based control and artificial sensory feedback to provide users with a sense of prosthesis state and improve the intuitiveness of control, hold the promise of bridging the gap between natural and bionic hands [1–3].

To use these sophisticated devices and interfaces, the prospective user needs to train to perform specific, often unintuitive, contractions of their residual muscles. Attaining expert-level skill in user-prosthesis interaction may require guided training over weeks and months [4–6]. This relatively long learning process is due to the inherent variability of EMG-based control and non-linear properties of the prosthesis, such as non-back-drivability. Quality training is crucial for successful control and poor training has been linked to device rejection [7]. Training is also needed for the feedback side of the interface since the user needs to learn to perceive the sensations artificially elicited [2] and to use this sensation to gain information on the prosthesis state. Quantifying the way and time course of the acquisition of skilled prosthesis control is a fundamental step to developing evidence-based training and rehabilitation protocols [8, 9], designing interfaces that are easier to learn and retain, and understanding the motor learning processes underlying complex human behaviors [10].

Previous studies that investigated prosthesis skill learning, have defined it in terms of improved accuracy, faster movement speed, reduced end-point variability or a combination thereof [8, 9, 11–13]. These studies mainly evaluated skill by asking participants to be as accurate as possible in the given task at a self-chosen comfortable pace, or as fast as possible. However, this approach neglects the effect of the self-chosen speed on the resulting movements and performance. Movement speed and accuracy are fundamentally coupled, and skill can only be inferred when both change in the expected direction [14–18]. Figure 1(A) illustrates this concept with a simple example. If the speed-accuracy measurements over two days for a participant are given by the filled circles as shown in the figure, it would be impossible to dissociate if the improved accuracy (blue circle) is due to better skill or merely due to performing the task at a slower speed (as compared to the gray circle). Consequently, determining speed-accuracy trade-off functions (SAFs, figure 1(A)) has been proposed as a solution to rigorously study skill learning [14, 16, 19].

Figure 1. Monitoring skill by measuring and modelling learning-induced changes in SAF—concept and experimental setup. (A) Blue and gray dots indicate plausible speed-accuracy measurements of a user recorded over two days. Such measurements, however, cannot dissociate whether the improvement in performance from one day (gray) to the next (blue) is due to an improvement in user skill or merely an artifact of slower execution speed (here, longer reach time). Measuring a speed-accuracy tradeoff function (solid curves, SAF) across training sessions alleviates this issue. Plausible changes to the SAF across training sessions are indicated by the dashed arrows. (B) Diagram showing the power law model of SAF and the effect of parameters and on it. The model was used to capture the changes in SAF observed experimentally. Changes in model parameters can be used to quantify the (subject-specific) differences in skill across time. (C) Experimental setup shows a healthy participant using a closed-loop prosthesis interface, combining dual-site proportional control and vibrotactile EMG feedback, to control the Michelangelo hand prosthesis. Salient experimental protocol details are also shown in the top right; EMG feedback spatial coding scheme is displayed on the right. Adapted from [22]. © IOP Publishing Ltd. All rights reserved.

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This approach evaluates task performance systematically and comprehensively by asking the participants to repeat the same task at different speeds. A SAF so measured, characterized by its shape (monotonically increasing), rate, and intercept, succinctly captures skill [20, 21]. Previous work in human motor control demonstrated that SAF changes across days in a way that is consistent across speeds [14, 19], which is mainly driven by better motor execution, reflected by decreased movement variability. However, such a detailed analysis is lacking for prosthesis control—it is unknown if SAF changes such that improvements are similar across speeds, or if some speeds experience larger gains than others (e.g. faster speeds might have larger gains as opposed to slower speeds, simply by having more scope for such gains (figure 1(A), dashed arrows)).

Apart from quantifying skill, SAFs have been used in a recent study to understand and compare how different feedback interfaces afford different speed-accuracy tradeoffs in prosthesis force control [22]. The study demonstrated the relevance of SAFs and showed how comparing the interfaces at a single speed (corresponding to a single point on the SAF profile), as commonly done in the literature, could generate misleading conclusions. However, it is still unknown how the tradeoff evolves across days during learning, or in other words, how skill develops over time. Quantifying learning-induced changes in the SAF enables us to thoroughly investigate how users acquire skills, and accordingly develop tools to monitor and track skill acquisition and retention.

In relation to the latter, Reis et al [14], proposed a model-based method to monitor skill progression. Given that the SAF reflects skill, it follows that if a parametric model of SAF can be obtained, then changes in the parameter values of such a model could be used to monitor skill over time, in a subject-specific manner (figure 1(B)). Notably, they proposed a simple 1-parameter model of SAF such that the single parameter reflected changes in skill. Similarly, Guiard et al [23], observed that the SAF in a cursor-pointing task could be captured using a 1-parameter power law model. However, it remains to be seen if such methods generalize to skill monitoring in prosthesis control.

In this study we therefore characterize the SAF resulting from the use of a closed-loop user-prosthesis interface for grip force control, to investigate skill learning and the behavioral changes subserving it. Participants used a closed-loop interface that included a dual-site direct proportional control of prosthesis closing speed and EMG-feedback [24, 25]. In this approach, an array of vibrotactors was employed to deliver the level of the myoelectric signal (prosthesis command input) as the feedback to the participants, thereby facilitating predictive control of grasping force by augmenting a sense of contraction strength. Over the course of 3 days, participants practiced a modified version of the box-and-blocks task where the blocks were required to be grasped at specified forces and speeds (timed force-matching paradigm). We hypothesized that the largest gains in accuracy would be experienced at faster speeds, due to a larger margin for improvement (as explained above) as well as the predictive nature of the feedback. We then built a parametric power-law model of the measured SAFs (figure 1(B)), following previous studies in motor skill learning [14] and human-computer interaction [23, 26]. Using the model, we characterized how the SAF changed across days for this type of closed-loop control interface and compared the results to those reported in the literature for human motor control of natural movements. Finally, we discuss if skill could be inferred from 'observational' data, where participants are simply asked to perform the task at their self-chosen comfortable pace to estimate the parameters of the SAF, such that the process of measuring the true SAF could be simplified.

2.1. Participants

Sixteen healthy participants (nine males and seven females with no limb loss, aged 23.5 ± 2.6 years) with no prior experience of myoelectric prosthetic control were recruited. One individual with a transradial limb loss (female, 50 years old, 11 years since traumatic amputation of the non-dominant hand, self-reported to have limited daily use of a single degree of freedom myoelectric prosthesis), who had prior experience with similar experimental setups was also recruited for the study. All participants signed an informed consent form before the start of the experiment. The experimental protocol was approved by the Research Ethics Committee of the Nordjylland Region (approval number N-20190036).

2.2. Experimental setup

The experimental paradigm follows from a previous experiment [22], which for the present study was extended across days. The methods are briefly described here. The experimental setup is shown in figure 1(C). Healthy participants wore an orthotic wrist immobilization splint to achieve near-isometric wrist flexion and extension movements. The Michelangelo prosthetic hand (OttoBock GmBH, DE) was attached to the splint, with the arm placed in the neutral position. Further, two dry EMG electrodes with embedded amplifiers (13E200, Otto Bock, DE) were placed over the wrist flexors and extensors of the right forearm. The electrode placement was determined by visually observing muscle contractions and palpating the forearm. In the case of the individual with limb loss, the prosthesis was attached to a custom-made socket with integrated EMG electrodes. For all participants, five vibrotactors (C-2, Engineering Acoustics Inc.) were positioned evenly around a cross-section of the upper arm and secured in place by an elastic band. A modified box-and-blocks setup was used for the experimental task, where the participants were asked to apply predefined forces when grasping the blocks and to perform the task within a set time interval, as explained in the section 'Experimental Design'. The prosthesis was connected to a standard laptop PC via Bluetooth, while the vibrotactors were connected via USB. The task instructions were displayed on a dedicated computer screen, positioned at a comfortable viewing angle and distance. The experiment was developed in MATLAB Simulink using a toolbox for testing human-in-the-loop control [27]. The control loop operated in real-time on the host PC at 100 Hz, through the Simulink Desktop Real-Time toolbox.

2.2.1. EMG control

All participants used near-isometric wrist flexion and proportional control to generate velocity commands to close the prosthesis. However, since fine control of prosthesis opening was not relevant to the study, it was simply triggered by a strong contraction of the wrist extensors. For the individual with limb loss, this meant that she was instructed to activate her residual wrist flexor and extensor muscles. The linear envelope of EMG was sampled at 100 Hz from two electrode systems, placed on the flexors and extensors, as explained above, through the embedded prosthesis controller and transmitted to the host PC. The signals were subsequently filtered using a 2nd-order Butterworth low-pass filter with a 0.5 Hz cutoff, and this 'myoelectric command' from each of the electrodes was normalized to 50% of that obtained during maximum voluntary contraction (MVC) (following the results of [28]). The normalized myoelectric commands obtained from the flexor EMG were translated into the normalized input command for the prosthesis using a piecewise linear mapping defined by the breakpoints given in table 1 (see [22]). Note that the EMG intervals were wider for higher amplitudes to compensate for the higher variability of the EMG at stronger contractions. The prosthesis input command determined closing velocity (1—maximum velocity) and generated grasping force, i.e. the stronger the command input, the faster the prosthesis closes and the higher the force generated after contact. The aforementioned mapping effectively translated the EMG 'levels' into the corresponding force levels (see the next section for a more detailed explanation of closed-loop control). Note that for EMG amplitude lower than 0.025 on the normalized scale, no input command was sent to the prosthesis (Level 0) to avoid unintentional prosthesis closing. To trigger prosthetic hand opening, however, participants simply needed to reach 0.4 on the normalized range (i.e. 20% MVC) of extensor EMG.

Table 1. The myoelectric command, prosthesis input and force 'level' boundaries for the discretized interface.

Level0123456Myoelectric command0.0250.10.270.470.690.951Prosthesis input00.250.420.590.760.91Force0.050.310.450.580.730.912.2.2. Vibrotactile EMG feedback

All participants received feedback on self-generated flexor EMG command through a vibrotactor array. A spatial coding scheme consisting of six stimulation patterns was used to convey the six discrete levels of the myoelectric command. To represent the first five levels, one of the tactors from the array was activated individually in a specific order. However, the sixth level was indicated by activating all the tactors simultaneously (see figure 1(C)). During setup, adjustments were made to the position and/or intensity of the vibrotactors if they caused unpleasant or poorly localized sensations, to ensure that the participants could easily differentiate all the stimulation patterns. The vibration frequency for all tactors was set to 200 Hz, and the stimulation pattern was updated at 50 Hz.

The six discrete levels were defined using the same piece-wise linear mapping reported in table 1. As soon as the participants contracted their wrist flexors (to generate a myoelectric command above level 0), they received feedback about the level (1–6) they were generating, thereby enabling them to modulate the prosthesis command input to the desired level using online feedback. The control and feedback interfaces were designed in such a way that if the participants generated a particular level of myoelectric command, the prosthesis applied the same level of force on the object. For instance, if a participant generated and maintained commands corresponding to level 2, the prosthesis closed at level 2 velocity and exerted level 2 force onto the grasped object. Note that while the feedback provided discrete information (a level of EMG), the command signal generated by the participant and transmitted to the prosthesis was still continuous and proportional (as in the commercial approach to prosthesis control). Therefore, if the EMG signal was in the higher range of level 2 (e.g. close to the threshold between levels 2 and 3), the generated grasping force would be in the higher range of level 2 of prosthesis forces, as defined by table 1.

2.3. Experimental design

The experiment was designed as a longitudinal trial over three sessions with a maximum of two days between the sessions. Here we describe the experimental design and protocol for the healthy participants first and point out the slight differences in the case study involving the individual with limb loss. In each session, the participants trained to perform the box-and-blocks task with the timed force-matching requirements. In each trial, they were required to (1) apply a specified level of force on the object (either level 3 or 5, see table 1), and (2) reach the target level within the specified time. Participants were required to perform the task in four speed conditions—Slow, Medium, Fast and Very Fast—which corresponded to time of execution in the range 4–8 s, 3–5 s, 2–4 s, and 1–3 s, respectively. The times of execution were defined to capture the relevant domains of the SAF curve and expand upon previous investigations [22]. Thereby, we used a time-band methodology to measure the SAF [20, 22] (i.e., to sample the shape of the SAF profile.

2.4. Experimental protocol

Initially, all equipment (the wrist immobilization splint (socket in the case of the individual with limb loss), prosthesis, EMG electrodes and vibrotactors) were placed on the participant. Then, a brief calibration and familiarization followed in all sessions. During EMG calibration, 3 repetitions of 5 s long MVC contractions were recorded independently for both the flexors and extensors. The MVC measurements were recorded in the same posture that the participants would use to perform the box-and-blocks task, to account for the effect of arm posture and prosthesis weight on the recorded EMG. Next, the participants were guided to explore the control interface, i.e. the relation between muscle contraction intensity and velocity in hand opening/closing. Subsequently, they were familiarized with the vibrotactile feedback interface. This involved a spatial discrimination task where they were presented with two sets of 18 stimulation patterns (3 repetitions × 6 levels, figure 1(C)) and asked to identify the patterns. The experiment proceeded once the participants achieved at least 95% success in the discrimination task, which usually required less than 5 min since the vibration patterns were designed to be easy to discriminate.

After familiarization with the control and feedback interfaces, participants performed 6 blocks of 32 trials (8 trials × 4 speed conditions) of the timed force-matching task. On the first day, an extra (familiarization) block of 32 trials was performed where the participant was guided through the task. In each trial, the force and speed targets were first displayed. Then, the participants used the proportional control interface and the provided EMG feedback to successfully complete the trial, as explained in section 'Vibrotactile EMG feedback'. Once the participant felt they successfully reached (or overshot) the target, they were instructed to trigger prosthesis opening. As the prosthesis was non-backdrivable, like most commercial devices, it was not possible to decrease the grasping force in a controlled manner (the prosthesis would open and release the object completely). Therefore, as explained before, the overshoot was also considered as a reason to open the hand and end the trial. Immediately after the trial ended, they received feedback on their performance, in terms of whether they acquired the target force and target speed. Such 'knowledge of results' has been shown to improve participants' motivation during the experiment and the rate of learning the task [29]. To some extent, this also reflects information that would be available in the daily use of a prosthesis (e.g. inappropriate force would lead to damaging or dropping of objects). However, the effect of this feedback is not explicitly addressed in this paper. During the familiarization trials, the participants were instructed on how to modulate their muscle contraction to control the closing velocity of the prosthesis. In each block of 32 trials, the target speed (Slow, Medium, Fast or Very Fast) was presented in a blocked fashion, i.e. it remained unchanged for 8 trials within which the target forces (3, 5) were presented 4 times each in random order. The target speeds were presented in a balanced random order, across blocks.

2.4.1. Experimental protocol for the individual with limb loss

The experimental protocol for the individual with a limb loss was slightly modified, where she performed 5 blocks (instead of 6) of trials with both force and speed targets on all three days. In addition, she performed 2 additional blocks of the same task but with no speed target (referred to as 'observational trials') on Day 2 and Day 3, to pilot test our model-based skill monitoring method. Given the additional blocks of observational trials on Days 2 and 3, we reduced the number of experimental blocks from 6 to 5 on all days, in the interest of not straining the participant. Apart from these modifications, the rest of the experiment proceeded identically to the healthy participants.

2.5. Outcome measures

During each trial, the recorded myoelectric commands and force measurements were processed to obtain the primary outcome measures—reach time and trial success, respectively. Reach time was calculated as the duration between the time when participant started generating the EMG input (above Level 0) and when the maximum force was reached during the trial. Therefore, a successful trial was defined as one where the reach time satisfied the speed requirement, and the maximum reached force was within the corresponding target force level. The trials were aggregated per speed condition to obtain percent success rates.

Further, to understand how the participants planned and executed the task across the sessions, we computed three behavioral metrics [22, 30]. We computed (1) the number of force corrections per trial that the participants made, by counting the number of distinct plateaus (longer than 250 ms) in the force trajectory [22], to gain insights into their control policies—specifically corresponding to how they included the supplementary feedback in their commands. Since EMG feedback promotes predictive modulation of commands, by allowing participants to adjust their muscle contraction during prosthesis closing so that the target force is generated at once, upon contact, without requiring further modulations [11, 25], the more successful the participants are in using this strategy, the lower the number of corrections. Further, we analyzed the quality of generated EMG commands, to understand if participants generated (2) smoother and (3) more repeatable EMG commands across days and speed targets. To evaluate smoothness, we calculated the spectral arc length (SPARC) of the EMG commands [31]. SPARC measures the negative arc length of the Fourier magnitude spectrum of the speed profile of a movement. Thereby, signals with a wider spectrum (and hence a greater absolute SPARC value) are less smooth. We chose SPARC as an alternative to jerk-based measures, because it is a more general measurement of the smoothness of any movement-related variable and is robust to high-frequency changes in the recorded signal. To measure the repeatability of commands, we computed the trial-by-trial variability as follows: we first normalized all commands to 200 time points between the start of the trial and reach time, and then measured the standard deviation at each of the 200 time points. As the final measure of variability, we computed the median of the obtained standard deviations across the time points.

2.6. Parametric models of SAF

To capture the changes in the shape of the SAF curve across training (see figure 1(B)), we built a parametric model of SAF as , where is success rate, is reach time (duration of trial), and is a function of and two parameters , bearing functional forms already investigated in the literature. Specifically, we considered the power law equation described in [23, 26], relating the success rates and reach time developed in the context of 1-D cursor movements. While different in the functional form, the power law model is similar to (and simpler than) another model developed in the motor learning literature for a task that involved the production of a sequence of isometric finger forces [14]. Here we modified the equation to reflect the –intercept (or asymptote) at 0.8 s, as it is impossible to get a successful trial below 0.8 s, due to limitations in the speed of the prosthesis response and EMG command generation:

Note that parameter in equation (1) is restricted to be negative.

2.6.1. Model fitting

The models were fit for day-wise pooled healthy participants' data (success rate and reach time) for each of the 3 days, using ordinary least squares-based fitting. Success rates and reach times from 2 consecutive blocks were averaged so that the mean success rate and its variance are well represented during model fitting. This way, the power-law model was fitted using 12 points (4 speeds × 3 points per speed). The parameters obtained through this fitting procedure are denoted by asterisks, such as . The goodness of fit was measured using the metric.

All models were log-transformed before fitting so that the parameters obtained would be easy to interpret. This way, parameter ' ' denotes the -intercept of the SAF in the - plane, while ' ' denotes the slope at which the success rate increases with reach time. A change (exclusively) in the intercept therefore indicates that the -success rates at all movement speeds are affected similarly (e.g. consistent increase at all speeds), while a change in slope indicates that different speeds may affect success rate differently (e.g. increase at low speeds and decrease for high speeds).

2.6.2. Reducing model complexity: from 2-parameter to 1-parameter models

Earlier studies have observed that the SAF models described above can be further simplified such that only a single parameter reflects skill-related changes [14, 23], but as explained before, this has been established for motor control tasks involving natural movements. Here, in a similar vein, we investigated if one parameter reflected skill improvements while the other parameter could be fixed in the context of closed-loop prosthesis control. In other words, we were interested in finding if or , where the underscore denotes the parameter being held constant. To start, let us denote the obtained by fitting a particular set of data to the 2-parameter model such that , where denotes the pooled success rate () and reach time () dataset of a particular day and , denote the best-fit parameters.

Then, represents the change in the goodness of fit () when using the 1-parameter model, e.g. obtained by fixing constant at and setting to in the vicinity of . A significant decrease in due to such a perturbation in one of the parameters ( or ) indicates that perturbing that parameter leads to worse fits with respect to the full 2-parameter model. By quantifying the sensitivity of the model fits to both parameters, we can rigorously quantify how they affect the goodness of fit and choose which parameter to set as a constant. Accordingly, we selected 1000 values of and in the range of the parameters in the vicinity of those observed by fitting the experimental data, and and computed the following set of values:

where index denotes the day. We then obtain the simplified 1-parameter model by finding the parameter that changed mean the least,

where denotes the mean of the set of values .

2.7. Statistical analysis

3-factor repeated measures ANOVAs for success rate and behavioral measures were fit with 3 within-subjects factors—day, target speed and target force. To analyze the total improvement between Day 1 and 3, we fit 2-factor ANOVAs with target force and target speed as the factors. The assumptions of normality, homogeneity of variance and sphericity were verified using Shapiro-Wilk's, Levene's and Mauchly's tests, respectively. Post-hoc analyses for all quantities of interest were performed by using pairwise t-tests, adjusted using the Holm–Bonferroni method. The threshold for statistical significance was set at p < 0.05. The mean ± standard deviation of outcomes per group of interest are reported throughout the paper.

3.1. Learning induced changes in the SAF

We analyzed how participants' SAFs (see figure 2(A)) changed across the experiment by fitting a 3-way ANOVA with day, target speed and target force as factors. We found that all three factors significantly influenced the success rate (day: F(2, 30) = 14.05, p = 5 × 10−5, target speed: F(3, 45) = 35.47, p = 6 × 10−12, and target force: F(1, 15) = 9.46, p = 7 × 10−3), but none of the factor interactions was significant. Participants exhibited a wide range of success rates across days and speeds, ranging from 66.3 ± 15.2% in the Very Fast speed on Day 1, to 90.2 ± 10% in the Slow speed on Day 3. Post-hoc analyses revealed that success rates improved significantly from Day 1–2 (p-adj = 0.01), and Day 1–3 (p-adj = 0.0008) while the difference from Day 2–3 was not significant (Day 1: 75.4 ± 14.6%, Day 2: 81.7 ± 13.3%, and Day 3: 85.3 ± 10.8%; average success rates across speeds). In a similar way, the participants' success rates significantly increased from Very Fast to Fast (p-adj = 0.005) and Fast to Medium (p-adj = 7 × 10−4) but not from Medium to Slow speed. A significant effect of target force meant that participants were more successful in target Level 5 than Level 3 throughout (Level 3: 77.8 ± 14.4%, Level 5: 83.8 ± 12.1%; averaged across speeds and days, figure 2(A), right).

Figure 2. Learning induced changes in the speed-accuracy trade-off. (A) (left) Average SAF across healthy participants and the individual with a limb loss is shown, on Day 1 and Day 3. Vertical dashed line indicates the –intercept of SAF (success rate is necessarily 0% when reach time < 0.8 s). (right) Average success rates across speeds are higher for target force level 5. (B) Total improvement in performance (from Day 1 to Day 3) is plotted per target speed (V.F: Very Fast, F: Fast, M: Medium, S: Slow). Notably, the improvement was similar across speeds. (C) Average number of corrections of force (p/trial) is plotted against target speeds. (D) Smoothness of generated EMG commands, measured by SPARC, decreased across days (greater values of SPARC imply smoother kinematics). (E) Trial-by-trial variability of EMG commands decreased across days for all speeds. Across all boxplots, the median and interquartile range are indicated by the central line and the boundaries of the box, while the whiskers extend to include all datapoints within 1.5 × IQR (inter-quartile range), black diamonds indicate outliers (> 3 standard deviations from the mean) outside the whiskers' range. Stars indicate the results of the individual with a limb loss.

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Next, we analyzed how SAF changed between Day 1 and Day 3. Interestingly, while participants' success rates improved across days, as explained above, there was no significant effect of target speed or target force on the observed improvement. That is, the increase in the success rate was similar across speeds though with large variability (Very Fast: 12.7 ± 15.6%, Fast: 7.6 ± 12.9%, Medium 9.8 ± 7.7%, and Slow 7.1 ± 9.7%, averaged across force levels, see figure 2(B)), and across force levels (Level 3: 9.8 ± 8.8%, Level 5: 8.8 ± 8.7%, averaged across speeds). Therefore, the SAF curve effectively 'shifted upwards' across days consistently for all speeds, at both force levels.

Results of the individual with a limb loss largely followed the trends of the healthy participants, however, her success rate improved only slightly from 84.8% on Day 1 to 86.3% on Day 3 (stars in figures 2(A) and (B)).

3.2. Behavioral analyses

We then analyzed how participants' behavior (planning and execution of EMG commands) changed across days. First, we investigated how participants' control policies changed with training, by looking at the number of force corrections generated (figure 2(C), the number of corrections are averaged over the two target forces to emphasize the effect of training (changes across days)). We found that the control policies were affected by the target speed (F(3, 45) = 634.0, p < 1 × 10−10), and target force (F(1, 15) = 843.7, p < 1 × 10−10). However, there was no significant effect of day, indicating that the overall strategy of how participants used the feedback remained consistent throughout the experiment. There was an interaction effect between target force and speed (F(3, 45) = 115.8, p < 1 × 10−10), whereby the number of corrections for target level 3 decreased more gradually with speed, compared to level 5. The number of corrections decreased steadily with the target speed (post-hoc tests were significant for all pairs, with each p-adj < 1 × 10−7), suggesting that at faster speeds, participants adjusted their muscle contractions prior to contacting the object, rather than using feedback post-contact to reach the required force. Finally, participants made fewer corrections to reach force level 3 than level 5 (p < 1 × 10−10).

Next, we analyzed how the smoothness and trial-by-trial variability of their movements were influenced by learning (figures 2(D) and (E)), both measures are shown by averaging across target force levels, similar to figure 2(C)). We found that there was a significant effect of all three independent variables—target speed, target force and day on both metrics (see table