
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39251727
71925
10.1038/s41598-024-71925-y
Article
Implicit sensorimotor learning in ballistic movement for transporting an object to a target
Matsuda Naoyoshi mnsmns@elms.hokudai.ac.jp

1
Abe Masaki O. moa@edu.hokudai.ac.jp

2
1 https://ror.org/02e16g702 grid.39158.36 0000 0001 2173 7691 Graduate School of Education, Hokkaido University, Kita-11, Nishi-7, Kita-ku, Sapporo, Hokkaido 060-0811 Japan
2 https://ror.org/02e16g702 grid.39158.36 0000 0001 2173 7691 Faculty of Education, Hokkaido University, Kita-11, Nishi-7, Kita-ku, Sapporo, Hokkaido 060-0811 Japan
9 9 2024
9 9 2024
2024
14 2100318 4 2024
2 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
To enhance and sustain movement accuracy, humans make corrections in subsequent trials based on previous errors. Trial-by-trial learning occurs unconsciously and has mostly been studied using reaching movements. Goal-directed projection movements, such as archery, have an inherent delay between releasing an object and observing an outcome (e.g. the arrival position of the object), and this delay may prevent trial-by-trial implicit learning. We aimed to investigate the learning in the projection movement and the impacts of the inherent delay. During the experiment, a joystick was flicked once to transport a cursor from the starting location to a target. To manipulate the length of the delay between the cursor release and outcome observation, the speed of the cursor movement was varied: a fast speed can lead to a short delay. We found trial-by-trial implicit learning under all speed conditions, and the error sensitivity was not significantly different across speed conditions. Furthermore, the error sensitivity depended on the target location, that is, the movement direction. The results indicate that trial-by-trial implicit learning occurred in goal-directed projection movement, despite the length of the inherent delay. Additionally, the degree of this learning was affected by the movement direction.

Keywords

Motor learning
Motor control
Implicit learning
Subject terms

Human behaviour
Motor control
The JST and the establishment of university fellowships toward the creation of science technology innovationJPMJFS2101 Matsuda Naoyoshi issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

A ballistic movement directed at a visual object is achieved by feedforward control. As states of the body and environment continuously change, we adjust movement based on perceived error to enhance and sustain the accuracy. For example, in the consecutive performance of dart throwing or free throws in basketball, accuracy improves with the number of trials; trial-by-trial sensorimotor learning is suggested to improve the accuracy1–3.

Trial-by-trial learning is driven both voluntarily and involuntarily4,5. This implicit process has often been studied using visual error-clamp feedback5–10. In reaching tasks with the clamp feedback, a cursor follows a fixed trajectory regardless of hand movements. Thus, this paradigm can force participants to experience a fixed visual error11. In the subsequent trial following the error presentation, participants’ reaching movements shift seemingly to counteract the task-irrelevant error, even though they receive an explanation of visual error-clamp feedback and an instruction to ignore the clamp feedback and reach the target directly.

Studies on trial-by-trial learning have generally employed reaching movements4–7,9,10,12–23. Contrarily, in sports, many opportunities are available to transport an object by performing a ballistic movement, such as dart throwing, basketball free throws, and archery. Nevertheless, there are limited findings of trial-by-trial learning in a discrete task of projecting an object to a target24–26. Furthermore, to our knowledge, no study has specifically focused on the implicit process. Thus, it remains unclear whether trial-by-trial learning implicitly occurs during ballistic movements to produce goal-directed movement of objects, referred to as goal-directed projection movement in this study. This study aimed to address this question.

Kusafuka et al.25 examined trial-by-trial learning using a goal-directed projection task. In this task, participants tilted a gamepad stick once toward a target, causing the cursor to move in the direction corresponding to the tilt without mid-flight corrections. The study occasionally presented a cursor trajectory indicating a visual error that was enlarged and reduced beyond the proprioceptive error corresponding to the actual stick movement. They assessed trial-by-trial learning using this paradigm and concluded that the learning was driven based on the proprioceptive error and the visual information could be ignored. According to this conclusion, trial-by-trial learning may not be driven by a visual error through visual error-clamp feedback in the goal-directed projection task.

However, we deduced that the diminished influence of visual feedback might be linked to a characteristic of projection movements: the delay between releasing an object and observing an outcome (e.g. the arrival position of the object). In simpler terms, this corresponds to a delay in endpoint feedback. Notably, in reaching tasks where the absence of visual feedback is observed during the movement, implicit visuomotor adaptation is diminished by the delay in endpoint feedback27–29—the endpoint in reaching tasks denotes the point where the movement stops or the movement amplitude exceeds the distance between the starting location and the target. Drawing on insights from reaching studies, we contemplated the prospect that the delay in endpoint feedback might also diminish implicit visuomotor learning in the goal-directed projection task, even though the trajectory of a projected object can be observed. Thus, we expected that in the projection task, trial-by-trial learning would be differently driven depending on the length of the delay in endpoint feedback.

In sum, this study aimed to examine the implicit process of trial-by-trial learning in ballistic movements for producing a goal-directed movement of objects and the impact of inherent delays in this type of movement.

Materials and methods

Participants

This study recruited 24 young adults for each of the main (13 women, 11 men, aged 19–32) and control (11 women, 13 men, aged 19–26) experiments. Sample size was determined by power analysis based on the effect size (η2 = 0.25) shown in Schween and Hegele27, which examined the impacts of the delay in endpoint feedback using a reaching task. According to G*Power 3.1.9 (α = 0.05, one group, three repeated measurements, ε = 0.5), 24 participants were needed when 1–β = 0.9. All participants were healthy and had no history of developmental or neurological disorders. Additionally, each participant in the main experiment was right-handed according to the Japanese version of the FLANDERS handedness questionnaire30. This study was approved by the Ethics Committee of the Faculty of Education at Hokkaido University (approval number: 21-08). Written informed consent was obtained from all participants. The study methods followed the approved procedures and the principles of the Declaration of Helsinki.

Main experiment

Goal-directed projection task

The experimental task was created based on the task used in Kusafuka et al.25. Participants sat in a chair in front of a 25-inch LCD monitor (GigaCrysta, I-O DATA, Japan). They held a gamepad (Xbox Controller, Microsoft, USA) and manipulated the right stick with their right thumb. Participants’ view of the gamepad was obscured by a wooden board (Fig. 1a). The experimental task was controlled by MATLAB R2019b (MathWorks, USA) using Psychtoolbox extensions31. The stick position was recorded at 120 Hz.Fig. 1 Goal-directed projection task. (a) Experimental setup. Participants manipulated a gamepad without looking at their hands. (b–d) Visual feedback on the monitor. In the trials illustrated here, the target (cyan circle) is placed from the starting location (green circle) at 90° relative to the rightward axis. (b) Null trial: the cursor (white circle) accurately corresponded to the stick movement direction (i.e. veridical feedback). (c) Perturbation trial: the cursor always deviated from the target by − 12°, 0°, or 12° regardless of the actual direction of the stick movement (i.e. visual error-clamp feedback)—positive and negative values indicated counterclockwise and clockwise deviations from the target. Here, a perturbation trial with a 12° error is illustrated. When the cursor’s displacement reached the distance between the starting location and the target, the cursor turned magenta. (d) No-feedback trial: the cursor trajectory was not displayed. (e) Trial order in the main phase. Each perturbation trial was preceded by one, two, or three null trials and followed by a no-feedback trial. Participants were required to pull the left trigger of the gamepad after completing each perturbation trial. (f) Experiment schedule in the main phase. Each speed condition was assigned to a distinct mini-block and was conducted in all orders of mini-blocks (i.e. 1st, 2nd, and 3rd) through the three blocks. The order of speed conditions here is just an example.

At the beginning of each trial, a starting location (green circle, 2 cm diameter) was displayed. Subsequently, a cursor (white circle, 1 cm diameter) and target (cyan circle, 2 cm diameter) appeared when participants waited for a brief moment (see “Speed conditions and procedures”) without touching the stick. The target was placed 15 cm from the starting location at 70°, 90°, or 110° for each trial—0° was to the right of the starting location. Following the presentation of the cursor and target, participants tilted the stick once to move the cursor to the target. At 90% of the stick’s maximum tilt, the cursor began to move in the direction corresponding to the tilt at a constant speed (see “Speed conditions and procedures”). The cursor moved until the displacement reached 15 cm, after which it froze for 0.5 s at that position (i.e. endpoint feedback). The cursor movement direction did not change during the course. Participants were instructed to release their right thumb from the stick after tilting it fully (i.e. a “flick” movement).

Visual feedback

This study employed three types of trials: null, no-feedback, and perturbation trials. In the null trial (Fig. 1b), the cursor accurately corresponded to the stick movement direction (i.e. veridical feedback). If the center of the cursor landed within the target, the target turned red and a “ding” sound was played. In the perturbation trial (Fig. 1c), the cursor always deviated from the target by − 12°, 0°, or 12° regardless of the actual direction of the stick movement (i.e. visual error-clamp feedback11)—positive and negative values indicated counterclockwise and clockwise deviations from the target, respectively. When the cursor’s displacement reached 15 cm, the cursor turned magenta and a “knocking” sound was played. In the no-feedback trial (Fig. 1d), cursor trajectories were not displayed, and participants did not receive any visual or auditory feedback. Participants were fully briefed on no-feedback and perturbation trials and instructed to flick the stick toward the target regardless of trial type.

To measure trial-by-trial learning, each perturbation trial was preceded by one, two, or three null trials and followed by the no-feedback trial7,14,16–18,22 (Fig. 1e). In trials just before and after the perturbation trial, the target location was the same as that in the perturbation trial.

Secondary task during the projection task

As mentioned in Visual feedback, this study explicitly informed participants that visual error-clamp feedback was presented through the auditory stimuli and change in the cursor color. Moreover, we required them to pull the left trigger of the gamepad with their left index finger after completing each perturbation trial. This secondary task was inserted to confirm their awareness of the clamp feedback, or self-irrelevant error. Warning messages were played in the following cases: (1) the trigger was “not pulled” in the interval between the disappearance of endpoint feedback in the perturbation trial and the execution of the stick movement in the next trial (i.e. “miss”) and (2) the trigger was “pulled” in the interval between the disappearance of endpoint feedback in the null or no-feedback trial and the execution of the stick movement in the next trial (i.e. “false alarm”). For each case, a visual and auditory message “Clamp” or “Not clamp” was presented at the end of the next trial.

Speed conditions and procedures

To examine the effects of the delay in endpoint feedback, this study varied the speed of the cursor movement. A fast speed can lead to a short interval between the performance of the stick movement and the presentation of the endpoint feedback or the observation of the outcome. Based on the cursor speed, the trials were categorized into three conditions: Slow (15 cm/s), Medium (25 cm/s; same as Kusafuka et al.25), and Fast (75 cm/s) conditions. Consequently, the movement-outcome interval was 1 s in the Slow condition, 0.6 s in the Medium condition, and 0.2 s in the Fast condition. Along with variations in the movement-outcome interval, we determined the waiting period before the appearance of the target and cursor (see “Goal-directed projection task”) as follows: 0.6 s in the Slow condition, 1 s in the Medium condition, and 1.4 s in the Fast condition. Herewith, the combined duration of the waiting period, cursor movement, and endpoint feedback remained constant (i.e. 2.1 s) across all speed conditions. Participants were informed that the speed of the cursor movement was unrelated to the stick movement.

The experiment proceeded to the baseline (45 null trials) and main phases (378 trials in total: 216 null, 81 no-feedback, and 81 perturbation trials). The main phase consisted of three blocks (126 trials per block), and each block was further divided into three mini-blocks (Fig. 1f). In the baseline phase, the order of speed conditions was pseudo-random so that the same condition did not occur consecutively for three trials; conversely, in the main phase, each speed condition was assigned to a distinct mini-block. We also ensured that each condition was performed in all orders of mini-blocks (i.e. 1st, 2nd, and 3rd) through the three blocks (Fig. 1f). Each mini-block began with six null trials to allow participants to become accustomed to the speed of the cursor movement and stabilize their performance, as the mini-blocks were preceded by an instruction or break. The secondary task was introduced during the main phase.

The baseline and main phases were preceded by 12 and 24 practice trials with the same procedure as in these phases. Regarding the main phase, before this practice, participants were fully briefed on no-feedback and perturbation trials and experienced both trial types three times each (Table S1a,b).

Control experiment

Two-alternative forced choice task

In the goal-directed projection task, we observed that trial-by-trial implicit learning was less pronounced under the 90° target than the 70° and 110° targets (see “Effects of target location”). One potential factor explaining these results is the perception of visual error: The size of the perceived error may vary depending on the target location when a visual error of size 12° is presented in the perturbation trial. If the error is perceived as smaller under the 90° target than others, then the magnitude of trial-by-trial learning may be reduced under the 90° target, leading to a decrease in the error sensitivity. Therefore, we conducted a two-alternative forced choice task to examine differences in perceived error size depending on the target location. The experimental setup and visual stimuli were identical to the projection task, except for the absence of a board to block the view of the gamepad (Figs. 1, 2). In each trial, the starting location appeared, followed by the first target after 0.5 s and the first cursor after 1 s. After 0.5 s, the first target and cursor disappeared and the second target appeared, followed by the second cursor after 1 s. After 0.5 s, the starting location, second target, and cursor disappeared, finally displaying the response screen. The cursors were magenta and placed 15 cm from the starting location, mimicking the endpoint feedback in the perturbation trial of the projection task. Participants were asked to judge which distance, between the first target and cursor or between the second target and cursor, was greater. The reference stimuli included the 90° target and the cursor deviated from the target by − 12° or 12°, similar to the error size in the perturbation trial. The test stimuli included the 70° or 110° target, and the cursor deviated from the target by ± 9°, 10°, 11°, 11.5°, 12.5°, 13°, 14°, or 15°. The order of the reference and test stimuli was pseudo-randomized to ensure equal numbers for both orders, and the sign of the cursor deviation was the same for both stimuli within each trial. Participants responded by pressing the arrow key corresponding to the target that had a greater distance to the cursor—the right, up, and left arrow keys corresponded to the 70°, 90°, and 110° targets. This two-alternative forced-choice task comprised two blocks, each consisting of 160 trials. Two targets in the test stimuli were presented in separate blocks, and the order of the two blocks was counterbalanced between participants.Fig. 2 Two-alternative forced choice task. Participants were asked to judge which, distance between the first target (cyan circle) and cursor (magenta circle) or between the second target and cursor, was greater. They responded by pressing the arrow key of the gamepad corresponding to the selected target—the right, up, and left arrow keys correspond to the 70°, 90°, and 110° targets, respectively. To the right of the starting location (green circle) was 0°. In the trial illustrated here, the test stimuli including the 110° target and the 9° error cursor, and reference stimuli including the 90° target and the 12° error cursor are presented in this order.

Data analysis

Trials identified as “miss” or “false alarm” in the secondary task were precluded from the analysis for the goal-directed projection task corresponding to the primary task. In the projection task, we measured the stick movement direction, which was also the cursor movement direction in the null trial (Fig. 1b). It was defined as the angle of the line connecting the x–y coordinates of the stationary stick and the tilted stick at 90% of the maximum, with the right of the stationary stick as the reference (0°). Trials where the stick movement direction was > 90° were also excluded from further analysis (0.03%). To assess trial-by-trial implicit learning driven by visual error, the error sensitivity was calculated using the following procedure10,13,14,16,21,23. First, Δ stick direction was computed by subtracting the stick movement direction in the perturbation trial from that in the following no-feedback trial (Fig. 1e). Second, we averaged Δ stick direction per combination of target location (70°, 90°, and 110° targets), speed condition (Slow, Medium, and Fast), and visual error presented in the perturbation trial (− 12°, 0°, and 12° errors; 27 patterns in total), and regressed the averaged Δ stick directions against the visual errors for each speed condition (Fig. 3a–c). A negative slope value indicates a movement change in the direction that counteracts the irrelevant error (i.e. a hallmark of trial-by-trial implicit learning). Last, the error sensitivity was defined as the flipped slope of the regression line to improve the readability (Fig. 3d).Fig. 3 Results for each speed condition in the goal-directed projection task. (a,b) Linear regression of Δ stick direction (no-feedback trial vs. preceding perturbation trial) against visual errors presented in the perturbation trial. (a) Slow condition. (b) Medium condition. (c) Fast condition. The dots and error bars denote the mean and standard deviation of Δ stick direction, respectively. The negative slope indicates that trial-by-trial learning was driven by visual errors. The dotted and thick lines represent the individuals and mean slope, respectively. (d) Comparison of error sensitivity across the speed conditions. The error sensitivity was defined as the flipped slope. The bars and error bars denote the mean and standard deviation of the error sensitivity, respectively.

In the analysis for the two-alternative forced choice task, data were collapsed across the cursor’s deviation directions. We calculated the selection ratio of the test target (i.e. 70° or 110°) to the reference target (i.e. 90°) for each error size of the test stimuli (i.e. 9°, 10°, 11°, 11.5°, 12.5°, 13°, 14°, and 15°). Subsequently, the point of subjective equality (PSE) was calculated as μ in a probit function fitted to the selection ratio through the glmfit function in MATLAB. The PSE represents the error under 70° or 110° that participants perceived as being the same size as the 12° error under the 90° target.

In a statistical analysis, we used a one-sample two-tailed t-test, paired-sample two-tailed t-test, and repeated measures analysis of variance (ANOVA). When the assumptions of sphericity for ANOVA were not met, Greenhouse–Geisser-corrected values were reported. The significance level was set at α = 0.05, and the Bonferroni correction was applied for multiple comparisons following ANOVA. All analyses were performed with MATLAB R2021b and JASP version 0.18.2.0.

Results

Performance of the secondary task

During the main phase of the goal-directed projection task, participants were required to pull the left trigger after completing each perturbation trial. The “miss” trials were 1.95 ± 1.78% of the perturbation trial, and the “false alarm” trials were 0.15 ± 0.26% of the null and no-feedback trials (means ± standard deviation [SD] across participants). Thus, in the vast majority of trials, participants discerned whether the clamp feedback or self-irrelevant error was presented. Moreover, excluding the “miss” and “false alarm” trials from the analysis for the projection task, this study focused on the implicit process of trial-by-trial learning.

Effects of the speed condition

To examine the effects of the delay in endpoint feedback, there were three conditions of the cursor movement speed. The slope of the regression line was calculated for each speed condition, and the value was negative under all speed conditions (Fig. 3a–c; Slow: t[23] = 8.899, p < 0.001, d = 1.817; Medium: t[23] = 6.754, p < 0.001, d = 1.379; Fast: t[23] = 4.703, p < 0.001, d = 0.960; one-sample t-test against zero). Subsequently, we conducted ANOVA on the error sensitivity (flipped slope) with the speed condition; however, the main effect was not significant (Fig. 3d; F [1.603, 36.876] = 2.335, p = 0.121, η2 = 0.092). To summarize these results, trial-by-trial learning was implicitly driven in the goal-directed projection task, but the delay in endpoint feedback did not significantly affect the learning.

Effects of the target location

Our data indicate that trial-by-trial learning was driven by visual error, despite the length of the delay in endpoint feedback. This finding appears to be inconsistent with the previous study using the goal-directed projection task, where the impact of visual feedback was less pronounced25. To explore factors contributing to the inconsistency, exploratory analyses were conducted. We focused on the target location. In the previous study, the target was always positioned directly above the starting location (90°), whereas in this study, it was positioned to the left above (110°), directly above (90°), or to the right above (70°) the starting location. Therefore, we regressed the averaged Δ stick directions against the visual errors for each target location and calculated the error sensitivity (see also “Data analysis”).

The slope of the regression line was negative under all target locations (Fig. 4a–c; 110°: t[23] = 6.943, p < 0.001, d = 1.417; 90°: t[23] = 6.148, p < 0.001, d = 1.255; 70°: t[23] = 8.404, p < 0.001, d = 1.715; one-sample t-test against zero). Subsequently, ANOVA on the error sensitivity (flipped slope) with the target showed a significant main effect (Fig. 4d; F[2, 46] = 11.158, p < 0.001, η2 = 0.327), and posthoc tests revealed that the sensitivity under the 90° target was lower than that under 70° and 110° targets (90° vs. 70°: t[23] = 3.669, padj = 0.002, d = 0.815; 90° vs. 110°: t[23] = 4.411, padj < 0.001, d = 0.979; 70° vs. 110°: t[23] = 0.742, padj > 1, d = 0.165). Therefore, albeit being significantly driven, the degree of trial-by-trial implicit learning was smallest under the 90° target that was also used in Kusafuka et al.25.Fig. 4 Results for each target in the goal-directed projection task. (a–c) Linear regression of Δ stick direction against visual errors in the perturbation trial. (a) 110° target. (b) 90° target. (c) 70° target. To the right of the starting location was 0°. The dots and error bars denote the mean and standard deviation of Δ stick direction, respectively. The dotted and thick lines represent the individuals and mean slope, respectively. (d,e) Comparison among target locations. (d) Error sensitivity: the flipped slope. (e) Movement variability: the standard deviation of the stick movement direction in the baseline phase. The bars and error bars denote the mean and standard deviation, respectively. **p < 0.01.

One potential factor contributing to the lowest error sensitivity under the 90° target is the perception of visual error: The perceived error might have been smaller under the 90° target compared to other targets when a visual error of size 12° was presented in the perturbation trial. To investigate differences in perceived errors between the 90° target and other targets, we conducted a two-alternative forced choice task in the control experiment. Consequently, PSEs were close to 12° (Fig. 5a,b; 110°: 12.0 ± 0.2; 70°: 11.9 ± 0.2), suggesting that the perceived error is comparable across target locations. Additionally, one-sample t-tests against 12° did not reveal a significant difference (Fig. 5c; 110°: t[23] = 0.662, p = 0.514, d = 0.135; 70°: t[23] = 1.734, p = 0.096, d = 0.354). Thus, the perceived error would not explain the low error sensitivity under the 90° target.Fig. 5 Results for the two-alternative forced choice task. (a,b) Selection ratio of the test target to the reference target (i.e. 90°) for each error size. (a) 110° target. (b) 70° target. The dots and error bars denote the mean and standard deviation of the selection ratio, respectively. The dotted and thick lines represent the individuals and mean psychometric function, respectively. (c) Comparison of the point of subjective equality (PSE) with 12° error. The PSEs represent the errors under the 70° and 110° targets that participants perceived as being the same size as the 12° error under the 90° target. The bars and error bars denote the mean and standard deviation, respectively.

Discussion

Visual error drives implicit learning in goal-directed projection movement

In the goal-directed projection task, we observed trial-by-trial implicit learning based on visual feedback under all speed conditions. These results are inconsistent with Kusafuka et al.25, although their projection task did not exclusively measure trial-by-trial learning regarding the implicit process. Our task differs in several aspects from theirs, and the task-related distinctions may account for the inconsistency in the results. One such distinction is whether the feedback cursor was anchored when its displacement reached 15 cm, which is the distance between the starting location and the target. In the previous task, the cursor passed through this point without fixation, while in the present task, it was anchored considering the rapid cursor movement under the Fast condition. However, our pilot study found the error sensitivity comparable to that observed in this study, even when the cursor passed through the 15 cm point at the same speed as the Medium condition, comparable to the previous study25. Accordingly, if the cursor had passed through the point under the Slow and Medium conditions, we would anticipate that trial-by-trial learning would have been significantly driven by visual errors.

We presume that the location and number of targets could modulate the impact of visual feedback on sensorimotor learning. The target was presented from the starting location only at 90° in the previous study25 and at 70°, 90°, and 110° in this study. Our exploratory analysis established a significant but modest trial-by-trial learning under the 90° target. Furthermore, as each trial in our task had three possible locations for the target, there were gaps where the stick movement was not performed for a specific target across up to 15 consecutive trials (note that in trials just before and after the perturbation trial, the target location was the same as that in the perturbation trial). According to the Bayesian view of sensorimotor learning13,32, the gaps could increase the uncertainty of a prior (i.e. prediction of sensory feedback: forward model), enhancing the weighting of likelihood (i.e. visual feedback). Contrarily, in Kusafuka et al., the target location was fixed at 90°, and the participants could focus solely on tilting the stick straight ahead25. This might have led to motor control relying on proprioceptive information rather than visual information. Hence, we speculate that in this study, a high weighting of visual feedback resulted in significant trial-by-trial learning based on visual feedback14.

Impact of delay in endpoint feedback in goal-directed projection movement

In our a priori hypothesis, we considered an inherent delay in goal-directed projection movement as a factor contributing to the non-dominance of visual information in sensorimotor learning in the previous projection task25. This delay refers to the time between releasing an object and observing an outcome (i.e. delay in endpoint feedback). Our task attempted to vary the delay via the cursor speed movement, but the error sensitivity was not different across speed conditions. This result may have been influenced by the visibility of the cursor trajectory until reaching the endpoint. The trajectory was displayed, considering alignment with the previous study25 and the fact that the trajectory is visible in a majority of goal-directed projection movements in our daily lives. However, in reaching studies indicating that implicit learning was diminished by the delay in endpoint feedback27–29, the cursor was invisible until the endpoint feedback was presented. Moreover, as the cursor moved linearly in our task, participants could have estimated visual errors before the endpoint feedback. In this study, the presentation of cursor trajectory may mitigate the impact of the delay in endpoint feedback.

From another perspective, a slow cursor speed implies that participants could receive prolonged and clear visual feedback during cursor movement, even though the endpoint feedback was provided in the same way regardless of the cursor speed. Implicit learning may be facilitated by visual feedback during cursor movement under slower speed conditions, leading to the numerically lowest error sensitivity under the Fast condition (Fig. 3d). Further studies are needed to reveal the impacts of the delay in endpoint feedback on implicit learning in goal-directed projection movement.

Why does target location modulate trial-by-trial implicit learning?

Our exploratory analysis revealed variations in the error sensitivity depending on the target. As a potential factor, we can naturally think of biomechanical differences in the stick movement required according to the target location. However, the required movements are similar between the 70° and 90° targets (e.g. flexion at the carpometacarpal thumb joint), which does not seem to be matched by the exceptionally low error sensitivity under the 90° target.

Notably, a Bayesian study of sensorimotor learning demonstrated that different priors were used between effectors33 (reaching vs. wrist rotation). Furthermore, a prior learned in one movement direction was only partially generalized to other directions at most34,35. Therefore, different priors are likely to be used depending on the movement direction or target location. We hypothesize that the prior uncertainty was low in the stick movement to the 90° target, resulting in less weighting of visual feedback and a lower error sensitivity. Indeed, movement variability, which can serve proxy of the prior uncertainty33,36, was small under the 90° target in the baseline phase (Fig. 4e; SD of stick movement direction: 11.9 ± 3.7, 95% CI [10.3, 13.5] under 110° target; 6.0 ± 2.4, 95% CI [4.9, 6.9] under 90° target; 10.8 ± 3.4, 95% CI [9.4, 12.2] under 70° target). These results are also in line with recent findings that indicate a positive relationship between trial-by-trial learning and movement variability in studies employing single-trial learning paradigms like this study7,12,16,23,33,37; however, He et al. diverges from this trend14.

Interestingly, variations in trial-by-trial learning across movement directions are rarely reported in reaching studies that incorporate multiple target locations15,16. Exceptionally, He et al. indicated that the error sensitivity was higher in the direction with lower movement variability and lower visual uncertainty than that with higher movement variability and higher visual uncertainty14. Humans are experts in reaching movements, with lifelong experience in this activity. Therefore, differences in the prior uncertainty may be small across movement directions owing to their proficiency in reaching in all directions, thereby emphasizing the impact of uncertainty in visual feedback.

Contrary to the prior, a variation in the error sensitivity across target locations is unlikely to be explained by differences in likelihood information under the Bayesian framework. Our control experiment indicates that the perceived error size was similar across the target location. Furthermore, visual perception has higher sensitivity to cardinal directions compared with oblique ones, namely oblique effect38. Accordingly, the likelihood uncertainty under the 90° target is likely to be smaller, which should lead to more weighting of likelihood and higher error sensitivity39. As this trend contrasted with our results, we believe that differences in likelihood across target locations have little impact on trial-by-trial learning in this study.

Conclusion and future directions

While the literature has extensively examined sensorimotor learning using arm-reaching movements for decades40, this study explicitly focused on a ballistic movement for transporting an object to a target (i.e. goal-directed projection movement). In sports, there are many opportunities to perform the projection movement, such as baseball pitching and basketball shots. Unlike reaching movements, projection movements are characterized by an inherent delay between releasing an object and observing an outcome. The characteristic specific to the projection movement may affect visuomotor learning 41, as previous studies indicate that implicit visuomotor adaptation is diminished by delay in endpoint feedback27–29. Nevertheless, we provide the first evidence that trial-by-trial learning is implicitly driven by a visual error in the projection task, in line with the findings of the reaching task, and that the length of inherent delay does not significantly influence the error sensitivity. Additionally, the exploratory analysis revealed that the error sensitivity depended on the direction of the projection movement, typically not considered in previous reaching studies42.

Notably, trial-by-trial implicit learning can play a direct role in improving sports. For instance, accuracy in the consecutive performances of dart throwing or basketball free throws improves with the number of trials, which is hypothesized to be attributed to trial-by-trial sensorimotor learning1–3. Our data demonstrate an implicit process of this learning in goal-directed projection movement, supporting this hypothesis. However, there are likely limitations in applying the findings from our experimental task to real-world movements. In the experimental task, the released object always moved straight and at a constant speed in a two-dimensional space. In contrast, in the real world, the released object moves in a three-dimensional space influenced by various factors such as gravity. It remains unclear from this study how trial-by-trial implicit learning appears in the complex conditions of the real world. Therefore, future studies should employ three-dimensional virtual reality environments to balance rigorous experimental control with ecological validity.

Supplementary Information

Supplementary Table S1.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-71925-y.

Author contributions

N.M. wrote the manuscript and M.A. commented on it. All authors reviewed the manuscript.

Funding

The funding was supported by The JST and the establishment of university fellowships toward the creation of science technology innovation, JPMJFS2101.

Data availability

The data presented in this study are openly available in FigShare at 10.6084/m9.figshare.25572135.v1.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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