Perception and prediction of the putting distance of robot putting movements under different visual/viewing conditions

Gerrit Kollegger; Josef Wiemeyer; Marco Ewerton; Jan Peters

doi:10.1371/journal.pone.0249518

Abstract

The purpose of this paper is to examine, whether and under which conditions humans are able to predict the putting distance of a robotic device. Based on the “flash-lag effect” (FLE) it was expected that the prediction errors increase with increasing putting velocity. Furthermore, we hypothesized that the predictions are more accurate and more confident if human observers operate under full vision (F-RCHB) compared to either temporal occlusion (I-RCHB) or spatial occlusion (invisible ball, F-RHC, or club, F-B). In two experiments, 48 video sequences of putt movements performed by a BioRob robot arm were presented to thirty-nine students (age: 24.49±3.20 years). In the experiments, video sequences included six putting distances (1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; experiment 1) under full versus incomplete vision (F-RCHB versus I-RCHB) and three putting distances (2. 0, 3.0, and 4.0 m; experiment 2) under the four visual conditions (F-RCHB, I-RCHB, F-RCH, and F-B). After the presentation of each video sequence, the participants estimated the putting distance on a scale from 0 to 6 m and provided their confidence of prediction on a 5-point scale. Both experiments show comparable results for the respective dependent variables (error and confidence measures). The participants consistently overestimated the putting distance under the full vision conditions; however, the experiments did not show a pattern that was consistent with the FLE. Under the temporal occlusion condition, a prediction was not possible; rather a random estimation pattern was found around the centre of the prediction scale (3 m). Spatial occlusion did not affect errors and confidence of prediction. The experiments indicate that temporal constraints seem to be more critical than spatial constraints. The FLE may not apply to distance prediction compared to location estimation.

Citation: Kollegger G, Wiemeyer J, Ewerton M, Peters J (2021) Perception and prediction of the putting distance of robot putting movements under different visual/viewing conditions. PLoS ONE 16(4): e0249518. https://doi.org/10.1371/journal.pone.0249518

Editor: Chiara Milanese, University of Verona, ITALY

Received: March 28, 2020; Accepted: March 22, 2021; Published: April 23, 2021

Copyright: © 2021 Kollegger et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: GK and ME were funded by the Forum for Interdisciplinary Research at Technische Universität Darmstadt (www.fif.tu-darmstadt.de). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The publication of the study was supported by Technische Universität Darmstadt (www.fif.tu-darmstadt.de) in the framework of the Open Access Publishing Program.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Human-robot interaction is gaining importance due to the increasing penetration of many areas by robotic devices, e.g., in rehabilitation, industrial production and motor skill learning in sports. The overlap of operating spaces between robots and humans is constantly growing. In this regard, an important question is how robots and humans can cooperate in an effective way. In an ideal cooperative scenario the perceptions and actions of humans and robots are perfectly coordinated taking the best of both, i.e., accuracy and precision of robot movements and flexibility and adaptability of human perception and action. This human-robot coordination has to be learned on both sides. Therefore, this paper focuses on motor skill learning of robot-human dyads. The learning of humans and robots raises numerous questions. There is an extensive research in human-robot interaction. Important current topics are—among others—the application of Artificial Intelligence and Machine learning (e.g., [1]), the significance of expert support (e.g., [2]), the impact of different forms of physical guidance (e.g., [3]) or the significance of motor variability (e.g., [4]). For example, if and under which conditions can robots profit from humans and vice versa. One possible scenario may be that at the beginning of the learning process humans teach robots by showing them a first solution and correcting big errors. After this initial phase of acquiring a rough solution (movement topology [5]) the robot may self-optimize its motions and may come up with solutions that are of value for the human. Taking the example of putting motion, the human guides the robot’s first attempts to hit the ball and approach the hole. The human teacher watches and corrects the motions if necessary. As soon as the robot motion has gained sufficient structural stability, a phase of self-optimization will follow. Finally, the robot presents its motions to the human who may use this information as visual or haptic guidance to improve her or his own putting (model or parameter learning [5]). In this hypothetic scenario, watching the robot motions plays an important role for the human to identify the relevant information in order to guide his or her own motion. A prototypical example of a motor learning application involving human-robot interaction in rehabilitation could start with a first demonstration of the movement to the robot, either by physical guidance of the robot or by visual demonstration to the robot. After this demonstration, the robot tries to imitate and further improve the movement. At specific time points, the robot presents the improved movements to the human, again either as visual demonstration or physical guidance, and the human may try to imitate the optimized robot movements. This human imitation may be measured and estimated by the robotic system which again adapts its movements to establish an individualized movement for the patient. This mutual support may lead to a more dynamic and personalized learning of both robot and human movements. Thus, sensorimotor rehabilitation becomes more flexible, more individual and more dynamic. Therefore, the question arises to what extent humans are able to perceive and predict robot motions.

In this paper, the issue of human perception of robot movements is addressed by two experiments where humans perceive and predict video-taped putting motions performed by a robot. Humans are able to perceive motions in several ways by monocular or binocular vision from dynamic and static input [6, 7]. One perceptual strategy is to keep the eyes still and let the moving object pass (afferent motion perception [8]). In this case, the brain constructs motions by integrating the successive projection of light on different retinal locations. This option is appropriate for the detection of motion, particularly in the periphery of the retina. However, due to the low visual acuity outside the fovea centralis, this strategy does not allow for identifying details of the moving object. As a consequence, velocity of a single moving object tends to be overestimated [8]. Respective experiments in psychophysics show, that the ability to discriminate velocity differences follows a U-shaped function favoring velocities of 8 to 64 degrees per second with a sensitivity threshold of about 5% for velocities over 2 degrees per second [9].

Another option allowing for more visual acuity and more accurate perception is to track the object with the eyes (efferent motion perception). In this case, the retinal location of the moving object is more or less stable and the impression of motion is elicited by integrating foveal and peripheral vision and proprioceptive feedback as well as control signals to the eye muscles. However, this second type of motion perception is limited to low object velocities, as object velocities beyond 70 degrees per second require saccadic eye movements [8].

Numerous experiments confirm that humans are able to perceive and classify biological movement, even if only few stimuli are available (“structure-from-motion studies” [10]). Furthermore, the human system for visual perception of motion seems to be hierarchically organized [11, 12]. In the point-light approach (review: [7]) introduced by Johansson [13], for example, human observers are able to judge the gender and identity of acting persons [14, 15], the weight of lifted boxes [16–18], specific motor actions like gait [19] and even emotions, intentions and attempted deceptions [18]. Based on these results, Runeson et al. [20] proposed the principle of “Kinematics Specify Dynamics” (KSD principle). The KSD principle claims that “movements specify the causal factors of events” [20]. However, human ability to perceive motions seems to be limited to nominal and ordinal judgement, i.e., classification and ranking. In a preliminary study, Ballreich [21] found that 29 expert coaches in jumping were able to rank kinematics (i.e., duration and velocity) and kinetics (i.e., force) but not joint angles of three successive high jumps. Cañal-Bruland and Williams [22] report evidence that distal cues, e.g. motion of the racquet, play an important role in predicting the directions of tennis strokes. The perception of human motion is subject to numerous influencing factors comprising features of the moving object (e.g., velocity, trajectory, size, and distance) and the observer (e.g., perceptual-motor experience, knowledge, and object-observer relation). An open question is whether the results found for biological motion transfer to non-biological motion. Recent evidence, both psychological and neurophysiological, suggests an interaction of distinct pathways processing biological and non-biological motion [23, 24]. Interestingly, the perception of animate motion can be elicited by simple visual stimuli with specific changes in velocity and direction [25]. Whereas the proposed experimental evidence confirms the hypothesis that kinematic parameters are integrated in the visual system to elicit nominal and ordinal judgements, it is unclear how well humans can estimate kinematics on a metric scale. The quantitative judgement of movements appears to be subject to numerous sources of error [8, 26]. For example, the “flash-lag effect” (FLE) indicates that the visual system commits errors when predicting the future position of moving objects [27, 28]. The FLE shows that under certain conditions humans tend to systematically overestimate the future position of moving objects. In soccer, for example, this perceptual error leads to a large number of false flags (offside [29]). The FLE is subject to numerous influences (review: [28]), for example, velocity of visual target, eye movements [30], attention [31] level of expertise, learning, and training [32], motion type, motion context [30], and expected dynamics [26]. Studies in neurosciences confirm an important contribution of area MT+ (medium temporal cortex) to the FLE [33], an area which is also involved in the perception of motion in general [34] and especially regarding motion direction [11, 35]. There are numerous theories trying to explain the FLE (for a review, see [28]). The purpose of this paper is to examine, whether and under which conditions humans are able to predict the putting distance of the putting motions of a robotic device. Due to the FLE it is expected that prediction errors increase with increasing putting velocity which is necessary to achieve different putting distances (hypothesis 1). Furthermore, the influence of watching different proportions of motion (temporal occlusion paradigm; [36]) as well as different vision conditions (spatial occlusion paradigm) is tested. It is expected that predictions are more accurate, more confident and faster if the human observers watch the full vision condition compared to the incomplete vision condition (temporal occlusion; hypothesis 2). In addition, it is expected that predictions are more accurate, more confident and faster with full vision (i.e. robot, club, and ball) compared to restricted vision after the impact, i.e., invisible ball or club (partial spatial occlusion; hypothesis 3) [36].

In the following, two consecutive experiments studies are described. In the first experiment, different movement sequences were presented at six different distances. Based on the results of the first experiment, the second experiment aimed at replicating the results of the first experiment and additionally manipulating the amount of information (visibility of club and ball in full vision condition).

Experiment 1—Full vs. incomplete vision condition

In this experiment, hypothesis 1 and 2 are addressed by applying the temporal occlusion paradigm. Video sequences of robot putts at six different distances are presented to the participants. For each distance, videos are shown under two different visual conditions, i.e. full vision condition with visible robot, club, club head, and ball (F-RCHB; Note: F = full vision condition; I = incomplete vision condition; R = visible Robot; C = visible club; H = visible club head; B = visible ball), including preliminary, backswing, downswing, and follow-through phase, and incomplete vision condition with visible robot, club, club head, and ball (I-RCHB) including preliminary, backswing, and downswing phase until the club-ball impact (Note: The abbreviations are introduced here to make it easier to understand the abbreviations for the second experiment.).

Materials and methods

Participants.

Twenty healthy students (13 males and 7 females), aged 20 to 31 years, volunteered to participate in the experiment. Inclusion criteria was no previous experience with perceptual studies. Demographic data are presented in Table 1. This sample size was chosen because no reference study was available which allowed for calculating optimal sample size.

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Table 1. Demographic data of the participants (mean±SD).

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All participants provided their experience (years of exercising and volume in hours per week) in four different groups of activities:

golf, field hockey, and similar;
returning games, e.g. tennis and volleyball;
ball games, e.g. soccer and basketball;
computer games.

Table 2 shows the information provided by participants regarding their previous experience.

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Table 2. Experience in selective sports and computer games (mean±SD).

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This experiment was conducted in accordance with the declaration of Helsinki in its latest version. All participants provided written informed consent before participation. The Ethical Committee of Technische Universität Darmstadt (TU Darmstadt) specifically approved this experiment.

Apparatus and task.

BioRob system. The BioRob robot arm was used as a technical platform for the experiments (see Fig 1). This system has four elastically actuated joints. Each joint is connected via four elastic springs with a separate actuator for each joint. The BioRob system was developed specifically for the physical interaction with humans. Due to its lightweight construction, the system generates low kinetic energy. The system is safe to use without collision detection. In order to adapt the system to the anthropometric properties of participants, the BioRob arm was attached to a special lightweight frame. This allows easy adjustment of the height and orientation of the robot arm [37].

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Fig 1. BioRob-system.

BioRob with 4 DOF on a movable lightweight frame construction for experiments.

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Artificial putting green. In order to enable a reproducible robot putt and a uniform rolling behavior of the golf balls, an artificial putting green was constructed (see Fig 2). The platform is six meters long and two meters wide. The surface consists of a short-pile carpet [37].

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Fig 2. Artificial putting green.

Schematic representation of the artificial putting green with substructure of aluminum profiles.

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Video material. The robot performed putting movements over 6 different putting distances (1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m) on an artificial putting green. The robot motions were recorded using a Camcorder (Sony FDRAX33) with 50 frames per second. The camera was positioned at a distance of 2.6 m from the ball, perpendicular to the putting direction. A black mollitan was used as a background, which also covered the mounting frame of the BioRob system (see Fig 3).

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Fig 3. Video recording setup.

Schematic representation of technical arrangement for the recording of the video material.

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The presented video material was produced with Adobe Creative Cloud Premiere Pro CC 2018 (Version 12.0.0). All 12 video scenes had the same basic structure (see Figs 4 and 5):

Preliminary phase: black screen (duration 3 s) with short beeps (duration 0.05 s) after 1 and 2 s, followed by a 1 s freeze frame of the robot in the starting position with a fixation cross centered on the handle and a 1 s beep;
Backswing phase: identical motion sequence from starting position to reversal point (duration 0.52 s). Regardless of the putting distance, velocity, joint angle, and reversal point were kept constant to avoid spatial stimuli in this phase;
Downswing phase: acceleration profiles from reversal to impact depending on putting distance;
Follow-through phase: rolling ball and club motion from impact until the ball passes the right boundary of the image.
Note: The follow-through phase was presented only in the full vision condition.

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Fig 4. Video sequence in the full vision condition.

Sequential presentation of a 2.0 m putt video in full vision condition with information about swing phase, audio signals and timing (video sequence see S1 Video).

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Fig 5. Video sequence in the incomplete vision condition.

Sequential presentation of a 2.0 m putt video in incomplete vision condition with information about swing phase, audio signals and timing (video sequence see S2 Video).

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Stimuli description. The duration of the different phases and the total duration of the video for the different putting distances are illustrated in Tables 3 and 4. In addition, the velocities of the club and the ball at the time of the impact are specified. The total duration of the preliminary (t_{preliminary phase}) and backswing (t_backswing) phases is the same (4 s) for all video sequences. The duration of the complete video sequences is reduced by 0.34 s from 5.54 s for a putting distance of 1.5 m to 5.20 s for a putting distance of 4.0 m. As the putting distance increases, the total duration of the downswing and follow-through phase decreases by 0.34 s from 1.02 s (downswing: 0.58 s; follow-through: 0.44 s) to 0.68 s (downswing: 0.46 s; follow-through: 0.22 s).

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Table 3. Temporal and kinematic differences between the 6 putting distances under full and incomplete vision conditions.

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Table 4. Temporal and kinematic differences between the 6 putting distances under full vision condition only.

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The velocity of the club head at impact and the ball velocity immediately after impact increase with increasing putting distances. In the incomplete vision condition, there is restricted information depending on the different putting distances, these are the duration of the downswing phase (t_downswing), the total duration of the video (t_Total-I-RCHB) and the resulting velocity of the club head before the impact (v_C-impact). Additional spatio-temporal information is available in the full vision condition, i.e., the velocity of the ball after impact (v_B-impact), duration of follow-through phase (t_{follow-through}), and total duration (t_Total-F-RCHB and Fig 6). Furthermore, three spatial stimuli are delivered (see Table 5):

The distance covered by the ball and the club head in the x-direction after impact, as illustrated in Fig 7 (left) for the putting distances of 1.5 m and 4.0 m. In both cases, similar ball-to-club head relationships exist.
The distance of the club in the y-direction after impact. The covered distance of the club head varies depending on the putting distance between 3.0 cm and 5.3 cm (see Fig 7 center).
The radial distance between ball and club head after impact (see Fig 7 right).

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Fig 6. Stimuli description.

Schematic representation of t_downswing = duration of the downswing phase; v_C-impact = resulting velocity of the club head before the impact; x_{club downswing} = distance covered by the club head in x-direction in the downswing phase; y_{club downswing} = distance covered by the club head in y-direction in the downswing phase; v_B-Impact = resulting velocity of the ball after the impact; t_{follow-through} = duration of follow-through phase; x_{club follow-through} = distance covered by the club head in x-direction in the follow-through phase; y_{club follow-through} = distance covered by the club head in y-direction in the follow-through phase; x_{ball follow-through} = distance covered by the ball in x-direction in the follow-through phase; rd = radial distance between club head and ball.

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Fig 7. Schematic representation of stimuli in the follow-through phase.

Left: Covered distance of ball and racket in x-direction after impact for putting distances 1.5 m and 4.0 m. Center: Covered distance of ball and racket in y-direction after impact for all putting distances. Right: Schematic representation of radial distance (rd) between club and ball. Note: Plots show real values measured with actual robot movements which were not perfectly smooth.

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Table 5. Comparison of available spatio-temporal information under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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Fig 7 shows a schematic representation of these additional stimuli.

Experimental setup. The video sequences were presented by a self-developed computer program. Video clips were displayed by a projector (EPSON EB-1860, resolution: 1024 x 768 px) in original size at the end of the artificial putting green with no sound. The BioRob system was projected in its real size, i.e., 1.42 m. Participants watched the video sequences from a distance of 3.0 m while sitting at a table (see Fig 8).

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Fig 8. Experimental setup.

Schematic representation of the experimental setup with the projection screen and the position of the participant.

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Each of the 12 video sequences was shown four times to the participants in randomized order (total of 48 clips). Upon completion of each sequence, a visual analog scale (0.0 to 6.0 m) was presented to the participants by the computer program. The scale was displayed with a width of 1.050 px (spatial resolution: 0.57 cm/px). Participants provided their length prediction by clicking at the respective point on the scale with the mouse cursor.

Following the estimation of the putting distance, participants provided the confidence of their decision on a five-point scale (very unsure, unsure, undecided, sure, and very sure). In addition to the prediction of the putting distance and the confidence, the response time, i.e. time elapsed between the end of the video presentation and the final click on the distance scale, was also recorded. After assessment, the next video was started by clicking a button. All data was stored by the computer program in one file for each participant.

Procedure. First, the participants were introduced to the laboratory and the experimental setup by the experimenter. After this introduction, all participants received an informed consent document and a participant questionnaire. After signing the consent and completing the questionnaire, the test software was presented to the participants and the experimental procedure including the collected data (e.g. prediction, reaction time) was described (Fig 8). The participants read the instructions and any questions were answered by the experimenter. After the introductory phase, the participants started the experiment autonomously according to the procedure explained in the previous section. After completion of the test program, the participants were debriefed.

Data processing and analysis. Based on the predicted putting distance, constant error (CE), absolute error (AE) and the variable error (VE) were calculated [38, p.55-64]. The CE measures the average error of responding and thus the accuracy [38, p.57]: (1)

The AE measures the overall accuracy and is the average absolute error between the predicted distance and the real put distance without regard to the direction [38, p.59]: (2)

The VE is the variability about the mean response and measures the inconsistency in predicting [38, p.58]: (3)

A two-way ANOVA with repeated measures was calculated with the two factors of putting distance (6 distances) and vision condition (full versus incomplete). Wilcoxon tests were applied for follow-up analysis. Bonferroni corrections were applied to multiple comparisons. All statistical analyses were calculated using SPSS 24 (SPSS Inc., Chicago, USA). Level of significance was set a priori to 0.05.

Results

The following section describes the results of the experiment 1. A dataset with the raw data and the calculated values can be found in the supporting information (see S1 Dataset).

Prediction of the putting distance.

Fig 9 (descriptive statistics see S1 Table) show the means and standard deviations of the predicted putting distance for the six real putting distances under the two experimental conditions. The prediction of the putting distance differs under the two conditions with the exception of the putting distance of 2.0 m. Under the full vision condition, all distances are overestimated and the estimated putting distance increases with increasing distance of the putts presented to the participants. The distance prediction under the incomplete vision condition does not correspond to the real distance; estimations show a slight increase (by 0.54 m) in the range of the real putting distance from 1.5 to 2.5 m. In the distance range from 2.5 to 4 m, the prediction remains constant (3.15 to 3.05 m). Shorter distances (1.5—3.0 m) are overestimated, while longer distances (3.5—4.0 m) are underestimated.

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Fig 9. Predicted putting distance.

Mean and standard deviation of the predicted putting distance under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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The two-factor ANOVA with repeated measures (6 distances: 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; 2 vision conditions: full and incomplete vision) revealed significant main effects of vision condition and distance as well as a significant interaction effect (see Table 6).

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Table 6. Results of the two-factor ANOVA with repeated measures (6 distances; 2 vision conditions) for the predicted putting distance.

Corrected by Greenhouse-Geisser ϵ.

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A follow-up analysis using a Wilcoxon test with Bonferroni correction (descriptive statistics see S1 Table) revealed significant differences between the vision conditions at all distances, except for the short putting distances of 1.5 and 2.0 m.

Constant error (CE).

The constant error indicates the accuracy of the prediction of the putting distance with respect to the actual length of the putt, i.e., the average error. Under the incomplete vision condition the constant error decreases from 1.11 m (1.5 m) to 0.15 m (3.0 m) with increasing distances for small and medium distances. For longer distances, the sign changes and the constant error increases to -0.95 m (4.0 m). In contrast, the constant error under the constant vision condition is fairly constant (within a range of 0.62 to 1.16 m), showing a slightly decreasing trend with increasing putting distance (see Fig 10, detail table see S1 Table).

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Fig 10. Constant error.

Mean and standard deviation of the constant error of predicted putting distance under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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The two-factor ANOVA with repeated measures (6 distances: 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; 2 vision conditions: full and incomplete vision) revealed significant main effects of vision condition and distance as well as a significant interaction effect (see Table 7).

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Table 7. Results of the two-factor ANOVA with repeated measures (6 distances; 2 vision conditions) for the constant error of the predicted putting distance.

Corrected by Greenhouse-Geisser ϵ.

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A follow-up analysis using a Wilcoxon test with Bonferroni correction (descriptive statistics see S1 Table) revealed significant differences between the vision conditions at all distances, except for short putting distance of 1.5 and 2.0 m.

Variable error (VE).

Variable error indicates the consistency of the estimate of the putting distance, i.e., the variability of the participants estimates around the mean of prediction of the putting distance. As can be seen in Fig 11 (descriptive statistics see S1 Table), variable error is rather constant under the full vision condition, whereas it slightly increases with increasing putting distance under the incomplete vision condition.

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Fig 11. Variable error.

Mean and standard deviation of the variable error of predicted putting distance under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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The two-factor ANOVA with repeated measures (6 distances: 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; 2 vision conditions: full and incomplete vision) revealed no significant main effects of vision condition and distance or interaction effect (see Table 8).

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Table 8. Results of the two-factor ANOVA with repeated measures (6 distances; 2 vision conditions) for the variable error of the predicted putt length.

Corrected by Greenhouse-Geisser ϵ.

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Absolute error (AE).

The absolute error measure is the absolute average between the prediction and the real distance. Under the incomplete vision condition, the absolute error initially decreases with increasing real putting distance and increases again at 4.0 m. Under the complete vision condition, the absolute error decreases from the real putting distance of 1.5 to 2.0 m, increases at a putting distance of 3.0 m and then decreases to its minimum at 4.0m (Fig 12, descriptive statistics see S1 Table).

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Fig 12. Absolute error.

Mean and standard deviation of the absolute error of predicted putting distance under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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The two-factor ANOVA with repeated measures (6 distances: 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; 2 vision conditions: full and incomplete vision) revealed no significant main or interaction effects (see Table 9).

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Table 9. Results of the two-factor ANOVA with repeated measures (6 distances; 2 vision conditions) for the absolute error of the predicted putt length.

Corrected by Greenhouse-Geisser ϵ.

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Confidence of prediction.

Confidence was recorded on a five-point scale with the values: (1) very unsure, (2) unsure, (3) undecided, (4) sure, and (5) very sure. Fig 13 (descriptive statistics see S1 Table) show the means and standard deviations of the confidence of the predicted putting distance of all participants for the six real putting distances under the two experimental conditions. The confidence of the predicted putting distance differs under the two conditions over all distances. Under the complete vision condition, confidence of prediction was higher and shows a slight increase with increasing putting distance from 3.09 at 2.0 m to 3.40 at 4.0 m. Under the incomplete vision condition, the confidence reaches the highest value at the putting distance of 1.5 m (2.70), remains nearly constant and decreases at the putting distance of 4.0 m to the lowest value of 2.57.

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Fig 13. Confidence of prediction.

Mean and standard deviation of the confidence of prediction depending on the real putting distance under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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The two-factor ANOVA with repeated measures (6 distances: 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; 2 vision conditions: full and incomplete vision) revealed a significant main effect of vision condition (see Table 10).

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Table 10. Results of the two-factor ANOVA with repeated measures (6 distances; 2 vision conditions) for the confidence of the prediction.

Corrected by Greenhouse-Geisser ϵ.

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Response time.

The response time was measured as the time between the end of the video sequence and the final mouse click on the meter scale. Fig 14 (descriptive statistics see S1 Table) show the means and standard deviations of the response time of all participants for the six real putting distances under the two experimental conditions. The response times in the two conditions differ over all distances and are lower under the complete vision condition. With increasing distance, the response time under the complete vision condition at shorter distances decreases from 4.64 s (1.5 m) to 4.17 s (2.5 m) followed by an increase to 5.13 s (3.0 m). For longer distances, the response time decreases again as the distance increases, reaching its minimum at 3.38 s (4.0 m). Under the incomplete vision condition, the response time decreases from 5.70 s (1.5 m) to 4.47 s (2.0 m) and increases to 5.61 and 5.77 s for medium distances (2.5 and 3.0 m). For long distances, the response time decreases from the medium distances to 4.99 s (3.5 m) and 5.33 s (4.0 m).

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Fig 14. Response time.

Mean and standard deviation of the response time depending on the real putting distance under full (F-RCHB) and incomplete (I-RCHB) vision condition.

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The two-factor ANOVA with repeated measures (6 distances: 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 m; 2 vision conditions: full and incomplete vision) revealed a significant main effect of vision condition (see Table 11).

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Table 11. Results of the two-factor ANOVA with repeated measures (6 distances; 2 vision conditions) for the response time.

Corrected by Greenhouse-Geisser ϵ.

https://doi.org/10.1371/journal.pone.0249518.t011

Discussion of experiment 1

The results show that participants were able to predict the putting distance of a robot putt under the complete vision condition. However, all six putting distances were overestimated by the participants, a linear course of the predicted putting distances is shown with increasing real putting distance. This systematic overestimation supports the predictions derived from the FLE. However, contrary to hypothesis 1, prediction error (CE) does not increase, but rather decreases with increasing putting distance. In contrast to the full vision condition, the participants could not predict the putting distance under the incomplete vision condition. The predicted values seem to be randomly chosen values that show a tendency to the centre of the prediction scale (0 to 6m) at 3.00 m. The confidence data support the prediction results. The visibility of the follow-through-phase was found to have a decisive influence on the quality of the prediction of the putting distance. This leads to the conclusion that the additional stimuli available under the full vision condition have a high relevance for the prediction of putting movements. It remains open what influence individual elements (e.g. club and robot) have on the prediction of the putting distance. Whereas hypothesis 2 (different prediction depending on vision condition) was confirmed, there was no evidence for hypothesis 1 (increasing error with increasing putting distance). Ex post calculations of power using the software G*Power 3.1.9.4 [39] revealed that experiment 1 was over-powered (1.0) regarding hypothesis 2 (Protocol of power analysis see S1 File). Power analysis for hypothesis 1 does not make sense due to the decrease of error, which is contrary to hypothesis 1.

Experiment 2—Prediction and visibility manipulation

This experiment is based on the results of experiment 1. In addition to a replication of the previous results (hypotheses 1 and 2), the influence of the visibility of the ball, club and robot after the impact on the prediction of the putting distance is investigated (spatial occlusion; hypothesis 3). In this experiment, video sequences of robot putts at three different distances are presented to the participants. For each distance, videos are shown under four different visual conditions, i.e. full vision condition (F-RCHB), incomplete vision condition (I-RCHB), full vision condition with visible robot, club and club head in the follow-through-phase (F-RCH), and full vision condition with visible ball in the follow-through-phase (F-B).

In the following, only differences in materials and methods compared to experiment 1 are presented.