Analysis of learning the bimanual control of (tele)operating joint space controlled robotic arms with 4 degrees of freedom using the two-timescales power law of learning

Abstract Training costs for operators of robotic arms in forestry and construction are high. A systematic analysis of skill development can help to make training more efficient. This research focuses on motor skill development by investigating the bimanual control of a four-DoF robotic arm. The two-time scale power law of learning was used to identify difficulties in control learning. Ten participants acquired the control of the robotic arm in a simulator over ten sessions within seven weeks. Eight movement targets were presented in each of six blocks per session, comprising 432 robotic arm movements. The results suggest that learning varies for each joystick axis, with control of the elbow joint showing the highest learning gain. The base and shoulder joints showed similar learning gains. The wrist joint showed mixed results in terms of use or disuse. Performance increased with retention, suggesting that a longer period of consolidation aided skill acquisition. Practitioner summary: A shortage of skilled operators, costly, and extensive training of heavy machine operators in robotic arm control requires to revisit control skill learning. This study showed that focus of training ought to be shifted to specific joints and training requires to emphasise longer resting periods between training sessions.


Introduction
Bimanual control of robotic arms requires independent control of multiple degrees of freedom (DoF), regardless of whether the joints are hydraulically or electrically actuated.Robotic arm control is a challenging task (Hartsch et al. 2022) and training human machine operators to perform efficiently and accurately is time consuming and costly (Dunston, Proctor, and Wang 2014).In this study, bimanual control refers to the use of two joysticks controlled by the two hands in the (tele)operation of a robotic arm, where the robotic arm is referred to as a single robotic manipulator with four DoF.The control concept, i.e., where joystick movements are mapped to the joint movements of the four-DoF robotic arms, is similar for machines in many industries, such as excavators, forestry machines, and truck cranes (Jin et al. 2021;Westerberg and Shiriaev 2013).Therefore, faster and more effective learning processes for machine operators to learn input-output transformation and control have far-reaching positive effects on productivity in many industries.

Current machine operator training
Machine operators, for example in forestry, are usually first trained in simulators to improve performance without the risk of damaging expensive machines (Harstela 2004;So, Proctor, and Dunston 2014).The control of the robotic arm is taught by experienced instructors (Hartsch et al. 2022).Analogously, experienced instructors in the construction industry also teach apprentices in their training (Bijleveld and Dor� ee 2014).The goal of the training is to quickly bring machine operators to a high level of productivity, whereby forest machine operators typically reach the first productivity plateau after nine months (Purf€ urst 2007(Purf€ urst , 2010)).After training, productivity continues to increase with work experience, and experienced operators are expected to be at least twice as productive consideration was given to the effect of exercise on the sensorimotor skill development of operators.For this purpose, mere performance measurements with respect to productivity are generally not sufficient to assess long-and short-term changes in control behaviour.Longer survey periods are required than are usually used in the productivity-oriented studies.

Learning analysis of robotic arm control
As mentioned above, mastering the control of a robotic arm control, especially in real-world environments, requires long periods of time with many repetitions.However, studies investigating long-term learning over several weeks or months are rare, and when they do exist, these studies focus on productivity improvement (cf., Manner et al. 2020;Purf€ urst 2010) rather than operator skill development.For example, studies of surgeon training have been criticised for using short observation periods that conclude before the emergence of learning plateaus (Papachristofi et al., 2016).Observing skill learning over several days could therefore provide detailed information about the permanent changes in performance and the transient adaptation and forgetting processes on short timescales.
Similar to learning studies in the human sensorimotor domain (Joseph, King, and Newell 2013;Newell 1985;Newell et al. 2009) an exponential learning function may also be useful for analysing skill development in learning to operate a robotic arm.
Learning functions jointly model the motor component of learning to control a robotic arm and the mental operations that underlie this process, namely procedural learning of the control mappings for skill-based behaviour (Arzi and Shtub 1997).The power law of learning (Heathcote, Brown, and Mewhort 2000;Wallace and Newell 1983) and exponential decay functions treat learning as a long-lasting behavioural change, which conflates skill acquisition and forgetting into an averaged performance metric.However, in experiments with a single measurement repetition (Bukchin, Luquer, and Shtub 2002;Goldstain, Ben-Gal, and Bukchin 2007;Joseph, King, and Newell 2013) or short intervals between sessions, the cost of forgetting is not considered.To assesses the effects of short-term adaptation processes in human motor learning Newell et al. (2009) introduced a second time scale into the exponential function.This allowed to model changes during the warm-up period at the beginning of an experimental session and to account for learning between and within sessions.Consequently, the added time scale may be useful to illuminate the challenges in short-and longterm motor learning (Newell, Mayer-Kress, andLiu 2006, Newell et al. 2009), which presumably also occurs when learning bimanual control of a robotic arm.

Specific difficulties in robotic arm control
Previous research has shown that some robotic arm movements are more challenging to learn than others.For instance, horizontal movements are easier to learn than oblique movements, and vertical movements are more challenging than either (Draper, Handel, and Hood 1990).Therefore, it seems useful to study not only the learning process of the entire robotic arm but also of the individual joints.Moreover, Suzuki and Harashima (2008) used Fitts' law to analyse control input movements of a remote controlled excavator, which was controlled with a single joystick-keyboard, as skill indicators.Here, hand movement complexity correlated with increasing skill, and abrupt changes in movement were negatively associated with task performance.Also Manner (2017) found in a field study that joystick use can serve as skill indicator in log loading with a forestry forwarder.Thus, a detailed analysis of operator joystick control movements across learning could reveal specific challenges in motor development.Therefore, the present study focuses specifically on the analysis of joystick activity.Another advantage of joystick activity analysis is the easy accessibility of the signals within heavy machines for the integration of future operator support systems.

Aim and hypotheses
The objective of the current study is to identify motor learning patterns that may challenge the learning of robotic arm control and, more generally, explain performance variability in skill development.It is hypothesised that joystick movements of all joints have similar learning curves, but contribute differently to performance enhancement depending on the complexity of the movement.In addition, due to naïve participants and the rather complex operating requirements, a drop in performance in control ability is expected when the robot is not operated for an extended period of time.

Participants
The study was conducted with ten participants (6f, 4 m).The participants were on average M ¼ 28 (SD ¼ 9.29) years old, right-hand dominant, and normal (or corrected-to-normal) vision.The research was approved by the ethics committee of the Leibniz Research Centre for Working Environment and Human Factors under the approval number 200.All participants consented to voluntary participation and had the right to abort participation at any time without negative consequences.

Simulator
The simulator consisted of a Chicago truck seat, two Thrustmaster Joysticks and a 40" Samsung TV-Screen.The eye point was kept at 1.25 m, so that the horizontal gaze of the participant intersected the screen at a height of two-thirds from the bottom edge.The distance from the eye point was set to 1.10 m (vis.Angl.V ¼ 43.83 � ).The simulator was controlled 2 m behind the participants' seat.The joysticks were mounted to an adjustable frame of the seat base and could be adjusted to the participants' anthropometrics.

Software and simulation
The simulator was based on a Linux system (Ubuntu; Beaver Creek).The simulation was created with ROS (Melodic), controlled by a Cþþ program, and visualised in GAZEBO.The simulated robot arm was the four-joint "Robotis open manipulator "(ROBOTIS Inc., Korea) with a gripper as an end-effector.The manipulator's dimensions were adapted to those of a CH8 knuckle boom, which features in forestry vehicles (i.e., harvesters, forwarders).The simulated environment was a plain white space with a ground plane, shown by a grid with 100 cm line space, which was based on internal dimensions of the simulated model.The robotic arm had a Base joint that allowed for a slewing angle of 342 � .The revolute joints (Shoulder, Elbow, Wrist) had a range of 172 � degree.Each joint was mapped to one of the joystick axes (Figure 1) aligned with the joystick mapping of forest or construction vehicles (cf.Elton, Enes, and Book 2009;Westerberg and Shiriaev 2013).The work range of the robotic arm was 5-100 cm.
The precision movements for lifting and lowering the robotic arm as well as the gripper control was mapped to the right joystick.The rotating and reaching was mapped to the left joystick.The simulator recorded at a sampling rate of 40 Hz.

Visualisation of Fitts inspired task
Within GAZEBO, circles were rendered that served as targets of the robotic arm reaching movement.All targets had the same size.The radius was 5 cm and the circles were coloured in purple or blue.The reaching movement was varied by the position of the circles on the ground, inspired by Fitts' Index of Difficulty.Two circles were present at any given time for the participant.The first circle was on the left side (of an imagery straight line separating the front view of the operator in left and right) the second circle was placed on the right side.Four different spacings of target circles were used.The circles were placed diagonal to each other so that the participants had to manipulate all degrees of freedom of the robotic arm to complete the task successfully.The colours blue and purple indicated the start of the tap series of aiming movements.Blue circles indicated to start on the left side whereas purple indicated to start at the right side with the movement.
The location of the targets was adapted to correspond to common robotic arm path in various application domains i.e., forestry or loading lorries (cf.Ovaskainen et al. 2011).For instance, gripping a tree in front of the machine and felling it to the side where the logs are piled.These movements were abstracted to the placement of the circular targets (see Figure 2), of which the difficulty was systematically manipulated by the distance between the two targets using Fitts Index of Difficulty (for details Soukoreff and MacKenzie 2004).The resulting four difficulties of the movements were Index of Difficulty ¼ 2.5, 3.0, 3.3 3.9.The target coordinates are shown in Table 1.All targets were positioned inside the workspace of the robotic arm.

Procedure and design
The experiment was conducted in a dimly lit laboratory room.After the participants were informed about the study details and provided signed consent, they received instructions on how the two joysticks controlled robotic arm movements.First, they performed a brief training session of four reaching movements with two oversized (diam.15 cm) target pairs to familiarise themselves with the joystick and testing procedure.After this training, the actual task was initiated.The task consisted of six blocks of trials, comprising 72 aiming movements (10 taps i.e., nine movements, with eight target pairs).Once the task was completed, participants filled a demographic survey that included questions of prior experience.Overall, the experiment lasted 3.5 h to 4 h depending on the learning performance.Each participant exercised an average of every 2.1 days over nine sessions.A tenth session was a conducted as a retention session, which took place exactly 14 days after the ninth session.
The experiment followed a 2 (Start) x 4 (Movement Target) x 6 (Block) x 10 (Session) repeated measures design.The presentation of targets was randomised.The tapping start was alternated for each block between left and right so that a single block had eight targets starting either on the left and then on the right side or vice versa.Between each target pair, nine movements with 10 taps resulted in a total of 80 taps and 72 paths per Block.Within one session, participants had to complete 480 taps and 432 movements.Overall, the data comprised 4800 taps and 4320 movements per participant.

Results
The statistical analysis was performed in MATLAB version 2021a and R version 4.1.1.All statistical analyses were performed with an alpha level of .05.

Performance and skill indicators and data preprocessing
The performance and skill indicators were chosen based on those used in Fitts' task and in teleoperation research on robotic arms, both of which analyse aiming movements (cf.Bukchin, Luquer, and Shtub 2002;Mower et al. 2019;Soukoreff and MacKenzie 2004).For each movement, the XY-position of the gripper was determined by the contact of the gripper with the ground plane at zero vertical height.The time (in seconds) between the release of the gripper (from the ground) and tap (on the ground/target) was treated as movement time (in seconds) and submitted as a dependent variable for subsequent analyses.Within each session, the movement time, and the distance (in cm) of the tap at ground contact to the target centre (constant error, CE) was calculated.Additionally, the variability of CE measured as standard deviation of CE (variable error, VE) was used.Movements longer than 2 SD of the mean average movement time of the target within the same block were excluded from further analyses.This reduced the total number of movements from 43200 to 40797.Excluded movements included trials where the gripper was stuck in the ground plane due to a lack of control skills, which created anomalies in the physics simulation.
Control skill was analysed based on the joystick control and the joystick deflection velocity signal used to derive the input acceleration.Before this, the velocity data was filtered with a second order Butterworth-low-pass-zero-phase filter with a cut of frequency of Fc ¼ 6 Hz (f s ¼ 40 Hz, f n ¼ 20 Hz) that is recommend for use in the biomechanical analysis of human movement (Crenna, Rossi, and Berardengo 2021;Winter 2009).The first zero-crossing before and after acceleration peaks was determined for the movements of the different joystick axes.The period from the zero-crossing before and to the zero-crossing after the acceleration peak was defined as control segment in each case.p ¼ 0.23).These analyses support a significant decline for VE (F(8, 81) ¼ 3.91, p < .001)but not for CE (F(8, 81) ¼ 9.25, p ¼ .068).Thus, the accuracy in terms of CE shows a tendency to significantly improve, and the accuracy in terms of VE significantly improves from session one to session nine as displayed in Figure 3.

Joystick input analysis (segments)
The number of joystick acceleration segments was treated as an indicator for control skill.Lower segment count is suggestive of more targeted movements and higher control skill.Segment counts were accounted for each of the four robotic arm joints (see Figure 2, Base, Shoulder, Elbow, Wrist).Segment counts of each joint were submitted to separate one-way repeated measures analyses of variance (ANOVAs) for the factor Session; corrected alpha level of .0125.The factor Session was significant for Base (F(1.88,16.88In other words, control performance was more fluid with completed sessions and participants demonstrated motor learning and furthermore acquired increasing control skill for three out of four joints.

Skill learning (in-depth analysis)
The learning curves of segment count were analysed to determine the exerted control skill of the joints separately (and in detail).Here, a two-time scale power law of learning function was fitted to the data of each participant (cf., Newell et al. 2009) to derive fitted estimates for five parameters.The formula considers slow (across sessions) and fast (within session) learning: The slowlearning parameter indicates general learning, while the fast-learning parameter denotes the decrement at the start of each session, which acknowledges the role of forgetting and adaptation.Forgetting can be regarded as a loss of control skill between training sessions, apparent in the re-uptake (warm-up decrement) of a task after the previous session; adaptation reflects the tuning of the motor system to the controls.
Fast þ Slow Time Scale: The model denotes V inf as asymptote performance and the initial start of slow learning a s and the learning rate − c s .The fast time scale is described by the initial start a j and the respective learning rate (warmup decrement) , −c j. n j is the last trial on day j.With nn j-1 resetting the trial number to 1 at the start of each session to account for the warm-up decrement.The fast time scale with five constant parameters was implemented as described in Newell (2009).The model was fitted with a Levenberg-Marquardt algorithm to the averaged control segment counts on block level across sessions for each participant and joint separately, using least squares to reduce error in estimation between predicted and the observed data.The parameters were bound during the fitting to have the appropriate sign and range (cf.Joseph, King, and Newell 2013).Next, estimates that did not show a positive r 2 fit (see Table 2) were excluded.This is congruent with the plots of learning curves where it is visually evident the Wrist joint data do not vary significantly across sessions (see Figure 4c and Figure 6).Notably, all excluded fits involved the Wrist joint data.This means that the learning model could not account for the Wrist joint data.Thus, all analyses from henceforth exclude Wrist joint data.This reduced the number of learning curves for further consideration from N ¼ 40 to n ¼ 30.The resulting data set comprised estimates for all five parameters (V inf, a s , c s , a j , c j ) and fits for the subsequent analyses of learning.The averaged joint model parameters are shown in Table 2.

Slow, fast learning and skill gain
The average slow learning rate − c s indicated overall skill development i.e., how fast the control of a joint is improved by the participants across all experimental sessions.Low slow learning rates were found for the control of Shoulder and Base joint, which showed that participants learned slower than the Elbow joint.With respect to fast within session learning, the Shoulder joint revealed the highest warm-up decrement (a j ) compared to the other joints.In contrast, the Base joint showed the lowest warm-up decrement (a j ).Both Elbow and Shoulder joints showed high within session learning rates (c j ).The learning curves of the participants are illustrated for each joint separately in Figure 4.

Parameter analysis
In addition, the joints were compared by all (V inf, a s , c s , a j , c j ) model parameters separately with five repeated measures ANOVAs.The start parameter a j of fast learning, the asymptote performance V inf as well as the slow and the fast-learning rate c s and c j did not show significant effects (p > .05).However, a significant effect for the start of the slow learning a s (F(1.16,10.43) ¼ 8.42, p ¼ .013,x 2 p ¼ 0.48) was found and thus overall learning.The estimated marginal means were calculated to make pairwise contrasts with Tukey adjusted p-values of the initial start performance (a s ).It was found that the Elbow joint (M ¼ 4.98, SD ¼ 3.05) was significantly higher than the Base joint (M ¼ 3.37, SD ¼ 2.21, p ¼ .003).Thus, the Elbow joint requires more control inputs at the start of the learning compared to the Base joint.
Furthermore, the actual gain of learned control (a s / V inf ) was calculated by determining the ratio of the initial skill a s and the trained (asymptote) skill level V inf .This ratio indicates the relative amount of learning and, hence, indexes control difficulty.Figure 5 shows that the mean skill gain is greatest for the Elbow (M as/Vinf ¼ 3.14) compared to the Base (M as/Vinf ¼ 1.78).and Shoulder joint (M as/Vinf ¼ 1.80) (F(1.54,13.88) ¼ 10.27, p ¼ .003,x 2 p ¼ 0.53).The loss of control skill at session start was determined by the ratio of the skill at session start and the trained (asymptote) skill level (a j /V inf ) (see Figure 5).Here, the Elbow joint (M aj/Vinf ¼ 0.81) showed on average the greatest loss of the control skill but not significantly different from Base (M aj/Vinf ¼ 0.61) and Shoulder (M aj/Vinf ¼ 0.64) joint (p > .05).

Retention (skill)
Retention session ten compared to session nine showed a significant reduction in control segments for all joints equally (F(1, 9) ¼ 11.24, p ¼ .008,g p 2 ¼ 0.55).Furthermore the joints showed a significant difference in control segments ((F(3, 27) Improvements over blocks were not observed and thus no change of control segments within a session occurred (p > .05).To compare learning rates within session nine and the retention session ten the slow time-scale power law of learning function was fitted.The model did not fit the data and was thus discarded (r 2 < 0).The data suggested a linear relationship.Therefore, a linear model based on ordinary least squares was fitted, that described the data (r 2 > 0) and the slopes were compared as learning rates.The learning rates showed no differences between learning session nine and retention session ten (p > .05).

Individual skill learning
In addition to the parameter evaluation and skill gain analyses, the slow (c s ) and fast (c j ) learning parameters for each participant were ranked in descending order based on their magnitude and the frequency of a joint within each rank was assessed.This analysis aimed to get a clearer picture of the demand that learning the joint control imposes on the learner and to account for individual learning characteristics (slopes) of the joints.The frequencies are shown for the slow learning rate in Table 3 and for the fast-learning rate in Table 4.
All joints (Wrist excluded) were represented within all ranks of slow learning.The Shoulder joint was most frequent in rank three.The Elbow joint was predominantly found in the first and second rank, showing most learning parameters in rank one.The Base joint was evenly distributed over ranks having the modal value in rank two.As example, the individual learning curves for each joint of participant four are illustrated in Figure 6.
The fast-learning parameters showed a similar pattern to the slow learning parameters for the Base joint.The learning parameter of the Elbow joints were most frequent in Rank one and three, whereas the Shoulder joint was most present in rank two.
In conclusion, the Elbow joint showed high learning rates for slow and either high or low fast learning rates.The Base joint showed evenly distributed learning rates for both slow and fast learning rates.The Shoulder joint showed low slow and intermediate to low fast learning rates.
In addition to the ranking of joint parameters, the learning rates were compared within a two-way repeated measures ANOVA to investigate if fast and slow learning rates interact with the controlled joint.No significant interaction of slow, fast learning rate, and joint was found.Nonetheless, a significant main effect was found for the controlled joints (F(2,17.97)¼ 3.58, p ¼ .049,x 2 p ¼ 0.28).Specifically, the Elbow joint (M ¼ 0.33, SD ¼ 0.4) showed higher learning rates than the Base (M ¼ 0.18, SD ¼ 0.29) and Shoulder joint (M ¼ 0.17, SD ¼ 0.27).

Control skill and performance prediction
To make use of the segment analyses in performance assessment, it was analysed which joint relates the most to movement time, constant error, and variable error.Therefore, a linear regression was fitted where each performance variable was predicted, given the number of control inputs measured in segment count.The Base joint was removed from the analysis due to a high variance inflation factor VIF > 10.Movement time was found to be significantly predicted by all remaining joints.Notably, an increase in control segments of Elbow and Shoulder joint increased movement time whereas an increase in control segments to the Wrist joint reduced movement time.The constant error and variable error were significantly predicted by the Wrist joint inputs.Here, an increase of control segments of the Wrist joint raised accuracy (see Table 5).

Discussion
The aim of this study was to analyse learning progress in the operation of a robotic arm to derive recommendations for improving the training of machine operators.To this end, novices were trained over nine days, and a tenth retention session, controlling a four-DoF robotic arm and analysed both short term adaptations and longer-term learning gains.Skill development and performance of the robotic arm movement was investigated both under the assumption that participants would continuously improve their skill and that the joints would contribute differently to performance.

Control performance
In line with Bukchin, Luquer, and Shtub (2002;2007;1994), a significant learning progression (across and within sessions) for all measures of control skill and performance was found.Participants were able to control the robotic arm from the beginning of the experiment with high accuracy and stabilised performance across sessions.However, they did not show improvements in constant error.In contrast, movement time and variable error decreased continuously across sessions with the largest decrease within the first session.Performance further improved in retention in terms of movement time and in contrast to our expectations no performance loss was observed.Accuracy was similar during learning and retention.Overall, the participants' learning strategy emphasised speed over accuracy.

Control skill development
Control skill is reflected in the deliberate bimanual inputs to the joysticks.Therefore, this study focused on the control movement reflected by the deflection of each joystick axis that mapped to the corresponding joint of  the robot arm.The fitted learning curves unveiled different learning rates for each controlled joint.More specifically, the Base joint control appears easy to learn as the required skill gain was lower compared to the Elbow joint.At the same time the Base joint showed a small warm-up decrement.The control of the lower robotic arm via the Elbow joint showed the highest skill gain.
For this joint learning is taking place at high rates, allowing the highest warm-up decrement between joints to be rapidly decreased.The control of the upper robotic arm via the Shoulder joint revealed intermediate learning gains and rates that were lower than the Elbow joint and comparable to the Base joint on slow and fast time scales.Learning to control the Wrist joint showed mixed findings.The Wrist joint data could only be fitted to few participants by the two time scale model.This suggests that learning to control the Wrist joint did not take place for most of the participants.Notably, the retention session showed that the required control input to the joysticks was reduced after 14 days.Thus, control skill further increased without active training which could be regarded to further consolidation of motor movement (Krakauer 2009).Differences in terms of learning rates in retention compared to acquisition did not occur.
The prediction of movement time by the control segments showed that all joints but the Base joint explain movement time variance.Movement time increased with more input actions of the lower and upper robotic arm.This suggests explorative or uncoordinated use of these joints, which could be improved by partial task training in which individual joints are first trained separately.
The result of low skill gain of the Base joint is consistent with the findings of Draper, Handel, and Hood (1990), who found horizontal movements to be easier than diagonal or vertical movements.However, as the slewing motion is concentric and not strictly linear, it was additionally assumed that the concentricity of the movement is responsible for the strong facilitation of control as found in Dreger, L Chuang, and Rinkenauer (2022).It appears that the upper robotic arm element controlled by the Shoulder joint is easier to resume in repeated sessions than the lower element (Elbow).The  Shoulder joint is, to a large extent, controlling both a single (vertical) dimension and is used to bridge longer distances.This may have eased the learning process.The high plateau of the learning function and the high number of control inputs within the entire movement may come from the involvement of the Shoulder joint in the gross movements of robotic arm motions.In contrast, the second arm element and the gripper are responsible for fine control.This is relevant for in-depth motion and movement accuracy that is visually demanding and largely carried out by extending the second element to enable full arm reach and using the gripper.A different mapping of the joystick axis such as mapping elbow and shoulder joint to the same joystick could thus be a remedy to overcome control challenges for in-depth motion.Moreover, these movements are off the concentric orbit and time-consuming due to challenging motions (cf.Dreger, L Chuang, and Rinkenauer 2022).This suggests that learning to control the Wrist joint did not take place for most of the participants, or if so, was following one or more time scales.The low control segment count and fitting problem of the Wrist joint may come from two different control strategies.A first strategy would be to neglect or minimise the use of the Wrist joint as much as possible, due to the required learning effort to skilfully manoeuvre the gripper to the target.This would explain the low number of control inputs to the Wrist joint in skilled performance as well as the low fit of the learning function compared to the other joints.Further this would also explain the lack of improved accuracy across sessions.The second strategy would be to integrate the Wrist control in the movement, which would lead to a higher number of control inputs compared to ignoring the joint.According to the learning curves, it was assumed that both occurred within the data, although with a strong emphasis towards neglecting the Wrist joint.To determine if the disuse of the Wrist joint is a well-developed strategy or simply reflects a freezing of DoFs in the initial phase of learning as proposed by (Bernstein, Nikolai A., 1967;Newell and Vaillancourt 2001) further analyses need to be conducted.

Implications for training and work design
The results suggest that training of the rotational (Base joint) and vertical movement (Shoulder joint) is only indicative for performance measured in terms of time.In contrast, the learner is challenged most by controlling both Elbow and Wrist joint that contribute to both accuracy and movement time.Therefore, we recommend focusing training on guiding the development of the forward model (cf.Wolpert, Diedrichsen, and Flanagan 2011) of the use of Elbow and Wrist joint.To effectively built the forward model the properties of control in terms of the required kinematic transformation from hand to Elbow joint and Wrist joint movement as well as the dynamics need to be trained.This can be achieved by exposing the trainee to isolated movements of the respective joint and further combine the joints.Movements must target a wide range of joint angles to induce variability.The Base and Shoulder joint could be fixed for this purpose.The dynamics can be trained by using different extents of deflection to control the joysticks, which means that participants need to apply different movement speeds.One way to achieve complex kinematics is by deviating from the concentric nature by avoiding rotation in the movement of joint velocity controlled robotic arms (see Dreger, L Chuang, and Rinkenauer 2022).In repetition training, this could be realised with allocating time on movements that require to reach ahead or to the base of the robotic arm.For example, in forestry, these movements would be gripping movements ahead and felling motions close to the base.In construction, the digging location could be located either close or directly in front of the machine.

Limitations
The aim of this study was to assess skill development via control inputs, as manual input determines the movement of the robotic crane.Nevertheless, the authors are aware that the general analyses of joystick-inputs have limitations in explaining motor behaviour that is synthesised from numerous basic actions.Therefore, the analysis of individual styles may be necessary to make training more effective.In addition, the limited visual fidelity of the virtual experimental setup used could be responsible for the continuous high constant error.

Conclusion
Learning the control of a four-DoF robotic arm with forward kinematics shows continuous improvements for all joints across the experimental session, although different learning curves were observed.To conclude, curvilinear (rotating) motions are easily learned while rectilinear precision movements challenge the operator.Regarding fine control, it was assumed that strategies such as deliberately reducing of DoFs were applied to reduce the control effort as much as possible.That is in line with theories that propose a reduction of active degrees of freedom in motor learning (Mitra, Amazeen, and Turvey 1998;Newell and Vaillancourt 2001).Future digital learning aids and conventional training ought to focus on supporting aiming in the depth of the 3D space with the robotic arm and facilitating the precision of the gripping.

Figure 1 .
Figure 1.Joysticks with control mapping (left).The arrows indicate the joystick movement direction and the effect on the controlled joint.Robotic arm with movement directions and labels (right).

Figure 2 .
Figure 2. Shown are four target pairs that indicated the movement start left (a, blue) and indicating the movement start on the right (b, purple).
Note X ¼ depth and Y ¼ lateral.

Figure 3 .
Figure 3. Left: average movement time in seconds (s) per experimental session.Error bars show the standard error of the mean.Right: average constant error (CE) in cm of movements per experimental session.The error bars show the variable error (VE) which is the standard deviation of the constant error.

Figure 4 .
Figure 4. Mean segment count of each participant (ID) for each block displayed for the Base (a), the Elbow (b), the Wrist (c), and the Shoulder (d) joint.Fitted are the learning curves of the two-time scale model (straight lines) to the empirical data (dots).Six blocks equal one session (S).Displayed are nine Sessions (S1-S9) comprising 54 experimental blocks.

Figure 5 .
Figure5.Averaged slow learning ratio (a s /V inf ) for each joint (left).Averaged fast learning (a j /V inf ) ratio for each joint (right).Arrows denote the standard error of the mean.� Note.Wrist joint data not included due to a low fit of learning curves.

Figure 6 .
Figure 6.Illustration of segment count across sessions for each controlled joint of participant 4.

Table 2 .
Mean model parameters and standard deviation listed for each joint.Wrist joint data was excluded from analysis due to low overall fits.

Table 3 .
Ranked frequencies of the joints based on the individual ranking of the slow learning rate (c s ).

Table 4 .
Ranked frequencies of the joints based on the individual ranking of the fast learning rate (c j ).

Table 5 .
Regression model parameters predicting movement time (MT), constant error (CE), and variable error (VE) from joystick input segments.