Category: 3. Business

Speaking on the Office Hours: Business Edition podcast, Farley said Ford had 5,000 open mechanic positions that it hasn’t been able to fill, despite an eye-popping $120,000 salary—nearly double the American worker’s median salary.

And it’s not just Ford, added Farley. The carmaker’s struggle to fill jobs that require training and manual labor are indicative of a general shortage for manual-labor jobs in the U.S., he added.

“We are in trouble in our country. We are not talking about this enough,” Farley told host Monica Langley. “We have over a million openings in critical jobs, emergency services, trucking, factory workers, plumbers, electricians, and tradesmen. It’s a very serious thing.”

While President Donald Trump has centered his economic agenda on bringing manufacturing back to the U.S., there remains a gap between the number of factory jobs open and the number of people willing to fill them.

There were more than 400,000 manufacturing jobs open as of August, according to preliminary data from the Bureau of Labor Statistics, despite a 4.3% unemployment rate, which is higher than in previous years. A 2024 study from the Manufacturing Institute and Deloitte also found more than half of the 200 manufacturing firms surveyed said recruiting and retaining workers was their top struggle.

Yet, Farley said jobs in the trades like those at Ford “made our country what it is,” and allowed people like his grandfather—who worked on the company’s flagship Model T and was employee 389 at the company—to have good lives.

Farley said the company is doing better on wages. It got rid of the lowest tier of its wage scale, and agreed to give workers a 25% salary bump over four years as part of its agreement with the United Auto Workers union in 2023. 

Still, part of the problem for the shortage of manufacturing jobs is the lack of education and training, according to Farley. He noted, for example, learning to take a diesel engine out of a Ford Super Duty truck takes at least five years. The current system is not meeting the standard, he added.

“We do not have trade schools,” he said. “We are not investing in educating a next generation of people like my grandfather who had nothing, who built a middle class life and a future for his family.” 

To be sure, younger people may be leading the charge on filling the gap in manufacturing positions. Gen Z is increasingly straying from the traditional college path and attending trade schools in an effort to avoid cumbersome student loans while also snagging a well paying job. 

Enrollment in vocational school jumped 16% last year, rising to the highest level since National Student Clearinghouse started tracking data in 2018, Fortune previously reported. However, the top jobs paying more than $200,000 per year mostly require advanced degrees, according to a study by job platform Ladders. 

Skims, founded by reality TV star and entrepreneur Kim Kardashian along with CEO Jens Grede, said on Wednesday it had raised $225mn in new capital, valuing the shapewear label at $5bn.

Kardashian’s ventures, including her cosmetics brand SKKN, have attracted young shoppers and benefited from her vast social media following. Similarly, other celebrity-backed brands have also drawn venture capital investment, as firms bet on the marketing power and built-in audiences of high-profile founders to drive consumer demand.

Elf Beauty agreed to buy Hailey Bieber’s makeup and skincare brand, Rhode, for about $1bn earlier this year, while Rihanna-backed Fenty Beauty and Khloé Kardashian’s Good American have also drawn venture capital funding.

Skims said it plans to use the new capital to broaden its intimates and shapewear lines, expand further into apparel and activewear and enhance its retail presence and international growth.

“This milestone reflects continued confidence in our long-term vision and coupled with disciplined execution, positions Skims to unlock its next phase of growth,” Grede said in a statement.

Skims, founded in 2019, said it was on track to exceed $1bn in net sales in 2025. Earlier this year, Coty sold a 20% stake in Kardashian’s beauty brand to Skims, consolidating the two businesses under a single brand.

The company, known for its focus on inclusive sizing, now operates 18 retail stores in the US and two franchise locations in Mexico. Skims said it was laying the groundwork to be a predominantly physical business over the next few years.

The company has also forged a partnership with sportswear giant Nike to launch activewear for women.

The latest fundraising in the apparel company was led by investment giant Goldman Sachs Alternatives with participation from BDT & MSD Partners’ affiliated funds.

SAN BRUNO, Calif. — The self-driving car company Waymo said Wednesday it would begin offering rides on freeways for robotaxi customers in Los Angeles, Phoenix and the San Francisco Bay Area in a significant step forward for autonomous vehicles.

Previously, Waymo has limited its robotaxis to city streets, saying it wanted to be sure its technology was safe before deploying it at the faster speeds of freeways. But after years of testing, the company said it now believed it was ready.

The ability to travel on interstate highways and expressways has been one of the missing puzzle pieces for self-driving technology since scientists began working on it decades ago, alongside such challenges as snowy weather and vandalism.

“This has been a long time in the making,” Waymo co-CEO Dmitri Dolgov said in a briefing with reporters.

“Freeway driving is one of those things that’s very easy to learn but very hard to master when we’re talking about full autonomy without a human driver as a backup, and at scale. So, it took time to do it properly,” he said.

Waymo, a spinoff of Google, appears to be the first company to offer fully autonomous freeway rides, without a human specialist in the car, to fare-paying riders in the United States, company spokesperson Sandy Karp said.

Wendy Ju, an associate professor of information science and design tech at Cornell University, said that freeways are a more controlled environment in some respects — fewer pedestrians, for example — but also riskier in other ways than city streets.

“The higher speed does pose a much higher risk,” she said. “In order to predict what’s going to happen 10 seconds from now, the car has to sense what’s happening much farther down the road.”

Ju, who has worked as a consultant in the past for autonomous vehicle companies but not for Waymo, said she has “guarded optimism” about the safety of the company’s technology.

In a 40-minute test ride with an NBC News reporter last week, a Waymo robotaxi traveled up and down freeways in Northern California without incident: merging on and off, obeying the speed limit, following at a safe distance and handling congestion slowdowns. At one point, it avoided a human driver who tried to cross a solid white line at an exit ramp.

The competition to deliver robotaxi services is heating up. This summer, Tesla began offering rides in Austin and in the San Francisco Bay Area with a prototype of its self-driving software. And although Tesla still has employees in each of its cars, CEO Elon Musk has said he plans to offer a rider-only service soon — something Waymo did in 2019.

Zoox, a self-driving subsidiary of Amazon, has a rider-only service in Las Vegas that serves a set of fixed pick-up and drop-off locations, with plans to expand. And several Chinese tech companies are racing ahead with robotaxi projects of their own.

Waymo’s decision to start using freeways coincides with major expansion plans. The company has announced plans to more than double the number of cities it operates in, with some cold-weather cities, such as Denver and Detroit, on its list. The company said Wednesday it would begin curbside service at San Jose’s airport, the second major airport to accept Waymo after Phoenix. The company is preparing to add a new van to its fleet called the Zeekr RT to supplement the Jaguars that it uses. And earlier this year, Waymo signed a partnership with Toyota to explore putting Waymo’s technology into personally owned vehicles.

Robotaxi services such as Waymo’s and Tesla’s work much like ridehailing from Lyft or Uber, with customers ordering a ride on a smartphone app by entering a destination and accepting a fare determined up front. But instead of humans behind the wheel, software generally drives the vehicles aided by cameras and, in the case of Waymo, other sensors such as lidar.

But safety concerns remain paramount. Cruise, a former subsidiary of General Motors, has stood as a cautionary tale since 2023 when California revoked its permits to operate a fleet of robotaxis, following a crash in San Francisco in which one of Cruise’s cars dragged a pedestrian for 20 feet while she was pinned underneath the vehicle. A Waymo recently struck and killed a cat in San Francisco, and its vehicles have sometimes been sitting ducks for arson or vandalism.

Waymo has not had a human fatality, and in July, the company said it had passed more than 100 million miles without a human behind the wheel.

Srikanth Saripalli, the director of the Center for Autonomous Vehicles and Sensor Systems at Texas A&M University, said he thinks Waymo’s technology is as good as a human driver and he praised the company’s safety record. But he said Waymo still needs to prove that it can safely handle situations outside California and the Sun Belt.

“Their safety record among all autonomous companies is amazing, but when you compare them to humans, they’ve been very careful about the kind of cities they want to drive in,” he said.

“In Phoenix, the roads are all perpendicular, the roads are nice, the weather is nice, and it still took them almost a decade to get to a freeway,” he said. He has worked as an industry consultant but not for Waymo.

About 18% of all traffic fatalities occur on interstate highways or other freeways and expressways, according to data compiled by federal safety regulators.

To tackle highways, Waymo said it had studied hazards such as aggressive cut-ins, construction on shoulders, hydroplaning and high-speed collisions. It said it has been giving freeway rides to employees and their guests for more than a year. And even now, the company said it would expand its use of freeways gradually as it watches for how the vehicles respond, rather than making it available to all of its customers at once.

The company said its robotaxis would stick to the speed limits on freeways, as they do city streets, even if human drivers around a vehicle are breaking the speed limit.

“The Waymo driver goes up to the posted speed limit. So, for example, if the speed limit is 65, that’s the maximum speed limit, and it does not exceed it, unless in extraordinary circumstances,” said Jacopo Sannazzaro, a product manager at Waymo.

Freeway capability is an important part of a car service, especially in cities such as Los Angeles and Phoenix, where it’s common for daily car trips to include at least some time on an interstate. Sticking to local streets often means a longer ride.

And while some traffic regulators and city-dwelling critics have braced for the possibility that robotaxis will add to traffic congestion, Waymo said it believes those concerns are unfounded.

“We do not expect Waymo to make congestion worse on the freeways,” said Pablo Abad, a Waymo product manager. He said the company had “not seen any impact on the congestion in the service areas where we operate.”

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Vladimir Putin has approved the sale of Citigroup’s Russian business, as the US bank continues to wind down its exposure to the country in the wake of its war in Ukraine.

In a statement on Wednesday, Putin’s office said it had approved the sale of Citi’s Russian subsidiary to Moscow-based investment bank Renaissance Capital for an undisclosed sum.

Citi confirmed the potential sale but did not name Renaissance as the buyer, adding that it would be subject to additional approvals. Renaissance confirmed the sale to the Financial Times, without providing further details.

The announcement brings the Wall Street bank closer to a full exit from Russia. Citi first announced plans to exit the country’s retail market in April 2021 as part of a wider retreat from consumer banking outside the US by chief executive Jane Fraser.

The bank then tried to sell its Russian business but faced a limited pool of buyers due to western sanctions imposed on the country as a result of Putin’s full-scale invasion of Ukraine in February 2022.

Citi said in August 2022 that it would wind down its retail and commercial banking operations in Russia after Putin banned foreign entities from “unfriendly” countries that imposed sanctions on Moscow over the war from selling their stakes in Russian companies, which further complicated the process.

Since then, Citi has closed nearly all of its institutional banking services in Russia and in 2024 closed its last retail branch in Russia and deactivated all of its debit cards.

This year, the Kremlin approved the sale of Goldman Sachs’ Russian subsidiary to an Armenian investment fund, shortly after Dutch lender ING also announced its exit.

Cucumber cultivars characterized by NFR

To demonstrate the potential effects of cultivar-dependent variation in shoot architecture on cucumber yield, we selected four commercially available Japanese cultivars (‘Josho’, ‘S-30’, ‘G-Flush’, and ‘Yusho’), which are recognized for their different levels of vigor. The experiment was conducted in 2021, with plants grown in a greenhouse under the conditions shown in Fig. 1. We assessed node numbers and found that ‘Josho’ had formed more nodes than all other cultivars by the end of cultivation period (Fig. 2A). Then, we analyzed changes in the NFR, calculated as the number of nodes formed per unit of daily average temperature, throughout the experiment (Fig. 2B). The NFR was higher in ‘Josho’ than in the other cultivars, particularly ‘S-30’ and ‘Yusho’. The mean NFRs were 2.2 × 10^–2 nodes °C^–1 day^–1 for ‘Josho’ and approximately 1.5 × 10^–2 nodes °C^–1 day^–1 for the other cultivars. A similar trend was observed in a separate short-term experiment conducted in a different greenhouse and year (Fig. S2), suggesting that the observed differences are cultivar-dependent rather than condition-dependent. We also noted cultivar-specific variation in the position of open female flowers along the stem. In ‘Josho’, open female flowers tended to appear at nodes farther from the shoot tip compared to the other cultivars (Fig. S3), implying more rapid stem growth. These findings indicate that the cultivars are distinguishable by their shoot architecture, particularly in terms of NFR and node number.

Comparison of fruit yield among cultivars

Final fresh yield was highest in ‘Josho’ (approximately 36.3 kg m^–2), consistent with its elevated NFR compared to the other cultivars (Fig. 2C). The number of harvested fruits followed a similar pattern: ‘Josho’ produced around 360 fruits per unit area, whereas the other cultivars yielded approximately 300 or fewer (Fig. 2D). Mean harvested fruit weight was around 100 g fruit^–1 (Fig. S4A). The ratio of aborted fruits, which were excluded from yield calculations, was higher in ‘Josho’ (approximately 7.4%) than in the others (1.0% or less, Fig. S4B). Female flowering rates were broadly similar across cultivars, although ‘G-Flush’ exhibited a slightly lower rate (Fig. S4C). These findings suggest that yield differences were primarily driven by variation in node formation, rather than by fruit abortion or female flowering frequency in the cultivars examined.

DM distribution

Next, we compared the cultivars in terms of how DM was partitioned to fruit. The experimental period was divided into five terms based on the timing of destructive measurements (term 1: 0–45 DAT; term 2: 45–66 DAT; term 3: 66–105 DAT; term 4: 105–142 DAT; term 5: 142–228 DAT), and DM partitioning was analyzed for each term. As shown in Fig. 3A, DM partitioning in ‘Josho’ during the first term was 0.15 g g^–1 and remained around 0.5 g g^–1 in later terms. In contrast, the other cultivars, particularly ‘Yusho’, showed higher early DM partitioning (approximately 0.2 g g^–1) but failed to maintain these levels beyond the third term. In the final term, DM partitioning in ‘S-30’, ‘G-Flush’, and ‘Yusho’ declined to approximately 0.4 g g^–1. As a result, the cumulative fruit dry yield relative to TDM in ‘Josho’ continued to increase, reaching 0.48 g g^–1 by the end of the experiment. In comparison, the other cultivars peaked at around 0.44 g g^–1 on 105 DAT and declined thereafter (Fig. S5A). Additionally, DM content per fruit was comparable across cultivars, confirming that fruit quality was consistent (Fig. S5B). Together, these results indicate that reduced node formation suppressed DM partitioning to fruit.

DM productivity

Although yield differences among the cultivars could be attributable to variation in both shoot architecture and DM productivity, this did not appear to be the case in the present experiment. TDM across the five experimental terms was largely comparable among cultivars, except during the third and final terms (Fig. 3A). Notably, ‘S-30’, but not ‘Josho’, tended to exhibit higher TDM. In the third and final terms, TDM in ‘S-30’ reached 417 and 1,484 g m^–2, respectively, while the values for ‘Josho’ were 348 and 1,431 g m^–2. ‘Yusho’ showed the lowest TDM in the final term (1,329 g m^–2). As LAI was maintained at approximately 2.4 m² m^–2 across all cultivars, cumulative IL was estimated to be similar among cultivars (around 650 MJ m^–2; Fig. S6). Consequently, LUE varied as shown in Figure S7, with ‘S-30’ exhibiting the highest LUE (4.26 g MJ^–1), followed by ‘G-Flush’ (4.08 g MJ^–1), ‘Josho’ (4.07 g MJ^–1), and ‘Yusho’ (3.86 g MJ^–1). Similar trends were observed in TDM at the end of the experiment (Fig. 3B). The discrepancies between yield and TDM or LUE suggest that DM productivity had only a marginal effect on yield differences among cultivars. Indeed, correlation analysis of the yield components revealed no significant relationship between yield and DM productivity. In contrast, a strong correlation was observed between node formation and fruit yield (Fig. 4). These findings demonstrate that cultivar-dependent shoot architecture can influence fruit yield independently of DM productivity in cucumber plants.

Transcriptomic diversity among cultivars

In cucumber plants, nodes are produced by the SAM while flowers develop from the leaf axil at each node [3], underscoring the importance of SAM activity for yield. Certain meristem identity-regulating genes determine whether the SAM exhibits determinate or indeterminate growth in Cucumis sativus [3]. These findings suggest genetic diversity among the shoot tips of the four cultivars. To explore this possibility, we performed mRNA-seq using RNA extracted from their shoot tips. We identified more than 500 differentially expressed genes (DEGs), assessed using the criteria |fold change|> 2 and false discovery rate (FDR) < 0.05, in pairwise comparisons between ‘Josho’ and the other cultivars (Figs. 5 and S8, and Dataset S1). We also examined the expression of genes previously reported to regulate SAM identity (Table S1), including PEBPs involved in floral meristem induction (CsFT, CsTFL1, CsTFL1d); subunits of protein complexes including CsFT or CsTFL1/CsTFL1d (CsNOT2a, CsFD, CsFDP, CsGF14-3, CsGF14-5); and transcription factors and their interactors involved in SAM maintenance and floral meristem differentiation (CsLFY, CsWUS, CsUFO, CsHAN1, CsHAN2, CsSTM, CsBP). We initially expected some of these genes to meet the criteria for differential expression, but none qualified as DEGs. However, CsTFL1 in ‘S-30’, CsGF14-3 and CsGF14-5 in ‘G-Flush’, and CsBP in all three cultivars showed modest reductions (approximately 30% on average) compared to ‘Josho’ (Dataset S2). To further investigate physiological differences, we conducted Gene Ontology (GO) enrichment analysis of DEGs common among ‘S-30’, ‘G-Flush’, and ‘Yusho’. We selected 42 downregulated and 16 upregulated genes and analyzed their enrichment in biological processes. Only one GO term was significantly enriched among upregulated genes, related to carbon fixation. This term included two DEGs: CsaV3_4G001210, which encodes a putative CP12 domain-containing protein, and CsaV3_6G048750, a putative RbcX homolog (Fig. S9A and Datasets S3 and S4). In contrast, downregulated DEGs were enriched for GO terms associated with heat response, cell division, and β-oxidation. These included putative condensin proteins (CsaV3_UNG044290, CsaV3_UNG075600, CsaV3_UNG088700, CsaV3_UNG225770), heat-shock proteins and co-chaperones (CsaV3_1G035820, CsaV3_1G035830, CsaV3_1G044020, CsaV3_3G006720, CsaV3_5G026520), a multiprotein bridging factor 1c (MBF1c) homolog (CsaV3_2G002310), an ankyrin repeat-containing protein (CsaV3_1G010260), and 3-hydroxyacyl-CoA dehydrogenase proteins (CsaV3_6G023960, CsaV3_6G024070, CsaV3_024110) (Fig. S9B and Datasets S3 and S4). These findings indicate that the shoot tips of the four cultivars differ at the transcriptional level, which may reflect genetic factors underlying the observed variation in NFR.

Experimental setup

The experimental setup included a (Delta.3) haptic robot (Force Dimension, Switzerland) placed on a desk next to a display monitor (Fig. 1). The device is capable of measuring positions and providing forces up to 20.0 N in the three translational directions (x, y, and z axes, Fig. 1). The device control was implemented in C++, operating at 4 kHz. Motion data was recorded at 1.67 kHz.

The pendulum game

The game, inspired by the work of [44] and created in Unity 3D (Unity Technologies, USA), consisted of controlling a virtual pendulum to hit moving targets approaching the participant. The pendulum consisted of a black ball (pivoting point) and a red ball (pendulum mass), with a rigid link connecting both balls, as shown in Figs. 1 and 2. The pendulum’s pivoting point could be moved horizontally and vertically (y and z axis in Fig. 2) by displacing the haptic device’s end-effector (black ball in Fig. 1 Right; 1:1 movement mapping). The pendulum could only swing in the vertical plane (y–z), and therefore, movements of the haptic device in the x-direction were not mapped to the pendulum.

The task consisted of hitting vertical targets with the pendulum mass. The targets were located on walls approaching the participants in the x direction, i.e., perpendicular to the screen plane. The walls were spaced by 1 m and their speed was set to 1 m/s. The targets could appear in three different positions: the center point of the wall or ± 0.12 m to the right/left. The target’s width was 0.02 m, and the pendulum ball and pivoting point diameter were set to 0.03 m.

By moving the pendulum pivoting point through the device end-effector, participants influenced the swing of the pendulum, which behaved according to the equation of motion of a simple pendulum:

where y and z are the horizontal and vertical coordinates of the robot end-effector position and (ddot{theta }) the angular acceleration of the pendulum’s internal degree of freedom (DoF). Since the internal DoF was located at the pendulum’s pivoting point, (theta ) was defined relative to the pendulum rod, as illustrated in Fig. 2. The robot’s coordinates were referenced with respect to its initial position after calibration, similar to the one shown in Fig. 1right. The pendulum mass was set to (m = 0.6) kg, the rod length to (l = 0.25) m, gravity to (g = 3.24) m/(s^2), and the constant (c = 3.00e^{-6}) N(cdot )s/rad. These parameters were adjusted and chosen in order to minimize passive stabilization of the pendulum and maintain task difficulty.

As the pendulum crossed a wall, a score based on the absolute distance of the pendulum’s mass to the center of the target in the y-direction (|Error|) was briefly displayed for 0.5 s to provide feedback regarding participants’ performance. The score ranged between 0 and 100 and was calculated as:

Each phase of the experiment was organized into wall sets, with 20 walls presented per set (see the Study protocol Section). A final score, based on the average of all 20 scores, was shown at the end of each set to inform participants of their overall performance in that set.

Haptic rendering and haptic guidance

To enhance the ecological validity of the task — ensuring the experimental conditions closely replicate real-world scenarios — we incorporated haptic rendering throughout the whole experiment, i.e., the provision of the forces originating from the pendulum dynamics on the device end-effector. Participants could feel the pendulum force dynamics ((F_{rod})), calculated as:

using the same constants as in Eq. (1).

Participants allocated to the Experimental group were also provided with haptic guidance during training to physically assist them in the target-hitting task. This was achieved by first calculating an optimal end-effector trajectory between the pendulum state at the moment of target wall collision and the target at the following wall, and then enforcing this trajectory using a Proportional-Derivative (PD) controller.

The optimal end-effector trajectory was calculated every time the pendulum hit a target wall using the ACADO toolkit [45]. The cost function included terms to maximize accuracy (i.e., minimize the distance between the pendulum ball and the next target’s centerline), maximize the pendulum stabilization (i.e., penalizing the velocity components of the pendulum ball), and minimize end-effector acceleration based on the current state of the pendulum, as described in the Appendix B.

The PD controller aimed to minimize the distance between the end-effector and the reference trajectory in the y-direction at each time point by applying a guiding force (F_{HG}) at the end-effector. We only provided guidance in the y-axis as it was sufficient to achieve the target-hitting tasks. By not guiding in the z-direction, we also reduced the potential masking effects of the guidance on the perception of the haptic rendering of the pendulum dynamics. The resulting equation for the PD controller is as follows:

where the y-axis error between the actual and the reference trajectory was denoted as e(t), and the proportional ((K_p)) and derivative ((K_d)) gains were set to 75.0 N/m and 15 N(cdot )s/m, respectively. The guiding force was added to the haptic rendering force ((F_{rod}) in Eq. (3)). The order of magnitude of the guidance force was around four times the haptic rendering.

Participants

Forty-two unimpaired participants performed the experiment. Data from two participants were excluded from further analysis. One participant exhibited errors three standard deviations higher than the average of all participants. We encountered a technical problem when recording the data of a second participant, leading to missing data within the dataset. Thus, 40 participants were included in the analysis (age = (27 pm 6,yrs); 19 identified as female, 21 identified as male; no participants identified as non-binary). The target sample size of approximately 40 participants was determined based on a power analysis, as detailed in Appendix A. Handedness was assessed using the Short-Form Edinburgh Handedness Inventory [46], resulting in 35 right-handed, four left-handed, and one ambidextrous participant. All participants signed the informed consent to participate in the study, which was approved by the TU Delft Human Research Ethics Committee (HREC).

Participants were allocated into two training groups: Control or Experimental. The Experimental group received haptic guidance during some parts of the training phase (see the Study protocol Section), while the Control group practiced without any physical assistance. To promote an even distribution between groups, we used an adaptive randomization method. We randomly allocated the first twenty participants into one of the two training groups and distributed new ones into each group based on their sex and results from the Locus of Control questionnaire (see the Outcome metrics Section), similar to [7]. The Locus of Control was employed as it directly relates to the perception of control, which aligned with the groups’ training conditions (guidance vs. no guidance).

Study protocol

The experiment was conducted in two locations: Delft University of Technology, Delft, the Netherlands, and Alten Netherlands B.V., Rotterdam, the Netherlands. The experimental setup and protocol were identical in both locations. Minor environmental differences (e.g., room layout, lighting) were not expected to systematically affect performance. The overview of the experimental protocol can be found in Fig. 3.

The experiment took place in two sessions on different days, with one to three days between sessions, following recommendations to evaluate motor learning [3]. At the beginning of the first session, participants were invited to sit at the set-up table. The chair height was adjusted based on personal preferences to ensure a comfortable arm movement within the robot’s workspace. The haptic device was placed at a reachable distance with a relaxed posture on the dominant hand’s side. The screen was placed on the opposite side of the device in front of the participant. Participants were informed about the goal of the pendulum task at the beginning of the first session. No extra information was given during the rest of the experiment.

The experiment began by inviting participants to fill out the first block of questionnaires, including demographic data collection and the questionnaires to quantify the personality traits (see the Outcome metrics Section). Participants were then invited to familiarize themselves with the haptic device and the virtual environment for 40 s. During this familiarization phase, they were asked to move the pendulum freely in the virtual environment without loading any target. They could observe the pendulum moving and feel the haptic rendering of the pendulum dynamics through the haptic device end-effector. Once the 40 s were over, participants were instructed again about the game goal: move the pendulum such that the red ball hits each wall as close as possible to the target’s center. They were then invited to play a first set of 20 targets.

Once the familiarization was completed, the main experiment began. Participants underwent three main phases during Session 1: baseline, training, and short-term retention. During these phases, participants performed one or three different tasks. The main task consisted of playing 20 targets in a specific order. Each time the main task was played, targets were set in the same sequence of positions, except during the training phase, in which some of the sets were mirrored (further explained later in this section). Participants also played two transfer tasks to asses the generalization of the acquired skill. Those tasks were similar to the main task but included slight design variations. In the position transfer task, the targets were randomly re-located (still appearing every 1 s) to introduce new movement sequences. During the dynamics transfer task, the target positions were kept the same as during the main task, but the pendulum dynamics were changed. While the appearance of the pendulum did not change, the pendulum rod length was reduced by 70% in Eq. (1) and (3). This variation affected the pendulum’s natural frequency, which increased from 0.573 Hz to 0.685 Hz. For both transfer tasks, the goal remained the same: Use the pendulum mass to hit each target.

The baseline included two sets of 20 targets for the main task. The game did not stop between sets within the same task, but there was an extended pause of three seconds in which no new targets were loaded. After the second set was finalized, participants completed a new set of questionnaires to assess motivation and agency. To keep our analysis focused on answering the listed hypotheses, the analysis of motivation and agency are out of the scope of this work. Participants were then asked to play the game two more times, for two sets of the position transfer task and two sets of the dynamics transfer task, with an on-demand break offered between the two tasks.

After the baseline trials were complete, participants began the training. They completed two rounds of 15 sets of the main task of 20 targets each. Participants had the opportunity to take a break between rounds. During training, the Experimental group received haptic guidance on top of the haptic rendering. However, to avoid participant reliance on the guidance, guidance was removed during the first set and once every five sets (“catch sets”). In addition, to avoid only learning the specific movement patterns and target positions, mirrored sets were interspersed within the non-catch sets for both groups. The position of the targets during these sets was mirrored with respect to the walls’ y-axis. The distribution of “catch sets” and mirrored sets can be found in Fig. 3. Participants were informed that they might or might not be assisted during training to promote active participation. The Control group only experienced the haptic rendering from the pendulum dynamics during training.

Immediately following the last training set, participants took a 10-minute break. During this time, they filled in a new set of questionnaires. The Experimental group was asked questions about their subjective experience with the robotic guidance, i.e., how disturbing, frustrating or restrictive it was perceived (see the Outcome metrics Section). Following the break, a washout set of the main task was conducted by both groups to mitigate any temporary effects from training with haptic guidance, e.g., “slacking” [47].

Right after the washout set, participants performed the short-term retention phase. The structure was similar to the baseline but without the questionnaire. Participants returned after one to three days to perform a long-term retention phase, which was structured identically to the baseline tests.

Outcome metrics

Personality traits questionnaires

Before the familiarization phase, participants completed a battery of questionnaires assessing the selected personality traits to study. These personality traits included the LOC scale [34], the Transform of Challenge and Transform of Boredom sub-scales from the Autotelic personality questionnaire [33], and the Achiever and Free Spirit sections of the Hexad Gaming style questionnaire [39]. All the questionnaires, except for the LOC, were formed by seven-point-based questions and normalized between 0 and 1 (low to high level of trait/characteristic). The LOC questionnaire was formed by 23 multiple-choice questions, and the overall score for the whole questionnaire ranged from 0 to 23. To improve interpretability and facilitate later modeling (see the Statistical analysis Section), this range was normalized from -1 to 1 to reflect the continuum between Internal LOC (-1) and External LOC (1), which are widely recognized classifications in literature and commonly used to interpret behavior. In addition, the LOC scores usually follow an approximate Gaussian distribution centered near zero. This makes this range statistically practical and close to the centered scale. Internal and external LOC differ in whether outcomes from an action are attributed to oneself or external circumstances, respectively. The employed questions for all the questionnaires can be found in the Appendix C.

Human-robot interaction experience questionnaire

Three questions were filled in by only the Experimental group after training. These questions related to frustration, disturbance, and restrictiveness perception during the training (see Appendix C). They were answered on a seven-point scale, which was then normalized between 0 and 1 (low to high).

Task performance: absolute error

To assess motor learning, the distance between the pendulum’s mass position and each target’s centerline at the time of pendulum-wall contact was calculated (|Error|), in meters. This was used as our performance metric and one value per wall was obtained.

Human-robot interaction: interaction force

To assess participants’ interaction with the haptic device, the human-robot interaction force was estimated. This estimate was computed using Reaction Torque Observers based on recorded motor currents and the robot dynamic model, as implemented in [44]. For the analysis, we used the average force per target in Newtons. We calculated this average force within the interval from consecutive midpoints between walls.

Statistical analysis

To evaluate the hypotheses outlined in the Introduction Section, we used Linear Mixed Models (LMMs). These models were fitted using the (texttt{lmer}) function from the (texttt{lmerTest}) package in (texttt{R}). Statistical significance was set at (p < 0.05), and p-values were adjusted for multiple comparisons using Bonferroni correction.

The employed LMMs were selected as outlined in Appendix D. We group them throughout the current section depending on the hypotheses they are tailored to evaluate. Table 1 summarizes the variables that can be included in the models. Task performance (|Error|) and human-robot interaction force (|IntForce|) metrics were analyzed as dependent variables depending on the model. Logarithmic transformations were applied to correct skewed distributions and achieve normality requirements.

Models to infer motor learning (M1.1 and M1.2)

To evaluate the impact of personality traits and the training condition on motor learning outcomes across different experimental phases (related to hypotheses H1 and H2) we employed two models, one for each dependent variable. These models include independent variables regarding the training group, the task type, the stage, and the personality traits (see description in Table 1). Given the extensive number of variables and potential interactions, a stepwise comparison between models of different complexity was performed using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to prevent overfitting and ensure stability (see Appendix D).

For the performance metric (|Error|), the following model (M1.1) with the smallest AIC and BIC was chosen:

In this equation, the normalized and centered results from the Transform of Challenge ((TC_c)) and Locus of Control (LOC_c) were included as traits of interest, as others did not show statistical significance during model selection. Therefore, the hypothesis related to the Achiever gaming style (H1.3) is not supported by the data. A nested random effect for wall index (wIndex : NewWalls) was adjusted to account for changes in wall positioning during the position-based transfer task.

A similar model (M1.2) was developed for the interaction force metric. Notably, this model included an additional interaction term, (Group times LOC_c times Stage). When compared with other configurations, the model with this extra interaction led to a lower AIC and slightly increased BIC (see Appendix D). In view of these competing results, previous literature was used to guide the choice. This extra relationship was considered of interest as LOC was found to correlate to the interaction force metric during the training phase when the haptic guidance was active (see [43]). The final model has the form:

Note that while this model does not include the Free Spirit gaming style, results from an alternative model (see Appendixes D and E) suggest a potential relationship between this trait and interaction force outcomes, which can be considered of interest for hypothesis H1.4. Yet, fully evaluating this effect would require studying the model complexity beyond the current study’s scope, complicating the understanding of the results. As such, we leave a thorough investigation of H1.4 for future work.    

Human-robot interaction perception model (M2)

To investigate whether subjective perceptions of human-robot interaction (HRI) influenced task performance (H3), we employed the following model:

where the HRIQuestion represents the normalized and centered response to each of the specific HRI perception questions. The normalized and centered version of four of the traits were considered of interest for this model, i.e., the Achiever ((AC_c)) and Free Spirit ((FS_c)) gaming styles, Transform of Challenge ((TC_c)), and Locus of Control ((LOC_c)). All the phases were included in this dataset (baseline, training, short- and long-term retention) while the transfer tasks were excluded as HRI questions were asked exclusively after the training phase, which did not include the transfer tasks.