Communication Delays in Telerobotics

All mobile telerobotic systems introduce communication delay, whether on Earth or in space [32]. On Earth, applications such as search and rescue [33, 3] or mining [34] encounter delays ranging from 100 ms to several seconds depending on network infrastructure. In space, the issue is more severe because communication is bounded by the speed of light: the Earth–Moon distance imposes a minimum round-trip time of about 2.56 s [30, 35]. Actual operational figures are higher; for example, NASA’s VIPER rover is expected to experience 6–10 s round-trip delay via the Deep Space Network [36]. Beyond these physical limits, real networks introduce variability through processing, routing, and bandwidth constraints [37, 38]. Many laboratory studies simplify experiments by treating delay as a fixed constant [23, 26, 39], although in practice operators must cope with both predictable and variable delay [25]. Delay also affects domains such as surgical teleoperation [40, 41, 42] and UAV control [43], where it reduces precision and safety. While this paper focuses on mobile teleoperation, these examples demonstrate that delay is a pervasive challenge across telerobotics.

Delay also alters operator behavior. Ferrell’s experiments [18] showed that under delay, operators adopt a "move-and-wait" behavior: issue a command, wait for confirmation, then act again. The strategy reduces instability but increases task time in proportion to the delay [44, 45]. Similar patterns are reported in space teleoperation, where delays beyond human cognitive timescales force cautious, stepwise control [46]. "Move-and-wait" has therefore become a common benchmark for evaluating new interfaces. These adaptations demonstrate that delay is not only a systems constraint but also a cognitive challenge [17].

Cognitive Effects of Delay

Empirical studies show that communication delay affects both control and cognition. Even relatively short delays of about 300 ms can create mismatches between operator expectations and the actual robot state [12, 13], increasing errors and perceived cognitive load. Experiments in lunar construction confirm that delay reduces control accuracy and increases mental demand compared to zero-delay conditions [47]. Dybvik et al. [22] similarly find that vehicle teleoperation under delay diminishes situational awareness and substantially increases perceived cognitive load. Comparable effects are reported in surgical teleoperation [40, 41] and in autonomous vehicle teleoperation [17], where delay undermines operator confidence and adds cognitive strain.

The mechanism underlying these effects is a disruption of situational awareness. Operators perceive the environment only through cameras and displays; when feedback is delayed, their mental model of the remote state is updated with stale information [15, 23]. This temporal misalignment introduces uncertainty about the robot’s actual state. Prior work shows that uncertainty can accumulate even when operators act correctly, forming "uncertainty loops" that erode trust and performance [48]. Interfaces that make a robot’s uncertainty visible can help preserve operator agency and decision quality [49], but poorly designed uncertainty visualizations risk confusion or mistrust [20, 21]. In telerobotics, delay exacerbates these issues by forcing reliance on memory and prediction; in extraterrestrial contexts, sparse visual cues further intensify the burden [47].

These outcomes align with established cognitive theory. In Endsley’s model, delay disrupts perception and comprehension, weakening projection of future states [16]. In Norman’s framework, delay widens the gulfs of execution and evaluation: Operators must issue commands before the effects of their previous inputs become visible, while delayed feedback prevents timely confirmation. [19]. Together, these accounts underscore the need for interface techniques that make uncertainty visible, sustain awareness, and support anticipation under delay.

Delay Mitigation Strategies

Various control strategies have been proposed to mitigate the effects of communication delay. Surveys highlight control-theoretic approaches that can improve stability and transparency of control under communication delay [44, 13]. Their performance, however, depends on accurate delay models and careful tuning, and they do not focus on the operator’s temporal uncertainty when directly interacting with the robot [44, 13]. A line of research targets the perception side via predictive displays, which render the robot’s near-future state from current commands and motion models to clarify the action to outcome loop [50, 23, 24]. Building on early work that introduced wire-frame and trajectory projections [23, 24] and subsequent variants such as ghost overlays [51], trajectory lines [52], and hybrid approaches [53, 54].

Moniruzzaman et al. [10] survey predictive displays extensively and report that they can reduce perceived communication delay, yet most implementations remain limited to first-order state predictions like a position or direction, and rarely represent uncertainty or the probabilistic nature of future events; mismatches between predictions and outcomes can undermine operator trust, consistent with broader findings on automation trust [55]. Consequently, existing predictive displays often emphasize what will happen without differentiating the distinct uncertainty sources that shape and support direct operator control. Our work addresses this gap: we decompose operator uncertainty into when commands take effect (communication), how input maps to motion (trajectory), and what external factors may alter outcomes (environmental), and we systematically evaluate facet-specific visualizations under fixed upper-bound delay.

Predictive displays are feedforward interfaces [27] that communicate the likely, but in this case not guaranteed, consequences of an action before execution, thereby narrowing Norman’s gulf of execution by making action-outcome relations visible [19]. Recent work formalizes the design space of feedforward cues: Yu et al. [56] characterize variations in level of indirection (explicit, implicit, abstract) and update strategy (discrete, continuous, autonomous); trajectory overlays instantiate implicit feedforward (showing the future indirectly), whereas ghost projections exemplify explicit feedforward (depicting the future directly and unambiguously) [57]. Complementing these taxonomies, Van Deurzen et al. [28] provide a framework and dashboard that help developers to include feedforward for working with (semi)-autonomic robots, highlighting where and when predictive cues are required, desired, or optional.

Robot Dynamics

In UNITE, robot dynamics are implemented as modular components. This means that the motion equations and physical limits of the robot are encapsulated in interchangeable models. For our study we used the Turtlebot3 Waffle Pi, a differential-drive robot, with kinematics based on its wheelbase and motor specifications. To support more precise control in our environment, we reduced the maximum rotational speed from 1.82 radianpers to 0.30 radianpers. Because dynamics are modular, different robots can be loaded without altering the interface details.

Noise Model

To approximate imperfections in real robot motion, we implemented a deterministic noise model aligned with the kinematics of a differential drive robot. This model introduces variation in the robot’s motion by adjusting the commanded left and right wheel velocities according to six uncertainty sources, applied before each update of the robot state:

1. Wheel slip: traction is reduced on rough terrain or at higher speeds, lowering effective velocity.
2. Motor variation: small, time-varying differences between the left and right motors introduce drift.
3. Terrain vibration: uneven ground causes oscillations that momentarily disrupt wheel-ground contact.
4. Encoder noise: measured wheel velocities include small inaccuracies, simulating sensor error.
5. Slope bias: when traversing inclines, load shifts unevenly across wheels, producing asymmetric motion.
6. Wheel performance dynamics: time-varying factors including thermal effects, material deformation, and debris accumulation create oscillating differences in effective wheel performance.

Effects (3–4) are generated using Perlin noise, a smooth noise function that produces gradual rather than abrupt changes [58]. Unlike random noise, which jumps unpredictably, Perlin noise creates continuous patterns over space and time, which better matches how disturbances such as terrain roughness or motor noise occur. Effects (1–2, 4, 6) are based on velocity data, whereas effects (3, 5) are based on positional data.

The noise model is seeded deterministically so identical inputs produce identical deviations across conditions. Its parameters were iteratively calibrated to produce clear, realistic trajectory variations representative of normal rough-terrain motion. The role of this approximation is to introduce enough variability for environmental uncertainty to matter, while keeping that variability constrained so the visualization conditions (see Section sec:design-process) can be compared reliably.

Fixed-delay model and implementation.

To isolate the effect of delayed feedback, UNITE applies a constant 2.56 s round-trip delay. Real networks often have variable delay, which can cause jitter, buffering, and dropped frames. This makes it harder to tell whether performance differences stem from the delay itself or from its fluctuations [12, 37]. A fixed delay removes this ambiguity. With a stable communication delay, we can compare how each visualization supports operator control [21, 20].

A fixed delay also reflects a practical abstraction. When delay varies within a known and bounded range, the system can treat the largest observed value as its effective delay (see Figure fig:comm-delay-assumption). This creates a consistent reference value for applying delay in the control loop. In UNITE, the fixed value is 2.56 s, which corresponds to the theoretical lower bound round-trip time for Earth to Moon communication [30], providing a concrete reference point for the scale of temporal separation implemented in the system. By enforcing a fixed delay, all interface conditions operate under the same temporal separation between action and feedback.

Technically, the delay is realized through a time-stamped command queue: inputs are stored with their execution times and applied only after 2.56 s. During this waiting period, queued commands are also used to generate the lookahead trajectories (Section sec:design-process), ensuring consistent delayed dynamics across all visualization conditions.

Environment Generation

Two terrains were generated in advance from publicly available displacement maps (Moonscapes). One terrain is used for training, and the other serves as the navigation environment. Both terrains remain fixed within the simulation, ensuring that rendering, physics integration and terrain-aware noise operate over consistent surface geometry.

The terrain supports two roles in the system. First, it provides the visual surface onto which trajectory predictions are projected so that visualizations follow local ground topology (see Section sec:design-process). Second, it acts as the collision and support surface for robot motion. The robot’s vertical position is updated via raycasting, while slope and roughness are estimated in real time using a three-point triangulation method. These terrain-derived values drive the position-based components of the noise model (effects 3 and 5), ensuring that disturbances originate from structured features of the surface rather than arbitrary perturbations.

To approximate lunar and space conditions, UNITE uses a single directional light (sun analog), no atmospheric scattering, and a dark sky. Figure fig:terrain shows the simulated robot traversing one of the generated terrains. For clarity in this paper, lighting in Figure fig:terrain was adjusted to make details of the robot and terrain more visible.

3D simulation scene showing a wheeled robot navigating a rugged lunar-like environment with steep slopes and rocky ground.

3D simulation scene showing a wheeled robot navigating a rugged lunar-like environment with steep slopes and rocky ground.

Network Visualization

The Network visualization targets communication uncertainty: the ambiguity about whether a command has been sent, and when its effects will become visible in the delayed camera feed (Figure fig:network-visualisation-horizontal). Under delay, this uncertainty forces operators to rely on memory or guesswork to keep track of input timing, which weakens their ability to coordinate actions effectively. For example, when approaching a turn, the operator must anticipate the delay and issue the turn command early enough for the robot to respond in time. To reduce this ambiguity, the Network visualization applies established HCI principles of system transparency and status visibility [19, 59]. It externalizes the command pipeline by visualizing the delay between input and execution, making command timing explicit and allowing operators to anticipate when their actions will take effect.

Two-part figure showing the Network visualization. Subfigure (a) is a simulation screenshot with timelines overlaid at the bottom of the interface, where green blocks represent operator commands in transit. Subfigure (b) is a schematic diagram with four parallel timelines corresponding to the arrow-key controls, illustrating command blocks moving across the delay interval before execution.

Two-part figure showing the Network visualization. Subfigure (a) is a simulation screenshot with timelines overlaid at the bottom of the interface, where green blocks represent operator commands in transit. Subfigure (b) is a schematic diagram with four parallel timelines corresponding to the arrow-key controls, illustrating command blocks moving across the delay interval before execution.

The Network visualization presents four parallel timelines, one for each arrow key, aligned spatially to match the layout of the physical keyboard. This spatial arrangement follows Norman’s principle of natural mapping [19], reinforcing intuitive associations between the user actions and the visualizations on the timelines. Each timeline functions as a communication channel, with the left side representing the operator’s input, and the right side representing the robot’s execution point. When a control signal is sent (arrow is pressed), a green block appears at the left end of the corresponding timeline. The block’s length encodes the duration of the keypress, and it animates rightward across the timeline, simulating the time it takes for the command to reach the robot, and the video feedback to propagate back—corresponding to the fixed communication delay (2.56 s). Once the block reaches the far end, the command is assumed to have taken effect and is observable in the delayed video feed. These timelines make the otherwise invisible delay visible and predictable. The steady animation speed provides a rhythmic, perceptible timeline that allows operators to offload timing calculations and anticipate when a command will take effect. Overlapping commands are displayed sequentially on their respective key channels.

Data Requirements. The visualization requires only input timestamps, keypress durations, control mappings, and the known fixed round-trip delay. It does not require access to robot pose, motion data, or kinematic models. As such, it offers a lightweight way to surface temporal uncertainty without introducing spatial prediction.

Path Visualization

The Path visualization addresses trajectory uncertainty: the difficulty of inferring how input commands will translate into robot motion under delay. Path visualization (Figure fig:path-visualisation-horizontal) does this by rendering a prediction in real-time of how input could translate into movements of the robot. Without explicit support, operators must mentally simulate the robot’s motion dynamics, which becomes increasingly error-prone as the delay grows. Such "predictive overlays" are an established design practice in vehicle interfaces (e.g., reversing camera path projections), where they help users anticipate the spatial outcome of steering. In delayed teleoperation, such feedforward cues allow operators to predict the robot’s behavior without waiting for delayed video feedback, thereby reducing the cognitive effort needed to maintain situational awareness.

Two-part figure showing Path visualization. Subfigure (a) is a simulation screenshot with three overlaid trajectory lines (left wheel, right wheel, center). Subfigure (b) is a schematic diagram labeling the wheel paths and center reference trajectory, indicating the prediction horizon under delay.

Two-part figure showing Path visualization. Subfigure (a) is a simulation screenshot with three overlaid trajectory lines (left wheel, right wheel, center). Subfigure (b) is a schematic diagram labeling the wheel paths and center reference trajectory, indicating the prediction horizon under delay.

The visualization projects where the robot will move next by applying an idealized motion model. It assumes perfect conditions: no wheel slippage, no external disturbance, and no environmental variability. The result is a feedforward prediction, an estimate of the robot’s path if the current command were executed exactly as intended. As shown in Figure fig:path-visualisation-horizontal, the interface overlays three trajectory lines on the video feed: one for each wheel and a third through the instantaneous center of rotation. These overlays update continuously with input: forward keypresses extend the lines outward, backward keypresses extend them inward, and left/right inputs bend them accordingly. Each segment is drawn cumulatively, so prior forward extensions remain visible when subsequent backward inputs are added. The trajectory length scales with the duration of keypresses and is capped by the fixed round-trip delay of 2.56 s, which defines the maximum lookahead window.

Kinematic Model. Trajectory prediction is computed using standard differential-drive kinematics: linear velocity $v = (v_L + v_R)/2$ and angular velocity $\omega = (v_R - v_L)/d$, where $v_L$ and $v_R$ are the left and right wheel velocities and $d$ is the wheelbase. These values are integrated forward in time to generate a continuous pose trace that approximates the robot’s motion over the lookahead window.

Data Requirements. Path visualization requires only three inputs: the robot’s current position, the user’s control commands, and the wheelbase parameter. These values define a noise-free kinematic model that predicts the trajectory the robot would follow under ideal execution. In our implementation, the position anchors the prediction in space, the commands define wheel velocities over time, and the wheelbase determines curvature. In our simulation, the robot’s current position is obtained directly from the Unity environment, control commands are captured from the keyboard input system, and the wheelbase is defined by the TurtleBot3 model. In real deployment, pose can be estimated via SLAM or GPS, user inputs are available directly from the control interfaces, and robot parameters are typically known from manufacturer specifications. Importantly, the visualization shows intended motion, not actual execution, reinforcing its role as a feedforward aid that supports planning and prediction.

Envelope Visualization

The Envelope visualization addresses environmental uncertainty: the variability in robot motion caused by environmental factors, such as slippage, terrain conditions, motor noise, or other external factors. The visualization extends the Path visualization: instead of projecting a single trajectory, it visualizes a cone-shaped region that represents the maximum possible deviation from the ideal path, given a set of modeled disturbances including terrain slippage and system noise (Figure fig:uncertainty-visualisation). This visualization helps operators not only anticipate the robot’s intended direction, but also reason about how actual motion might diverge under uncertain environmental conditions.

Two-part figure showing the Envelope visualization. Subfigure (a) is a simulation screenshot with a cone-shaped shaded region projected ahead of the robot, representing possible motion deviations. Subfigure (b) is a schematic diagram with a center reference line and two outward bounding curves, forming an envelope that indicates maximum possible divergence.

Two-part figure showing the Envelope visualization. Subfigure (a) is a simulation screenshot with a cone-shaped shaded region projected ahead of the robot, representing possible motion deviations. Subfigure (b) is a schematic diagram with a center reference line and two outward bounding curves, forming an envelope that indicates maximum possible divergence.

As shown in Figure fig:uncertainty-visualisation, the envelope is rendered as a translucent, cone-shaped region aligned with the robot’s apex point. The center of the cone shows the ideal, noise-free trajectory (identical to the Path visualization), while the left and right bounds mark the maximum deviation under modeled disturbances. The envelope dynamically expands in both width and length as keypress duration increases, up to the limit imposed by the fixed round-trip delay of 2.56 s. The shaded region thus reflects the cumulative effect of uncertainty over time. Importantly, this is not a probabilistic estimate, it reflects a worst-case spread, guaranteeing that the actual trajectory remains within the envelope under the modeled assumptions.

Kinematic Model. The model uses the same kinematic equations as the Path visualization ($v = (v_L+v_R)/2$, $\omega = (v_R-v_L)/d$), but modifies the input velocities to account for environmental disturbances. As detailed in the noise model (Section sec:research-platform), six disturbances are modeled: wheel slip, motor variation, terrain vibration, encoder noise, slope bias, and wheel dynamics. While the simulation applies these disturbances dynamically via seeded noise, the Envelope visualization instead uses deterministic upper bounds derived from the same model parameters. These bounds are then propagated through the kinematic equations to compute the largest possible divergence from the intended trajectory. The adjusted velocities ($v’_L$, $v’_R$) define the left and right envelope boundaries.

Data Requirements. In our simulation, the Envelope visualization uses the robot’s current position (from the Unity environment), the user’s control commands (from keyboard input), the wheelbase (from the TurtleBot3 model). Disturbance parameters are sourced from the simulation’s noise model (Section sec:research-platform). In real-world settings, obtaining reliable disturbance bounds is more challenging. Some parameters—such as slope or surface roughness—can be inferred from onboard sensors (e.g., LiDAR or stereo vision), while others, like motor slippage or vibration, are harder to sense directly and often require offline testing or empirical calibration. As such, practical deployment of this visualization would require careful tuning of the uncertainty model.

Study Objectives

The central challenge in delayed teleoperation is operator uncertainty: delayed feedback obscures when commands take effect, how they map to motion, and how environmental factors may alter outcomes. Without support, operators fall back on reactive "move-and-wait" control, which increases task time and cognitive load.

Our objective is to test whether externalizing the distinct facets of uncertainty through feedforward visualizations can reduce reliance on reactive control and improve direct teleoperation. This motivates the following research question:

What are the effects of the three facets of uncertainty on operator performance and cognitive load under delayed mobile teleoperation?

To answer this question, we test two hypotheses:

H1: Feedforward visualizations reduce task completion time under communication delay compared to delayed-video feedback alone.

H2: Feedforward visualizations will reduce subjective cognitive load under communication delay compared to delayed-video feedback alone.

Participants

We recruited 24 participants (M = 26.1 years, SD = 6.5, range = 20–44; 14 men, 10 women). Non-binary/other and prefer-not-to-say options were offered, although none were selected. All participants were novices; experts in telerobotics were not included in the study.

Participants were recruited via the research lab’s mailing lists and the research team’s personal networks. While this reflects a convenience sample, we sought variation in gaming background, as pilot observations suggested this might influence operator behavior. Gaming background was self-reported on a five-point scale: never (n = 7), less than once a month (n = 4), 1–3 times a month (n = 3), weekly (n = 3), or several times per week (n = 7). For exploratory analyses, we grouped participants into two categories: those who reported gaming at least weekly (coded as high gaming experience, $n=10$) and those who reported less frequent or no gaming (coded as low/no gaming experience, $n=14$).

All participants provided informed consent prior to participation. The study was approved by the university’s Social and Societal Ethics Committee (SMEC). Participation was voluntary, with no compensation, and participants were informed that they could withdraw from the study at any time without consequence.

Setup and Apparatus

Participants used UNITE (see Section sec:research-platform) to control a simulated UGV in a lunar-terrain environment (see Section subsec:terrain-generation). UNITE ran on a remote virtual machine (4 CPU cores, 8 GB RAM, 200 GB SSD, 200 Mbit/s network). The simulation ran at 50 Hz physics update and rendered at 120 FPS, streamed in real time applying a communication delay. The interface was presented in a 2560 $\times$ 1360 px browser window on a 27 inch Dell UltraSharp U2717D monitor (native resolution 2560 $\times$ 1440 px). Participants used a Logitech MX Keys keyboard with numpad, which they were free to position according to their preference.

We used a dual-window setup: one browser window hosted the Qualtrics questionnaire, while the second window was used for UNITE. The questionnaire window communicated with the experiment server to trigger the loading of condition sequences and to synchronize trial progression. UNITE continuously queried the server for updates and transmitted trials back to the central database on completion. All trial data was stored under unique participant identifiers and linked to the questionnaire responses. Questionnaires were hosted externally in Qualtrics, rather than integrated into the Unity interface, to ensure consistency in survey delivery, robust data export, and reduced development overhead.

Experimental Design

We used a within-subjects design: all 24 participants experienced four conditions: a Baseline showing only the delayed video feed, and three visualization conditions (Network, Path, Envelope). Order was counterbalanced with a Williams Latin square [60], assigning each of the four base sequences to six participants. The independent variable was the visualization’s information level (see Section sec:design-process). Dependent variables were completion time, perceived cognitive load (adapted NASA-TLX), responses to the post-condition questionnaire, and reliance on reactive "move-and-wait" behavior.

Task performance was measured as (a) completion time, defined as elapsed time from task start (click into the simulation window) to reaching the target within 300 s, and (b) completion rate for unsuccessful trials. Completion rate was the proportion of a reference trajectory reached (Figure fig:completion-demo). This trajectory was derived from successful attempts and discretized into 101 evenly spaced waypoints. For each unsuccessful trial, the participant’s endpoint was matched to the closest waypoint (Euclidean distance), and completion rate was defined as its index divided by 100.

Reactive "move-and-wait" behavior was coded as pauses of at least 2.56 s between inputs, matching the round-trip delay and Ferrell’s definition [18]. Reduced reliance on reactive behavior was coded as shorter intervals, indicating proactive input during motion.

Perceived cognitive load was measured with an adapted NASA-TLX [61], all items scored 0–20. The frustration item was excluded but captured in the final questionnaire for cross-condition comparison. We used the Mental Demand item as a proxy for cognitive load, following prior ergonomics and HCI work [62]. Additional measures included Likert ratings of visualization effectiveness, self-assessments of performance, efficiency, and mental model clarity. The comparative questionnaire captured relative rankings and open-ended feedback.

Procedure

Participants were seated behind a monitor. After a short study introduction, they read an information sheet on data handling, ethics, and voluntary participation, and gave informed consent. They then completed a demographics questionnaire (age, gender, gaming experience) and received task instructions describing training and study tasks, time limits (90 s training, 300 s study), and keyboard controls.

Each condition began in Qualtrics, which triggered the assigned visualization. The experimenter switched to the simulation window, where task instructions appeared. Input was accepted only after participants clicked into the window, ensuring keyboard focus and explicit awareness of task start.

Each condition included a short training task, followed by the main task. Training familiarized participants with terrain and visualization and lasted up to 90 s, ending automatically or via spacebar if participants felt prepared.

The study task required navigating to a target area (green circle) as quickly as possible within 300 s. The target was inspired by Mars Perseverance goal-setting [63]. Participants were instructed to drive forward to reach the path, which always began ahead of the start position. The target was initially not visible; participants were reminded to approach hills cautiously. Because the study examined visualization under delay rather than path-finding, participants could confirm with the experimenter whether they remained on the correct route. This safeguard reduced variance from disorientation and was applied sparingly. Success was defined as reaching the target within 300 s; otherwise, performance was measured as proportion of a reference trajectory reached.

After each condition, participants completed an adapted NASA-TLX, Likert items on visualization effectiveness, and short ratings of performance, efficiency, and mental model clarity, plus two optional open-ended questions on difficulties and advantages.

At the end of the study, participants completed a comparative questionnaire ranking the visualizations on usefulness, interpretability, perceived control, and frustration, followed by an open-ended question about preferred visualization and general comments. Informal feedback was recorded separately.

Quantitative Analysis

We analyzed 96 trials from 24 participants across four visualization conditions. Eight trials reached the 300 s ceiling, and an additional trial in the Path condition was flagged as a high outlier (282 s) by the $1.5\times IQR$ rule. All were retained because they reflect real operator difficulties. Analyses used within-subject non-parametric tests (Friedman with Wilcoxon post-hoc, Holm correction) and report effect sizes ($r = Z / \sqrt{N}$). Robustness checks excluding timeouts and the outlier produced consistent results. For the NASA-TLX items, we report Mental Demand and Performance, as they reflect perceived cognitive load and task performance best.

Task Completion Time. Completion times varied across conditions, with several trials reaching the 300 s ceiling, which were retained in the analysis (Figure fig:completion(a)). Median times were shortest for Path (Mdn = 135.2 s) and longest for Baseline (Mdn = 209.9 s). A Friedman test showed significant differences ($\chi^2(3)=15.35, p=0.002, W=0.21$). Holm-corrected Wilcoxon tests found Path faster than Baseline ($p=0.008$, $r=0.65$), Network ($p=0.001$, $r=0.80$), and Envelope ($p=0.028$, $r=0.55$); Baseline, Network, and Envelope did not differ. Kaplan–Meier curves (Figure fig:completion(b)) confirmed this pattern: Path completed all trials, while the others showed slower progress and timeouts. Table tab:descriptives provides descriptive statistics for all dependent measures.

These findings provide only partial support for H1: only the Path visualization improved completion time significantly. We performed independent-samples t-tests on the participant-averaged data, which showed that gaming experience did not affect completion time, High gaming experience ($n = 10$, $M = 171.9$, $SD = 35.9$), Low/No gaming experience ($n = 14$, $M = 188.3$, $SD = 49.2$), $t(22) = -0.95$, $p = .35$, $d = -0.37$.

Completion Rates. Completion rates, defined as the proportion of the reference path reached before timeout, were evaluated only for failed trials. Failures were rare: Baseline (2/24), Network (4/24), Path (0/24), and Envelope (2/24). When failures occurred, Baseline and Envelope trials typically ended close to the target (Mdn = 96% and Mdn = 90%), whereas Network failures stopped earlier and were more variable (Mdn = 73%, range 35–91%). Because the number of failures per condition was very small, these outcomes are reported descriptively only, as sample sizes were too small for reliable statistical testing.

Reactive "move-and-wait" Behavior. Reactive behavior, defined as pauses $\geq$ 2.56 s (matching the round-trip delay), occurred in 72 of 96 trials (75%). By condition: Baseline (20/24), Network (21/24), Path (14/24), Envelope (17/24). Pause counts differed significantly (Friedman $\chi^2(3)=17.59, p<.001, W=0.24$, see Figure fig:pauses-boxplot). Medians were highest in Network (Mdn = 8.5, IQR [1.0–17.5]) and Baseline (Mdn = 5.0, IQR [1.0–10.8]), and lowest in Path (Mdn = 1.0, IQR [0.0–2.3]) and Envelope (Mdn = 1.0, IQR [0.0–10.3]). Post-hoc Wilcoxon tests with Holm correction showed significantly fewer pauses in Path than in Baseline ($p=0.012$, $r=0.22$) and in Path than in Network ($p=0.006$, $r=0.26$); other contrasts were non-significant. Thus, Path reduced reliance on "move-and-wait" compared to Baseline and Network, while Envelope showed similarly low medians but higher variability and no reliable differences. We performed independent-samples t-tests on the participant-averaged data, which indicated that gaming experience did not significantly affect reactive behavior, High gaming experience ($n = 10$, $M = 5.2$, $SD = 5.4$), Low/No gaming experience ($n = 14$, $M = 9.4$, $SD = 11.5$), $t(19.6) = -1.17$, $p = .26$, $d = -0.43$.

Pause durations were stable across conditions, with medians of Baseline (Mdn = 3.18 s, IQR [3.02–3.42]), Network (Mdn = 3.10 s, IQR [2.89–3.36]), Path (Mdn = 3.22 s, IQR [3.02–3.62]), and Envelope (Mdn = 3.14 s, IQR [2.93–3.38]). Although a Friedman test indicated overall differences ($\chi^2(3)=10.90, p=0.012, W=0.30$), Holm-corrected post-hoc tests found no reliable pairwise contrasts ($p_{\text{holm}} \geq 0.15$). This indicates that the frequency, rather than the length, of pauses varied systematically with condition.

Correlation Between Reactive Behavior and Completion Time. A mixed-effects model with random intercepts for participants showed that pause frequency (pauses $\geq$2.56 s) predicted completion time ($\beta=3.97$, 95% CI [3.09, 4.85], $p<.001$); each additional pause added about 4 s. For descriptive reference, a pooled Spearman correlation across all 96 trials was also large ($\rho=0.71$, $p<.001$). Condition-wise correlations with BCa bootstrap CIs (5{,}000 iterations) corroborated this pattern: Baseline ($\rho=0.57$, CI [0.15, 0.81]), Network ($\rho=0.72$, CI [0.47, 0.87]), Path ($\rho=0.66$, CI [0.21, 0.86]), and Envelope ($\rho=0.69$, CI [0.31, 0.87]); all remained significant after Holm correction. Together with stable pause durations across conditions, these results indicate that pause frequency, not length, drove completion time (see Figure fig:ct-pause-corr).

Subjective Cognitive Load. Subjective cognitive load, measured with the NASA-TLX Mental Demand item (0–20 scale), differed across conditions. Scores were highest in Baseline (M=13.21, SD=4.51) and Network (M=12.08, SD=4.38), lower in Envelope ($M=9.25, SD=4.28$), and lowest in Path (M=7.29, SD=4.44). A Friedman test indicated differences ($\chi^2(3)=33.20, p<.001, W=0.46$). Post-hoc Wilcoxon tests (Holm corrected) showed that Path reduced demand compared to all other conditions ($p<.03$), and Envelope reduced demand compared to Baseline and Network ($p=.005$); Baseline and Network did not differ ($p=.45$).

These results provide partial support for H2. Path reduced demand most; Envelope reduced demand relative to Baseline and Network; Network matched Baseline. Thus, not all uncertainty facets are equally effective: externalizing the reference path lowered demand, whereas visualizing network delay added cues without measurable benefit.

Subjective Performance. Perceived task performance, measured with the NASA–TLX (0–20 scale, reverse-coded so that higher values indicate better perceived performance), differed across conditions. Ratings were highest in Path (M = 15.88, SD = 3.01), followed by Envelope (M = 13.50, SD = 4.36), Baseline (M = 12.17, SD = 4.47), and Network (M = 12.12, SD = 4.95). A Friedman test indicated a significant effect ($\chi^2(3)=20.09, p<.001$, $W=.28$). Post-hoc Wilcoxon tests (Holm corrected) showed that Path was rated higher than Baseline ($p=.002$, $r=.79$), Network ($p<.001$, $r=.85$), and Envelope ($p=.037$, $r=.43$). No other contrasts were significant. Thus, only Path improved subjective performance relative to the alternatives.

Relations Among Performance, Cognitive Load, and Completion Time. To assess alignment between subjective ratings and objective outcomes, we examined correlations among perceived performance (NASA-TLX), perceived cognitive load, and completion time within each condition. We expected higher self-rated performance to align with shorter times and lower demand, and higher demand to align with longer times. Spearman correlations with BCa bootstrap confidence intervals (5{,}000 iterations) and Holm correction ($3 \times 4$ tests) showed that most associations were negative, as expected, but did not reach significance after correction. The only robust effect appeared in the Network condition, where higher perceived performance was strongly associated with lower perceived cognitive load ($\rho=-.62$, 95% CI $[-.85,-.18]$, $p_\text{Holm}=.016$). Other correlations, such as performance vs.\ time in Path and Envelope, were negative but did not survive correction (all $p_\text{Holm}>.08$). Overall, convergence between subjective and objective indicators was limited, with reliable alignment only under the Network visualization (Figure fig:convergent).

Comparative Questionnaire Responses. Comparative questionnaire responses (Likert ratings, rankings, and open-ended preferences) converged on a clear preference for Path. Path received the highest Likert ratings for control ($M{=}4.25, SD{=}0.90$), understanding ($M{=}4.04, SD{=}1.04$), and ease of interpretation ($M{=}4.33, SD{=}1.01$), and the lowest for frustration ($M{=}1.46, SD{=}0.72$). It was most often ranked first for control (19/24, 79%), performance (15/24, 63%), and helpfulness (18/24, 75%).

Qualitative Analysis

To examine participants’ subjective experiences of teleoperation under delay, we conducted an inductive thematic analysis [64]. Adopting an essentialist epistemology, we treated participant responses as direct reflections of their experience, prioritizing semantic content over latent interpretation. The analysis followed a systematic, data-driven process in which two authors first coded the dataset independently to establish an initial pool of descriptive codes, documented in a codebook with inclusion and exclusion criteria to ensure consistent coding and minimize overlap between conceptually similar codes (Table tab:codebook). These codes were then reviewed collaboratively to develop a shared understanding of their meaning. During theme development, we treated codes as provisional and grouped together codes that described the same underlying idea. By collapsing these related codes into broader patterns, we moved from individual observations toward the themes presented below (see Figure fig:thematic-analysis-diagram).

Theme 1: spatial prediction as control foundation. Spatial prediction was the central concept that shaped how participants understood control under delay. Participants consistently treated control as the problem of acting without knowing where the robot would end up, rather than a problem of judging when their inputs would take effect. Participants described control as feeling deliberate, when a visualization showed a clear future position, and it became reactive when that position was uncertain. The theme captures this shared view, with subthemes showing how operators separated prediction that supported purposeful action from information that described system behavior but did not help them control it.

The subtheme enabling proactive control captures cases where a clear endpoint allowed operators to plan ahead rather than constantly fixing mistakes. Participants described the Path visualization as enabling deliberate anticipation: "the feedforward provided by the path visualizations helped me adapt my actions" (P11, Path). Other participants used the predicted path to regulate their timing, explaining that "the change in visualization showed me that I needed to halt my inputs, reassess, and consider my actions carefully" (P5, Path). Several noted that this shift toward planning reduced frustration, stating that "the task was much less frustrating" (P15, Path) when a stable future position was visible. We interpreted this pattern as showing that prediction improved control because participants could plan their movements instead of constantly correcting them.

The subtheme system transparency captures situations where visualizations clarified the robot’s behavior but still did not provide the clear future position needed for confident control. Participants valued cues about timing and possible drift but found them difficult to turn into reliable action. Some reported that rotation was easier to judge, noting that "during rotation it was clearer when the rotation would finish" (P12, Network). Others used the Envelope to assess risk, explaining that "you can see if the robot would hit a rock" (P24, Envelope). Despite this, participants stressed that these cues did not help them steer, stating that "it makes me understand what will happen but it’s not supportive of controlling the robot" (P2, Network). When the visualization felt too spread out to act on, some focused on a single point to keep it usable: "in the end I mainly looked at the middle corner of the yellow surface" (P12, Envelope). We understood this as transparency improving understanding, but without a clear future position to guide action, it could not support effective control.

Theme 2: making information actionable. This theme captures how participants experienced control as something they had to work out themselves when the system no longer showed a clear future position. Participants repeatedly described receiving information they could not act on until they transformed it into spatial expectations. This shift made control a mental task: instead of responding to a predicted outcome, operators had to create that outcome through their own judgment. We interpreted this as a pattern where prediction shifted to the operator, requiring them to build the robot’s future position from their own reasoning rather than from the video feed. The subthemes show how operators handled this shift either by converting non-spatial information about the robot’s state into a future position, or by creating that position themselves when the system offered no information at all.

The subtheme translation demand captures cases where participants converted non-spatial cues into spatial predictions. They described the mental load directly: "I had to multitask more in analyzing the arrows I pressed and should press in the future" (P21, Network); "this condition required more mental input as I was focused on timing my inputs" (P24, Network). Some improved with practice: "At the start it seemed very bad, but I learned throughout" (P16, Network). Others used calibration strategies: "I tested in the training phase what the distance or the angle is for a full bar" (P8, Network). But translation came with tradeoffs: "I felt like I could be more precise but anticipated uncertain terrain less, as this required me to be more focused" (P5, Network). For some, it produced distraction: "The visualization made it more confusing, it added a level of distraction" (P20, Network), or was only useful reactively: "I only really looked at this when I had already ended up in a problematic situation" (P12, Network). We interpret this as a case of resource competition: the mental effort required to translate these cues consumed the attention that operators otherwise needed to plan ahead.

The subtheme internal generation captures cases where participants constructed predictions entirely from internal resources when no external cue existed. Some formed workable strategies: "imagining a ‘ghost car’ it was easy to predict where the robot would turn" (P2, Baseline); "I would turn a certain amount of time and hence ‘pre-fire’ that input if I anticipated that I would need to turn" (P5, Baseline). Others adapted over time: "After some time I learned to think ahead for my robot" (P16, Baseline). But internal generation was fragile. Environmental uncertainty disrupted predictions: "I noticed that it was harder to overcome uncertain terrain when in this situation" (P5, Baseline); "I had trouble anticipating difficult terrain" (P5, Baseline). Some reported abrupt failures: "even when at some point I thought I ‘mastered’ the actions to compensate the delay, I just ‘got stuck’" (P11, Baseline). Others noted the full burden of unsupported control: "No visualization of the delay made it much more difficult to interpret" (P22, Baseline). Still, some described creative effort when support was absent: "I realized that the system would not provide me any help and that it was ‘all on me’ inciting me to be more creative" (P5, Baseline). We interpret this pattern as showing that internally generated predictions can support control, but they are fragile and quickly lose reliability when the environment becomes uncertain.