Over the past decade, autonomous surface vessels (ASVs) have increasingly operated in a range of challenging environments involving safety-critical scenarios. Their navigational capabilities rely on rich and reliable sensor data, enabling accurate localisation, situational awareness and environmental perception. This allows ASVs to perform motion planning, collision avoidance and navigational control tasks. To ensure maritime safety, faults affecting onboard navigational sensors must be diagnosed. This paper presents a model-based fault diagnosis scheme for ASVs affected by multiple sensor faults. Model-based methods utilise available sensors and dynamical models for residual generation. However, models describing the navigation may vary considerably for ASVs due to differences in vessel types, actuator configurations and sensor setups. To address this challenge, multiple residuals are synthesised using observer-based monitoring modules in the navigational sensors. Considering the impact of uncertainties, the residuals are designed to be bounded by adaptive thresholds proposed for each monitoring module. Fault isolation is then performed using a combinatorial decision logic, achieved by grouping the available sensors into multiple sensor sets and supported by model-based sensitivity analysis. Finally, the effectiveness of the proposed scheme is verified through simulation examples of two real-world vessels of different types with different sensor and actuator configurations, thereby illustrating its application.

This erratum applies to the following published paper [1]. In Fig. 10(e) and (f) of the published version of the paper, the measured values for the t _f and T _l,f (both having values around 1 s for the considered dataset) were interchanged. This erratum includes both the published and corrected versions of Fig. 10 and the related paragraph in the paper's Results section. PUBLISHED VERSION In preview tasks, bandwidth changes yield only minor adaptations in the model parameters, see Fig. 10. Only the average look-ahead time t _f decreases slightly with bandwidth from around 1.05 to 0.9 s, Fig. 10(e) but with substantial between-participant variability, as indicated by the overlapping confidence intervals. The lower t _f may not reflect a systematic adaptation to the bandwidth, but a more subtle adaptation to minimize the errors due to the additional high-amplitude sinusoids at 2.5 and 4 rad/s, see also Fig. 8c. The general way in which participants use the available preview for control is, however, not affected by the target signal bandwidth: the target response gain (K _f ≈ 0.95, Fig. 10(d)) and lag time-constant (T _{l, f} ≈ 1.15 s, Fig. 10(f)) are approximately invariant. The estimated control dynamics in Fig. 12 show that the target trajectory is tracked almost perfectly at all frequencies below 4 rad/s, mostly because the phase lead due to τ _f allows for synchronizing the CE output with the target signal (as opposed to pursuit tasks, see Fig. 11, bottom right). Therefore, different-bandwidth target signals provide no incentive for HCs to strongly adapt their control behavior in preview tasks. (Figure Presneted) CORRECTED VERSION In preview tasks, bandwidth changes yield only minor adaptations in the model parameters, see Fig. 10. Only the average target smoothing time-constant T _{l, f} decreases slightly with bandwidth [from around 1.05 to 0.9 s, Fig. 10(f)], but with substantial between-participant variability, as indicated by the overlapping confidence intervals. The lower T _{l, f} indicates that slightly more smoothing is applied to reduce tracking of the more high-amplitude high-frequency sinusoids in the 2.5 and 4 rad/s bandwidth signals through the feedforward response, see also Fig. 8(c). The general way in which participants use the available preview for control is, however, not affected by the target signal bandwidth: the target response gain [K _f ≈ 0.95, Fig. 10(d)] and look-ahead time [τ _f ≈ 1.15 s, Fig. 10(e)] are approximately invariant. The estimated control dynamics in Fig. 12 show that the target trajectory is tracked almost perfectly at all frequencies below 4 rad/s, mostly because the phase lead due to τ _f allows for synchronizing the CE output with the target signal (as opposed to pursuit tasks, see Fig. 11, bottom right). Therefore, different-bandwidth target signals provide no incentive for HCs to strongly adapt their control behavior in preview tasks. (Figure presented).

In the design of human-like steering support systems, driver models are essential for matching the supporting automation's behavior to that of the human driver. However, current driver models are very limited in capturing the driver's adaptation to key task variables such as road width and visibility (i.e., 'preview' of the road ahead). This paper uses a recently proposed, novel control-theoretical model for centerline tracking to investigate driver steering in lane-keeping tasks with restricted and unrestricted preview, in an attempt to substantially extend this model's validity. Using data from a tailored driving simulator experiment, three driver control loops (feedforward, heading and position feedback) are separately quantified using system identification techniques. The results show that when preview is restricted, drivers use all of the remaining preview to anticipate the curves of the road ahead, and are no longer able to 'smooth' tight curves in the road trajectory (i.e., corner cutting). When sufficient preview and lane width are available, the time to line crossing increases, and steering behavior is less aggressive and more intermittent, or more 'satisficing'. The novel driver steering model captures these adaptations very well (over 95% of the steering actions) and can thereby be instrumental in realizing human-like steering automation and support systems.

Cyberneticists develop mathematical human control models which are used to tune manual control systems and understand human performance limits. Neuroscientists explore the physiology and circuitry of the central nervous system to understand how the brain works. Both research human visuomotor control tasks, such as the pursuit tracking task. In this paper we discuss some commonalities and differences in both approaches to better understand the adapting human controller. Special attention is given to Adaptive Model Theory, which studied adaptive human control using several linear and nonlinear control engineering techniques. The insights gained yield schemes and concepts which pave the way for key future work on this topic.

Better understanding of manual control requires more research on human anticipatory feedforward behaviour. Recent advances include a human control model for preview tracking, and a subsystem identification (SSID) technique that uses a candidate pool approach to identify the human feedforward and feedback responses. This paper discusses the performance of the SSID method when estimating the preview control model parameters. Through simulations of a preview task with two controlled element dynamics, the SSID performance with different remnant noise levels and candidate pool densities is quantified. We demonstrate its successful application to the preview model and show that its performance deteriorates for higher noise levels. While the feedforward parameters are estimated accurately, the high-frequency compensatory feedback dynamics cannot be reliably determined. Future work focuses on alternative formulations for using SSID to estimate preview model parameters. Since in manual control the closed-loop magnitude decreases at higher frequencies, effects of manipulating the weightings of the closed-loop fitting cost values at these frequencies must be further analyzed.

Mathematical human control models are widely used in tuning manual control systems and understanding human performance. Human behavior is commonly described using linear time-invariant models, averaging-out all non-linear and time-varying effects, which are gathered into the remnant. These models are limited in their capability to capture particular tracking strategies that an experienced subject may learn to use. In this paper, we consider manual control from a different perspective, namely through investigating the probability densities of the tracking error for different regions of the target signal amplitude. Results show that distinct strategies become apparent for compensatory, pursuit and preview tracking tasks. Effects of these strategies are often averaged-out by current models and can only be captured in situation-dependent models. Modeling this systematic human adaptation not captured in linear models could potentially lead to better model fits and explain/reduce part of the remnant.

The 1960s crossover model is widely applied to quantitatively predict a human controller's (HC's) manual control behavior. Unfortunately, the theory captures only compensatory tracking behavior and, as such, a limited range of real-world manual control tasks. This article finalizes recent advances in manual control theory toward more general pursuit and preview tracking tasks. It is quantified how HCs adapt their control behavior to a final crucial task variable: the target trajectory bandwidth. Beneficial adaptation strategies are first explored offline with computer simulations, using an extended crossover model theory for pursuit and preview tracking. The predictions are then verified with data from a human-in-the-loop experiment, in which participants tracked a target trajectory with bandwidths of 1.5, 2.5, and 4 rad/s, using compensatory, as well as pursuit and preview displays. In stark contrast to the crossover regression found in compensatory tasks, humans attenuate only their feedforward response when tracking higher-bandwidth trajectories in pursuit tasks, while their behavior is generally invariant in preview tasks. A full quantitative theory is now available to predict HC manual control behavior in tracking tasks, which includes HC adaptation to all key task variables.

Drivers rely on a variety of cues from different modalities while steering, but which exact cues are most important and how these different cues are used is still mostly unclear. The goal of our research project is to increase understanding of driver steering behavior; through a measuring and modeling approach we aim to extend the validity of McRuer et al.'s crossover model for compensatory tracking to curve driving tasks. As part of this larger research project, this paper first analyzes the four main differences between compensatory tracking and curve driving: (1) pursuit and preview, (2) viewing perspective, (3) multiple feedback cues, and (4) boundary-avoidance strategies due to available lane width. Second, this paper introduces multiloop system identification as a method for explicitly disentangling the driver's simultaneous responses to various cues, which is subsequently applied to two sets of human-in-the-loop experimental data from a preview tracking and a curve driving experiment. The results suggest that recent human modeling advances for preview tracking can be extended to curve driving, by including the human's adaptation to viewing perspective, multiple feedback cues, and lane width. Such a model's physically interpretable parameters promise to provide unmatched insights into between-driver steering variations, and facilitate the systematic design of novel individualized driver support systems.

Novel driver support systems potentially enhance road safety by cooperating with the human driver. To optimize the design of emerging steering support systems, a profound understanding of driver steering behavior is required. This article proposes a new theory of driver steering, which unifies visual perception and control models. The theory is derived directly from measured steering data, without any a priori assumptions on driver inputs or control dynamics. Results of a human-in-the-loop simulator experiment are presented, in which drivers tracked the centerline of straight and winding roads. Multiloop frequency response function (FRF) estimates reveal how drivers use visual preview, lateral position feedback, and heading feedback for control. Classical control theory is used to model all three FRF estimates. The model has physically interpretable parameters, which indicate that drivers minimize the bearing angle to an 'aim point' (located 0.25-0.75 s ahead) through simple compensatory control, both on straight and winding roads. The resulting unifying perception and control theory provides a new tool for rationalizing driver steering behavior, and for optimizing modern steering support systems.

Human modelling approaches are typically limited to feedback-only, compensatory tracking tasks. Advances in system identification techniques allow us to consider more realistic tasks that involve feedforward and even precognitive control. In this paper we study the human development of a feedforward control response while learning to accurately follow a ramp-shaped target signal in the presence of a disturbance acting on the controlled element. An experiment was conducted in which two groups of eight subjects each tracked ramps of different steepnesses in a random or ordered fashion. In addition, ordered runs were followed by a 'surprise' run with a random ramp steepness. Results show that operators learn rapidly, continue to learn during the entire experiment, and can adapt very quickly to surprise situations. Experiments involving learning operators are challenging, as it is difficult to balance-out all experimental conditions and control for inevitable differences between (groups of) subjects.

Mathematical control models are widely used in tuning manual control systems and understanding human performance. The most common model, the crossover model, is severely limited, however, in describing realistic human control behaviour in relevant control tasks as it is only valid for tracking with a compensatory display. This paper first discusses the state-of-the-art in modelling human control in tracking with pursuit displays. It is shown that, although both tasks seem very similar, the separate presentation of target and system output signals allows operators to adopt a huge variety in control strategies, which makes the development of a universal model for pursuit control a challenge. Two recent models are then described which can act as precursors to such a universal model. Third, system identification choices and issues are discussed for pursuit tracking tasks. Finally, it is argued that it is inevitable that time-varying rather than time-invariant methods are needed to properly describe human behaviour in the pursuit tracking task, as skilled operators will learn to characterize the probabilistic nature of the task, which cannot be captured in a single, linear, time-invariant model.

The understanding of human responses to visual information in car driving tasks requires the use of system identification tools that put constraints on the design of data collection experiments. Most importantly, multisine perturbation signals are required, including a multisine road geometry, to separately identify the different driver steering responses in the frequency domain. It is as of yet unclear, however, to what extent drivers steer differently along such multisine roads than they do for real roads. This paper presents a method for approximating real-world road geometries with multisine signals, and applies it to a stretch of road used in an earlier investigation into driver steering. In addition, a human-in-the-loop experiment is performed to collect driver steering data for both the realistic real-world road and its multisine approximation. Overall, the analysis of driver performance metrics and driver identification data shows that drivers adopt equivalent control behaviour when steering along both roads. Hence, the use of such multisine approximations allows for the realization of realistic roads and driver behaviour in car driving experiments, in addition to supporting the application of quantitative driver identification techniques for data analysis.

In manual pursuit and preview tracking tasks, humans apply feedforward control to exploit available information of the target trajectory to follow. While the human's linear, time-invariant dynamics in such tasks are well-understood and have been modeled in the quasi-linear framework, the remaining nonlinear and time-invariant control behavior, the human remnant, is typically ignored. This paper extends the current state-of-the-art theories of human remnant, which are applicable to compensatory tracking tasks only, to the more common and relevant pursuit and preview tracking tasks. Data are presented from three human-in-the-loop tracking experiments. The ratio of the remnant relative to the linear control output is quantified in the frequency domain, and remnant spectra are computed and modeled. The results show that the injected remnant is identical in compensatory, pursuit, and preview tasks, regardless of the task's controlled element dynamics, preview time, and target trajectory bandwidth. The presented remnant data and models can be used together with already available linear, time-invariant models, to better predict characteristics of human control behavior in pursuit and preview tracking tasks, enabling the design of human assistance systems.

In manual control tasks, preview of the target trajectory ahead is often limited by poor lighting, objects, or display edges. This paper investigates the effects of limited preview, or preview time, in manual tracking tasks with single- and double-integrator controlled element dynamics. A quasi-linear human controller model is used to predict the human behavior adaptations offline, by finding the model parameters that yield optimal performance at each preview time. These predictions are then verified by fitting the same model to measurements from a human-in-the-loop experiment, where subjects performed a tracking task with eight different preview time settings between 0 and 2 s. Results show that the tracking performance improves and the model’s “look-ahead” time parameters increase with increasing preview time. Beyond a certain preview time, approximately 0.6 s and 1.15 s in single- and double-integrator tasks, respectively, additional preview evokes no further adaptations. The offline model predictions closely match the experimental results, which thereby promises to facilitate similar quantitative insights in other tasks with restricted preview.

Due to linear perspective, the visual stimulus provided by a previewed reference trajectory reduces with increasing distance ahead. This paper investigates the effects of linear perspective on human use of preview in manual control tasks. Results of a human-in-the-loop tracking experiment are presented, where the linear perspective's horizontal and vertical deformations along the previewed trajectory were applied separately and combined, or were absent (plan-view task). Measurements are analyzed with both nonparametric and parametric system identification techniques, in combination with a quasi-linear human controller model for plan-view preview tracking tasks. Results show that reduced visual stimuli in perspective tasks evoke less aggressive control behavior, but that the human's underlying control mechanisms are still accurately captured by the model. We conclude that human controllers use preview information similar in plan-view and perspective tasks.

This paper investigates how humans use a previewed target trajectory for control in tracking tasks with various controlled element dynamics. The human's hypothesized "near" and "far" control mechanisms are first analyzed offline in simulations with a quasi-linear model. Second, human control behavior is quantified by fitting the same model to measurements from a human-in-the-loop experiment, where subjects tracked identical target trajectories with a pursuit and a preview display, each with gain, single-, and double-integrator controlled element dynamics. Results show that target-tracking performance improves with preview, primarily due to the far-viewpoint response, which allows humans to cancel their own and the controlled element's lags, without additional control activity. The near-viewpoint response yields better target tracking at higher frequencies, but requires substantially more control activity. The control-theoretic approach adopted in this paper provides unique quantitative insights into human use of preview, which can help to explain human behavior observed in other preview control tasks, like driving.