Exploring unknown environments and locating multiple targets with multi-robot teams remains challenging due to uncertainty about such environments and the high computational cost of existing planning methods. Model Predictive Control (MPC) is a widely used and effective approach for planning under constraints; however, traditional MPC relies on Bayesian representations and stochastic cost functions, which limit scalability and decision-making horizons in complex search scenarios. This paper introduces fuzzy-logic-based model predictive control (FLMPC), integrated with dynamic fuzzy maps of the environment, to emulate human-like reasoning and to simplify optimization, while preserving and leveraging the predictive structure of MPC and its systematic handling of constraints within the decision-making loop. Building on this foundation, we present a multi-robot exploration framework based on FLMPC for efficient target search in unknown environments. Instead of optimizing stochastic cost functions, FLMPC uses fuzzy abstractions of environmental attributes, such as passability and certainty, derived from probability distributions and local observations. This approach enables longer-horizon planning and efficient handling of multiple objectives. To enhance coordination among robots, FLMPC is extended into a bi-level parent–child architecture, where a high-level parent controller guides global exploration while local child controllers handle short-term planning. This structure not only improves coordination, but also increases robustness to environmental uncertainty thanks to combining long-term strategic decisions with reactive local adjustments that allow handling unexpected changes and environmental uncertainties more effectively. Extensive simulations in unknown 2D environments with randomly placed obstacles and human targets evaluate the proposed FLMPC framework embedded within a parent-child architecture against conventional MPC with stochastic cost functions. Results demonstrate up to 50× faster optimization and significantly improved search performance under environmental uncertainty, positioning FLMPC as a scalable and efficient planning method for large-scale search-and-rescue missions that require coordinated multi-robot exploration.

Social robots (SRs) are increasingly expected to assist in healthcare, education, and companionship, thereby addressing the growing need for personalized and affordable health and social care. However, sustaining long-term user engagement remains a major challenge for SRs, largely due to their limited understanding of human mental states. Accordingly, we leverage a recently introduced mathematical dynamic model of human perception, cognition, and decision-making for behavioral control of SRs. By identifying the parameters of this model and deploying it within a model-based behavioral steering system, SRs can autonomously adapt their actions to evolving user mental states, enhancing long-term engagement and personalization. To achieve this, we introduce the first integration of a systems-theoretic cognitive model into a closed-loop predictive behavioral control framework for SRs, formulated as a constrained multi-objective optimization problem that enables transparent, cognition-aware adaptation. In experiments with participants interacting with a Nao robot across three chess puzzle sessions (to minutes each), the identified model achieved a mean squared error (MSE) of (i.e., of the maximum possible MSE) in tracking beliefs, goals, and emotions of participants, and increased engagement by () compared to a model-free baseline. Post-interaction participant questionnaires further confirmed the perceived engagement and awareness of the model-based controller. Overall, the framework provides a practical pathway toward SRs that autonomously adapt to users in real time, sustain long-term engagement, and ultimately deliver more effective and personalized assistance in domains such as healthcare, education, and companionship.

Social robots are increasingly deployed in fields such as health care and education to support users through social interactions. Nonetheless, these robots mostly rely on black-box machine learning methods that lack awareness of the mental states of their users, which often leads to unnatural behavior. To address this, we propose three model-based techniques for real-time estimation of invisible mental states of humans. Each method adapts the extended Kalman filter and incorporates a validated dynamic model of human mental states. These mental state estimators are designed for human-robot social interactions and personalize their parameters using initial user data. When tested with 10 human participants interacting with a NAO robot, the mental state estimators reduced the average error in estimation and prediction of mental states across all participants by 3% (i.e., from 12% to 9%), with improvements of up to 13% for individual participants. These results demonstrate the potential of integrating such state estimators into the behavioral control systems of social robots to enhance their awareness of the mental states of users.

The catastrophic impact of disasters on affected populations necessitates effective management practices to minimize the societal and economical damages caused by disasters. This pertains planning effective measures to find and rescue trapped victims in time. Search and rescue in general is very challenging, as the number of the trapped victims may be unknown and their behaviour while trying to evacuate the disaster area is prone to variations, depending on their individual cognition and social interactions. Evacuation robots have attracted attention for their role in assisting search and rescue teams to locate and save victims. A behavioural model of the victims can provide insights for both the staff and the robots in search and rescue missions on how the trapped victims act during an evacuation, and to plan the search and rescue mission accordingly. Such a model, after being validated, can also be used for analysis of the influence of the robots in search and rescue missions. This paper proposes a novel evacuation model that integrates game theory and the belief-desire-intention (BDI) framework, in order to incorporate both the interactions of the trapped victims and their cognitive processes at the individual level. The model is validated using existing benchmark models for evacuation behaviour. Furthermore, the validated model is used to assess the effectiveness of the evacuation robots within the evacuation procedure. It is found that the presence of evacuation robots does reduce the evacuation time, as a function of the trust of the victims in these robots.

Socially assistive robotics is an emerging field that, through effective human-robot cognitive interactions (HRCIs), offers potential solutions for personalized care, education, and entertainment. For improved impact and for acceptance by humans, socially assistive robots (SARs) should autonomously personalize and adapt their behavior to, respectively, the personality and the changes in the states-of-mind of people they interact with. Despite extensive research on the ethical, societal, and psychological aspects of SARs, bridging systems-and-control-based methods and socially assistive robotics for developing control approaches that automate the personalization and adaptation of HRCIs remains under-attended. We propose the first systematic and generalizable paradigm for personalization and adaptation of the social interactive behaviors of SARs, combining two highly promising modeling and decision making approaches, namely fuzzy logic control (FLC) and reinforcement learning (RL). By replicating the rule-based decision making of humans, FLC provides a highly effective personalization mechanism and warm-starts the RL algorithm, which takes care of adapting the behaviors of SARs to the dynamics of people's state-of-mind. Fuzzy logic is also used to develop two consecutive processes inside the RL-based adaptation module that, from the emotional responses of humans, estimate their state-of-mind and assign a reward to the most recent action of the SAR. Our extensive experiments for validation of this combined paradigm and for comparing it with conventional RL methods show meaningful improvements in the criteria that assess the personalization, convergence of learning, and performance accuracy of the proposed steering system for SARs.

Robots will bring Search and Rescue (SaR) in disaster response to another level, in case they can autonomously take over dangerous SaR tasks from humans. A main challenge for autonomous SaR robots is to safely navigate in cluttered environments with uncertainties, while avoiding static and moving obstacles. We propose an integrated control framework for SaR robots in dynamic, uncertain environments, including a computationally efficient heuristic motion planning system that provides a nominal (assuming there are no uncertainties) collision-free trajectory for SaR robots and a robust motion tracking system that steers the robot to track this reference trajectory, taking into account the impact of uncertainties. The control architecture guarantees a balanced trade-off among various SaR objectives, while handling the hard constraints, including safety. The results of various computer-based simulations, presented in this paper, showed significant out-performance (of up to 42.3%) of the proposed integrated control architecture compared to two commonly used state-of-the-art methods (Rapidly-exploring Random Tree and Artificial Potential Function) in reaching targets (e.g., trapped victims in SaR) safely, collision-free, and in the shortest possible time.

Parameterized model predictive control (PMPC) is one of the many approaches that have been developed to alleviate the high computational requirement of model predictive control (MPC), and it has been shown to significantly reduce the computational complexity while providing comparable control performance with conventional MPC. However, PMPC methods still require a sufficiently accurate model to guarantee the control performance. To deal with model mismatches caused by the changing environment and by disturbances, this paper first proposes a novel framework that uses reinforcement learning (RL) to adapt all components of the PMPC scheme in an online way. More specifically, the novel framework integrates various strategies to adjust different components of PMPC (e.g., objective function, state-feedback control function, optimization settings, and system model), which results in a synthesis framework for RL-based adaptive PMPC. We show that existing adaptive (P)MPC approaches can also be embedded in this synthesis framework. The resulting combined RL-PMPC framework provides a solution for an efficient MPC approach that can deal with model mismatches. A case study is performed in which the framework is applied to freeway traffic control. Simulation results show that for the given case study the RL-based adaptive PMPC approach reduces computational complexity by 98% on average compared to conventional MPC while achieving better control performance than the other controllers, in the presence of model mismatches and disturbances.

Ensuring safety in autonomous systems is essential as they become more integrated with modern society. One way to accomplish this is to identify and maintain a safe operating space. To this end, much effort has been devoted in the field of reachability analysis to obtaining control-invariant sets which ensure that a system inside of these sets can remain in these sets, and are thus essential for guaranteeing a system's safety. However, control invariance does not imply that a system can move from any state in the control-invariant set to any other state in the control-invariant set, within a given time horizon. In this paper, we develop an algorithm to obtain a control-invariant set that allows a given system to move from any state in the set to any other state in the set within a given time horizon without having to leave the set. We call this the 'maneuver set', M. We substantiate the algorithm's efficacy through mathematical proof, affirming that the maneuver set obtained through the algorithm is indeed control-invariant. Furthermore, we prove that the system is indeed able to move from any state within this set to any other state in the set. To illustrate the use of our algorithm, we provide the numerical example of a Dubins car, utilising Hamilton-Jacobi-Bellman reachability analysis along with the proposed algorithm in order to obtain M.

Most real-world systems are affected by external disturbances, which may be impossible or costly to measure. For instance, when autonomous robots move in dusty environments, the perception of their sensors is disturbed. Moreover, uneven terrains can cause ground robots to deviate from their planned trajectories. Thus, learning the external disturbances and incorporating this knowledge into the future predictions in decision-making can significantly contribute to improved performance. Our core idea is to learn the external disturbances that vary with the states of the system, and to incorporate this knowledge into a novel formulation for robust tube model predictive control (TMPC). Robust TMPC provides robustness to bounded disturbances considering the known (fixed) upper bound of the disturbances, but it does not consider the dynamics of the disturbances. This can lead to highly conservative solutions. We propose a new dynamic version of robust TMPC (with proven robust stability), called state-dependent dynamic TMPC (SDD-TMPC), which incorporates the dynamics of the disturbances into the decision-making of TMPC. In order to learn the dynamics of the disturbances as a function of the system states, a fuzzy model is proposed. We compare the performance of SDD-TMPC, MPC, and TMPC via simulations, in designed search-and-rescue scenarios. The results show that, while remaining robust to bounded external disturbances, SDD-TMPC generates less conservative solutions and remains feasible in more cases, compared to TMPC.

Search and rescue (SaR) is challenging, due to the unknown environmental situation after disasters occur. Robotics has become indispensable for precise mapping of the environment and for locating the victims. Combining flying and ground robots more effectively serves this purpose, due to their complementary features in terms of viewpoint and maneuvering. To this end, a novel, cost-effective framework for mapping unknown environments is introduced that leverages You Only Look Once and video streams transmitted by a ground and a flying robot. The integrated mapping approach is for performing three crucial SaR tasks: localizing the victims, i.e., determining their position in the environment and their body pose, tracking the moving victims, and providing a map of the ground elevation that assists both the ground robot and the SaR crew in navigating the SaR environment. In real-life experiments at the CyberZoo of the Delft University of Technology, the framework proved very effective and precise for all these tasks, particularly in occluded and complex environments.

Recent advances in robotics and artificial intelligence have made it necessary or desired for humans to get involved in interactions with social robots. A key factor for the human acceptance of these robots is their awareness of environmental and social norms. In this paper, we introduce SONAR (for SOcial Norm Aware Robots), a novel robot-agnostic control architecture aimed at enabling social agents to autonomously recognize, act upon, and learn over time social norms during interactions with humans. SONAR integrates several state-of-the-art theories and technologies, including the belief-desire-intention (BDI) model of reasoning and decision making for rational agents, fuzzy logic theory, and large language models, to support adaptive and norm-aware autonomous decision making. We demonstrate the feasibility and applicability of SONAR via real-life experiments involving human-robot interactions (HRI) using a Nao robot for scenarios of casual conversations between the robot and each participant. The results of our experiments show that our SONAR implementation can effectively and efficiently be used in HRI to provide the robot with environmental and social and norm awareness. Compared to a robot with no explicit social and norm awareness, introducing social and norm awareness via SONAR results in interactions that are perceived as more positive and enjoyable by humans, as well as in higher perceived trust in the social robot. Moreover, we investigate, via computer-based simulations, the extent to which SONAR can be used to learn and adapt to the social norms of different societies. The results of these simulations illustrate that SONAR can successfully learn adequate behaviors in a society from a relatively small amount of data. We publicly release the source code of SONAR, along with data and experiments logs.

Humans and autonomous vehicles will jointly use the roads in smart cities. Therefore, it is a requirement for autonomous vehicles to properly handle the information and uncertainties that are introduced by humans (e.g., drivers, pedestrians, traffic managers) into the traffic, to accordingly make proper decisions. Such information is commonly available as linguistic, fuzzy (non-quantified) terms. Thus, we need mathematical modeling approaches that, at the same time, handle mixed (i.e., quantified and non-quantified) data. For this, we introduce novel type-2 sets and membership functions to translate such mixed traffic data into mathematical concepts that handle different levels and types of uncertainties and that can undergo mathematical operations. Next, we propose rule-based data processing and modeling approaches to exploit the advantages of these sets. This is inspired by the rule-based reasoning of humans, which has proven to be very effective and efficient in various applications, especially in traffic. The resulting models, hence, handle more than one level and type of uncertainty, which results in precise estimations of traffic dynamics that are comparable in accuracy with similar analyses if only one level of uncertainty (either probabilistic or fuzzy) would exist in the dataset. This will significantly improve the analysis, prediction, management, and safety of traffic in future smart cities.

Model Predictive Control (MPC) optimizes an objective function within a prediction window under constraints. In the presence of bounded disturbances, robust versions are used. Recently, a promising robust MPC was introduced that outperforms SOTA approaches. However, solving the optimization problem online is computationally expensive. An efficient approximation method, such as neural networks (NN), can be substituted to accelerate the online computation. There are discrepancies between the control inputs due to the approximation. We propose to model them as bounded state-dependent disturbances to robustly control nonlinear wheeled robots. We consider a spiking NN to ensure that small robots could use it.

Search-and-rescue (SaR) in unknown environments is a crucial task with life-threatening risks. SaR requires precise, optimal, and fast decisions to be made. Robots are promising candidates expected to execute various SaR tasks autonomously. While humans use heuristics to effectively deal with uncertainties of SaR, optimisation of multiple objectives (e.g., the mission time, the area covered, the number of victims detected), in the presence of physical and control constraints, is a mathematical challenge that requires machine computations. Thus including both human-inspired and mathematical capabilities in decision making of SaR robots is highly desired. However, developing control approaches that exhibit both capabilities has been significantly ignored in literature. Moreover, coordinating the decisions of the robots in large-scale SaR missions with affordable computation costs is an open challenge. Finally, in real-life, due to defects (e.g., in the sensors of the robots) or environmental factors (e.g., smoke) data perceived by SaR robots may be prone to uncertainties. We introduce a hierarchical multi-agent control architecture that simultaneously provides the following advantages: exploiting non-homogeneous and imperfect perception capabilities of SaR robots; improving the global performance as it is provided by centralised controllers; computational efficiency and robustness to failure of the central controller as offered by decentralised control methods. The integrated structure of the proposed control framework allows to combine human-inspired and mathematical decision making methods, via respectively fuzzy logic and model predictive control, in a coordinated and computationally efficient way. Our results for various computer-based simulations show that while the area coverage with the proposed control approach is comparable to existing heuristic methods that are particularly developed for coverage-oriented SaR, our approach has a significantly better performance regarding locating the trapped victims. Furthermore, with comparable computation times, the proposed control approach successfully avoids conflicts that may appear in non-cooperative control methods. In summary, the proposed multi-agent control system is capable of combining coverage-oriented and target-oriented SaR in a balanced and coordinated way.

Interactive machines should establish and maintain meaningful social interactions with humans. Thus, they need to understand and predict the mental states and actions of humans. Based on Theory of Mind (ToM), in order to understand and interact with each other, humans develop cognitive models of one another. Our main goal is to provide a mathematical framework based on ToM to improve the understanding of interactive machines regarding the perception, cognition, and decision-making of humans. Most state-of-the-art models of behavioral theories based on machine learning are focused on input-output black-box representations. Thus, they lack transparency and generalizability, and exhaustive training procedures are needed to personalize them for various humans. Moreover, these models lack dynamics, i.e., they do not mathematically describe the evolution of the mental states and actions of humans in time. Following a systems-and-control-theoretic point-of-view, we represent for the first time the perception, cognition, and decision-making of humans via a dynamic, mathematical framework by introducing a novel formalization and an extension to Fuzzy Cognitive Maps (FCMs). The resulting models are given in a general state-space representation, which can be used by interactive machines within known model-based state estimation and control methods. In a case study, the resulting models were identified and validated for 21 participants, in scenarios where predicting the intentions and behavior of the participants required understanding the dynamics of their mental procedures. The results of these experiments show that our model is capable of incorporating the dynamics to estimate the intentions and predict the behavior of the participants, with an accuracy of, respectively, 81.55% and 66.06%. Moreover, we compared our model with a state-of-the-art formalization of human cognition, which was made dynamic using our introduced FCM framework. Our model, which in addition to the elements of the state-of-the-art model included emotions, personality traits, and biases (thus providing a more transparent insight about the mental procedures of the participants) showed 6.25% and 2.45% more accuracy in, respectively, estimating the intentions and predicting the behavior of the participants.