Model Predictive Control

The repeated forward-reverse maneuvers performed by wheel loaders during earthmoving operations make them well suited for automation. However, the nonlinear dynamics of articulated vehicles and complex vehicle-terrain interactions limit the effectiveness of conventional model-based approaches. This paper presents a hierarchical framework that combines long-horizon geometric planning with data-driven predictive control for autonomous wheel-loader operation. A reduced-order articulated kinematic model is used to generate the maneuver geometry, where the forward and reverse trajectories are jointly optimized through a shared intermediate state. To capture the vehicle dynamics, two data-driven deep bilinear Koopman models are learned for the forward and reverse motions using data generated from high-fidelity simulations in Algoryx Dynamics. The learned Koopman representations are subsequently incorporated into a computationally efficient model predictive control (MPC) formulation for trajectory tracking. The resulting controller operates in real time within a 50-ms execution loop. High-fidelity simulation results demonstrate that the proposed end-to-end framework enables accurate and computationally efficient execution of wheel-loader V-cycle maneuvers, providing a promising approach toward autonomous operation of articulated heavy-duty machinery.

Adaptive regulation can itself perturb the state it is intended to stabilize. In replicated simulations of an adaptive agent, we compare external disturbance, persistent internally generated disturbance, and control-generated disturbance under regulation-first and disturbance-first ordering. Persistent internal disturbance produces the largest exposure and regulatory burden within the tested parameter grid. When positive controller updates generate an immediate disturbance cost, increasing that cost produces a nonmonotonic response: effective disturbance initially rises, variability across stochastic runs increases over an intermediate range, and corrective activity becomes strongly suppressed at higher costs. The results show how disturbance source and timing shape exposure and controller burden in this model. They motivate testing adaptive agents with distinct disturbance sources and assessing regulatory activity alongside exposure.

Providing safe and effective mobility assistance plays a crucial role in restoring independence and enhancing the quality of life for individuals with motor impairments. In this context, robotic walking assistive devices have recently emerged as promising solutions to provide physically compliant interaction while ensuring user safety and support. This paper presents a novel control framework for an omnidirectional Walking Assistive Robot (I-WANDER) that integrates a Control Barrier Function (CBF) formulation into a Model Predictive Control (MPC) scheme to explicitly enforce collision-avoidance safety constraints while optimizing for energy efficiency and smooth human-robot collaboration. The method was experimentally evaluated with 12 healthy participants performing two different walking tasks using both the proposed CBF-based MPC controller (CB-MPC) and a variable admittance controller (AC). The first task involved structured navigation through a U-shaped corridor, whereas the second consisted of a single-obstacle avoidance task performed blindfolded to ensure the obstacle was unexpected. Comparative results show that the CB-MPC architecture significantly reduces energy consumption and mechanical work (p < 0.01) without compromising motion smoothness, while also decreasing the number of obstacle collisions. Overall, the findings highlight the potential of the proposed control architecture to enhance both safety and efficiency in robotic walking assistance.

Safety evaluation in sampling-based stochastic model predictive control often requires numerical estimation of exit functionals. The approximation of first-exit times and exit indicators is therefore a key numerical bottleneck, and discretization error in these quantities directly affects the resulting controller. This paper studies how existing higher-order methods for strong approximation of exit times can be brought into safe control. Two cases are highlighted. For general noncommutative dynamics, an adaptive order-1 Milstein discretization is used together with Lévy-area simulation via Wiktorsson's method. For commutative dynamics, an adaptive order-1.5 construction achieves a stronger exit-time rate. Under a local anti-concentration condition on the exit-time law, we show that strong exit-time approximation transfers to strong approximation of the failure indicator. The methods are then studied in the context of chance-constrained path integral control, which provides an exact continuous-time representation of safety through exit events. Numerical experiments compare the two cases in terms of strong exit-time error, failure-indicator error, and closed-loop constraint satisfaction, showing improvement over Euler-Maruyama and thereby enabling existing and future techniques whose applicability depends on improved strong approximation.

The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives, thereby facilitating a fully data-driven feedback linearization framework. Furthermore, practical closed-loop stability is established by deriving sufficient conditions under which bounded identification errors lead to bounded tracking errors. The derived theoretical results are validated through their application to an armature controlled DC motor.

Hyper-redundant robots are well suited for confined-space manipulation due to their high dexterity, but safe operation in cluttered environments remains challenging. In addition, their slender structures often lead to uneven load distributions and nonuniform tracking errors along the body. To address these issues, this work proposes a weighted control barrier functions (W-CBFs) framework that enforces safety constraints while reducing tracking errors caused by uneven loading. The proposed controller was first evaluated on a circular path-following task under different obstacle configurations. With fixed weights, compared to the non-weighted method, the maximum reduction in root-mean-square (RMS) tracking error was 59.6% in simulation and 87.7% in physical experiments. An adaptive weighting strategy was then investigated based on the discrepancy between simulated and experimental performance under different mapping functions. The RMS errors were further reduced by 21.9% and 8.5%, respectively, although the error increases when obstacles were located close to the robot body. Finally, the robot was evaluated in a cleaning task requiring coverage of a rectangular area and compared with manual teleoperation. Although the controller was not explicitly optimized for area coverage, the autonomous strategy achieved comparable or better coverage performance while avoiding collisions with the surrounding frame, whereas collisions occurred during manual operation.

Control barrier functions (CBFs) have become one of the most popular tools for encoding and enforcing state constraints in safety-critical robotics. Standard CBF approaches are inherently myopic in nature as they enforce safety only at the current time step. Consequently, the system can be driven toward the boundary of the safe set where no feasible safe control exists at a future timestep. Model predictive control (MPC) based approaches address this by enforcing state constraints over a receding horizon. However, such approaches generally require the model to be known for solving a constrained optimization problem at every step, which is computationally expensive for real-time deployment. We propose BarrierFormer, a barrier-supervised transformer framework that addresses these limitations by encoding rollout-level CBF constraints in learning a model-free safe policy. A causal transformer encodes observation-action history, autoregressively generates a predictive rollout through the dynamics head to replace the model, and provides a residual correction to a nominal controller through the action head to replace the online computation. A barrier critic operating on local observations evaluates CBF constraint violations along this rollout, and a safety teacher computes barrier-consistent actions satisfying these constraints as direct supervision targets for the learned control policy. During inference, the policy maps observation-action history to control actions without any online optimization or model knowledge, enabling real-time model-free predictive safety enforcement. Evaluations across linear and nonlinear, 2D and 3D dynamical systems for safe goal-directed navigation demonstrate that BarrierFormer outperforms existing reinforcement learning (RL)-based, diffusion-based, MPC-based, and transformer-based approaches in safety rate and inference latency.

Vision-based underwater target tracking is challenged by unreliable depth measurements and unknown target motion. This paper proposes a stereo visual-servoing framework for an autonomous underwater vehicle (AUV). For perception, the framework derives a stable 3D relative state from stereo images through target-specific depth extraction and Kalman filtering. It constructs a target-depth mask from color, disparity, and temporal cues to select reliable target pixels, and then filters the resulting depth measurement and detected image center separately. For control, the framework decouples yaw regulation from translational control, avoiding computationally expensive coupled multi-DOF optimization and enabling real-time translational MPC. The translational controller employs adaptive model-fusion predictive control, combining constant-velocity and zero-velocity target models to accommodate different target-motion patterns. It updates the model weights using historical prediction errors and computes translational commands subject to actuation, following-distance, and field-of-view constraints. Through simulations and real-world experiments, we validate the effectiveness of the proposed framework and show it has better performance than existing frameworks.

Learning visual policies for locomotion and manipulation requires coordinating contact with the environment and can incur substantial computation and GPU memory costs. First-order policy gradients (FoPG) reduce training cost through differentiable simulation, but local optimization can converge to unintended contact patterns. To address this shortfall, we propose Sampling-Guided Policy Search (SGPS), which couples recurring action-target refinement by sampling-based model-predictive control with first-order policy optimization. Behavior cloning initializes the policy from sampled actions; training then alternates sampling-based refinement with short-horizon FoPG updates under perturbed initial states and randomized dynamics. For visual policy training, we use a decoupled FoPG formulation that excludes rendering from the computation graph, enabling direct learning from depth observations without a state-policy teacher. On a single GPU, SGPS learns policies for locomotion, obstacle traversal, crate pushing, and bimanual carrying on simulated Unitree Go2 and G1 robots. Our experiments further show that refinement improves policy learning beyond initialization and tracking alone. For hardware deployment, the distilled policy transfers zero-shot to a real Go2 and uses onboard depth to autonomously trot, crawl, clear hurdles, and switch between these behaviors.

This work proposes a physics-enhanced machine learning approach for the system identification of Linear Time-Varying (LTV) systems under time-varying operating conditions in terms of fast-varying natural frequencies and damping ratios by combining a long short-term memory network with an Extended Kalman Filter (EKF). The proposed approach uses vibration data (displacement and velocity measurements), domain knowledge of modal damping ratios, and a physics-based model that can yield an approximate natural frequencies time-dependency model. The approach is validated using synthetic data generated from a finite element model of a 2-blade offshore wind turbine under realistic environmental and operating conditions. This system displays fast time-varying frequencies due to operating conditions, whose identification is particularly challenging because of the wind and wave loading. The robustness of the proposed approach is assessed under assumed incorrect system information (e.g. damping ratio). The proposed approach is evaluated across different environmental and operating conditions to show its applicability to different operating regimes. The results show the approach can accurately identify the selected fast-varying natural frequency, 1st Fore-Aft (FA-1) mode, with a maximum root mean square error of 0.0012 Hz. The results demonstrate that the model trained on EKF estimates depends on accurate damping values, whereas the model trained on physics-based data exhibits robustness to incorrect damping assumptions. The approach is extended to damping ratio identification for the selected mode by estimating the root mean square error between models trained on EKF estimates and physics-based data. The results show that the approach can yield a good approximation of the FA-1 mode damping ratio using grid search, offering an improvement over covariance-driven stochastic subspace identification.

This paper presents dynamics-relaxed model predictive control (DR-MPC), a novel MPC formulation for legged locomotion, and a tailored interior-point method (IPM) solver. The formulation combines online optimization feasibility by construction with a contact-aware input parameterization. DR-MPC moves the dynamics equality and affine input constraints into quadratic penalties and retains only nonempty box constraints. The resulting box-constrained quadratic program (QP) has a block-arrow Hessian that enables the state and affine-output directions to be eliminated through a Schur complement. The solver factors only the reduced control system after swing-force elimination and contact-aligned move blocking. For the evaluated implementations using the same DR-MPC formulation, our method achieves median end-to-end MPC speedups of $16.0\times$ over HPIPM and $4.4\times$ over OSQP, with comparable locomotion performance in simulation. DR-MPC achieves a median onboard MPC end-to-end time of $4.4$ ms and is validated on a Unitree Go1 quadruped. Open-source code will be made available after publication.

Teams of mobile robots rely on continuous communication with their neighbors for coordination, yet most distributed model predictive control (DMPC) schemes assume the communication network stays connected rather than actively enforcing it. Adding such a guarantee is hard since the usual mathematical condition for connectivity is nonconvex and links every agent to every other, which is incompatible with a scalable distributed real-time controller. We propose a DMPC framework in which each agent is assigned a connectivity contract: a local region prescribing where its predicted positions may lie over the prediction horizon. The contracts are designed so that, as long as every agent stays within its own contract, the team is guaranteed to remain connected. Given the maintained contract graph, an agent builds its contract from a single exchange with its immediate neighbors, after which every agent solves its own optimization problem independently. We prove that the resulting closed-loop system maintains connectivity, avoids collisions, and respects local state and input constraints. Simulation and hardware experiments on miniature autonomous car-like robots demonstrate the approach.

Online residual learning can reduce model mismatch in predictive control, but passive data collection may fail to adequately cover states that become important later in the task. Task-agnostic active learning targets uncertain or informative regions, but information acquired in such regions does not necessarily improve task performance. This paper introduces Task-Oriented Information Acquisition (ToIA), an active-learning criterion for model predictive path integral control (MPPI) with online Gaussian process (GP) residual learning. For each sampled control sequence, ToIA estimates how much an observation obtained early in the rollout would reduce predictive uncertainty at later states on the same rollout, and weights this reduction by the rollout's relevance to the task. The score is evaluated over the existing MPPI rollout batch without sampling future observations or re-optimizing control under hypothetical posterior updates. In simulated off-road navigation across held-out maps with heterogeneous terrain, ToIA improved the goal-reaching success rate over passive GP learning by 19.3 and 27.4 percentage points and outperformed task-agnostic active-learning baselines across dense and sparse online-learning intervals. An ablation study indicates that task relevance is particularly important under sparse model updates. The implementation supports online control at 20 Hz on an NVIDIA RTX 2080 Ti.

Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting their reuse across systems. In this paper, we study the Lyapunov solution operator that maps a vector field to the corresponding Lyapunov function defined by a dissipation-based Lyapunov PDE. We establish that, on compact subsets of the domain of attraction and under exponential stability assumptions, this operator is well-defined, unique, and continuous with respect to perturbations of both the vector field and the dissipation function. These results provide a theoretical foundation for approximating Lyapunov functions uniformly over families of nonlinear systems. Building on these theoretical foundations, we employ Fourier Neural Operators (FNOs) as a data-driven approximation of the Lyapunov solution operator. Numerical experiments demonstrate that a single trained operator can accurately approximate the numerical Lyapunov functions across parameterized families of dynamics. This illustrates the potential of neural operators for approximating Lyapunov functions.

We present a hierarchical UAV navigation framework that aligns natural-language intent with dynamically feasible flight behaviors in cluttered indoor environments. To bridge the gap between abstract semantics and low-level control, we employ a parallelized ensemble of six behavior-conditioned Model Predictive Path Integral (MPPI) planners. Crucially, by designing mode-specific guiding costs and sampling biases, we induce distinct trajectory modes that converge to unique behavioral means, yielding a compact set of intentionally diverse candidates rather than mere stochastic variations. We project these 3D candidates onto the onboard first-person-view RGB stream, turning language grounding into a visual action selection problem. A pretrained vision--language model (VLM) asynchronously selects the candidate index given the overlaid FPV image and a natural-language prompt, while MPPI replans at 20Hz and a PID-based low-level controller tracks the selected trajectory. We implement the full pipeline in NVIDIA Isaac Sim and on a real-world quadrotor platform equipped with LiDAR and RGB sensing. Experiments in both simulation and real-world flights show semantically meaningful behavior diversity, robust language alignment despite VLM latency, and safe, repeatable flight across all modes, achieving 100% task success in our evaluated scenarios.

Selective state space models (SSMs) have recently emerged as a compelling alternative to transformers, combining competitive performance with substantially improved inference efficiency. At each SSM layer, a sequence of hidden states are propagated by a recurrence, mixing information of different tokens. Despite using a different mechanism, this mixing plays a role analogous to attention in transformers. In fact, recent works have shown that the two architectures may be closer than they first appear, as this recurrence admits a formulation akin to linear attention. In transformers, attention is known to drive the tokens to cluster, i.e., to reach consensus, collapsing in the limit to a single direction. Thus, we ask: does the recurrence at the core of SSMs drive the tokens to consensus, as attention does in transformers? To answer this question, we take a dynamical systems perspective on SSMs, modeling the evolution of tokens across layers as an ordinary differential equation. By exploiting input-to-state stability arguments, we establish local exponential stability of the consensus equilibria and characterize their domain of attraction for time-varying weight matrices, a setting not addressed by previous results. We thereby show that the resemblance between SSMs and transformers does run deeper: the recurrence at the core of SSMs aggregates tokens just as attention does. Numerical experiments on a pretrained Mamba-2 model point to the output gate as the component that regulates the extent of this consensus, preventing the tokens from reaching it in full.

This paper extends Mixed-Integer Differentiable Predictive Control (MI-DPC) to multi-modal discrete decisions and nonconvex polynomial dynamics arising in Underground Pumped Hydro Energy Storage Systems (UPHES). A neural policy mapping problem parameters to continuous setpoints and integer mode selections via a Gumbel-Softmax layer is trained in a self-supervised manner by differentiating the expectation of the finite horizon control objective through the nonlinear dynamics model. Three methodological contributions enable this extension: a parallel differentiable simulator that preserves gradient magnitude, a Transformer encoder that captures long-range temporal dependencies, and a Gumbel-Softmax temperature annealing schedule that regularizes the combinatorial search. We demonstrate the framework on day-ahead scheduling of a UPHES, a large-scale mixed-integer optimal control problem with nonlinear unit performance curves and volume-head coupling. MI-DPC achieves only 1.6% suboptimality relative to a piecewise mixed-integer quadratic programming baseline, while providing five orders of magnitude speedup in online scheduling time.

Legged robots have demonstrated a remarkable ability to traverse various terrains, yet generating effective loco-manipulation behaviors remains challenging. A key difficulty is that object and terrain parameters are typically unknown to the robot, and mismatches between these parameters and their simulated counterparts introduce a sim-to-real gap that degrades control performance. Classical system identification (Sys-ID) methods often assume differentiable dynamics, an assumption that does not hold for contact-rich legged systems. Sampling-based Sys-ID avoids this restriction by directly matching simulated and recorded state trajectories through massively parallel rollouts, but existing approaches are typically applied offline and do not adapt as environmental conditions change. We present Adaptive-MHE an online sampling-based Sys-ID framework, based on moving horizon estimation (MHE), that estimates the physical parameters of objects and terrain in the environment (e.g., mass, friction) and couples this estimate with a sampling-based model predictive controller, enabling adaptive loco-manipulation in changing and uncertain environments. In simulation and hardware experiments, our framework consistently outperforms baselines and matches the performance of a controller with access to ground-truth parameters.

Deep Reinforcement Learning has demonstrated remarkable capability in quadrotor control, yet learned policies offer no guarantee of respecting safety constraints during training or deployment. We present CALOS (Control-Affine Lyapunov On-manifold Safety), a runtime safety layer that enforces attitude constraints on a quadrotor without modifying the underlying learning algorithm. CALOS formulates four tilt-angle inequalities and a Lyapunov descent condition as a single quadratic program whose solution is the minimum-norm correction to the nominal torque output of the policy. The quadratic program is solved exactly via active-set enumeration over the three-dimensional torque space, with a computational cost low enough to enforce constraints in real time across thousands of parallel simulation environments, as required by modern massively parallel Deep Reinforcement Learning training. Evaluated on trajectory-tracking tasks in NVIDIA Isaac Lab, CALOS reduces lateral tracking error by 55-60% relative to an unconstrained Proximal Policy Optimization baseline while achieving zero attitude-constraint violations on the training trajectory. By restricting exploration to safe regions of the state space, the safety layer also accelerates training convergence and improves data efficiency without producing suboptimal policies.

Integrated deep reinforcement learning (DRL) and model predictive control (MPC) methods are increasingly used to control autonomous systems by combining their complementary capabilities. DRL learns control policies through interaction with the environment. MPC uses a system model to optimize control inputs while accounting for constraints. In DRL-MPC frameworks with shared control authority, both the DRL agent and the MPC controller each determine part of the control inputs. However, common learning formulations treat MPC as part of the environment and therefore do not explicitly account for MPC's contribution to control or its interaction with the DRL agent. This paper proposes a novel composite-gradient learning (CGL) method that integrates the MPC controller into the learning process by representing the DRL and MPC control inputs as a joint action and accounting for their interaction when updating the DRL agent during training. CGL is evaluated on two multi-class freeway traffic networks with different strengths of interaction between the DRL and MPC control inputs and it is compared with alternative methods that treat MPC as part of the environment or that only partially incorporate MPC into learning. The results show that CGL offers limited benefit under weak interaction, but learns higher-performing control policies than the alternative methods in a subset of training runs under strong interaction, although the average control-performance gains remain modest.

Dexterous in-hand manipulation requires coordinated control of multiple actuated joints, and a runtime joint fault can abruptly disrupt the contact configuration required for successful manipulation. In this work, we propose residual fault adaptation (RFA), a teacher-anchored framework for compensating for hidden command-channel faults. RFA retains a frozen healthy teacher to provide nominal behavior and trains a recurrent residual policy to infer corrective actions from proprioceptive and command-response history. During training, fault-injection domain randomization (FIDR) varies the fault mode, affected joint, severity, and onset time, while adaptive sampling increases the frequency of fault modes associated with lower recent performance. A frozen Direct FIDR policy provides a distributional reference only on fault-active training samples and is absent from deployment. The deployed controller receives neither fault labels nor controller-switching signals. Simulation experiments on the dexterous hand indicate that RFA can improve manipulation performance relative to the healthy policy under a fixed mixed-fault protocol. Real-robot experiments with software-injected faults further demonstrate zero-shot deployment of the learned adaptation policy.

Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mechanics, producing predictions that exhibit artificial energy growth and diverge under recursive propagation. This work presents a structure-preserving Koopman framework for Euler-Lagrange systems built on generalized-momentum coordinates. The momentum transformation exposes the mechanical actuation as a known, state-independent port, which is preserved explicitly in the lifted dynamics. A structure-constrained neural architecture is developed to jointly learn the lifting functions and a port-Hamiltonian Koopman generator, rendering the learned dynamics passive by construction rather than through penalty terms or post-hoc projection. A Cayley-midpoint discretization further preserves the corresponding storage-dissipation balance exactly in discrete time. These properties are established analytically by deriving the discrete storage balance and associated stability guarantees of the learned predictor. Simulation and experimental studies demonstrate improved prediction accuracy, data efficiency, and closed-loop tracking over Koopman baselines, with increasing gains for higher-dimensional systems.

Ensuring that multilingual language models generate coherent text in a specific target language is a major issue in multilingual language modeling. We develop an optimal control method for target-language text generation as well as a framework for evaluating the quality of generated text in terms of language adherence, linguistic coherence, and semantic coherence. We find that the proposed method performs at least as well as the prominent difference-in-means activation steering method for the majority of models tested, with substantially less hyperparameter tuning required.

Autonomous excavator control is challenged by coupled kinematics, actuation lag, and uncertainty. We propose imitation learning and adaptive Cartesian tracking (IL-ACT), a novel motion control framework for a 30-ton-class excavator. An anchored, 14-input imitation policy pretrained on operator demonstrations generates nominal joint rates; adaptive Cartesian feedback and gated gain/bias estimation correct these commands before a stopping-distance governor constrains joint-reference generation. Simscape evaluation covers 100 sequential goals and spiral, figure-eight, and rounded-raster tracking, including 88 additional runs across three training seeds, two initializations, and speeds, under hydraulic response and sensing conditions. Compared with Teacher+ACT, IL-ACT completes all goals with shorter duration and lower terminal errors under both response conditions. Telemetry-initialized IL-ACT lowers RMSE in all 24 figure-eight and rounded-raster seed comparisons and lowers additional-load spiral mean RMSE by approximately 29%. Original spiral RMSE also improves over IL-only and PID. Under a shared sensor-noise realization, telemetry-initialized IL-ACT achieves 27.67% lower mean RMSE than Teacher+ACT; enabling estimation reduces mean RMSE by $22.44\%$ relative to the frozen estimator. Pretrained-weight effects remain mixed, and the original teacher comparison exhibits a spiral RMSE--maximum-error tradeoff. Analysis establishes bounded adaptive states and Cartesian feedback, with reference admissibility conditional on governor feasibility.

Manufacturing consumes one third of global energy and still has significant room for improvement in terms of energy efficiency. Optimal process control is essential for this purpose. However, synthesizing mathematical optimization models from messy, real-world industrial specifications requires bridging unstructured natural language and spatial diagrams with rigorous mathematical syntax. This poses a profound challenge for general-purpose Large Language Models (LLMs), which may introduce invalid constraints when tasked with modeling continuous multi-physics dynamics. To address this, we introduce little m, an AI agent designed to assist the formulation of industrial process control models. Combining a domain-specific knowledge repository with LLM-driven interaction, the proposed framework formulates real-world optimization problems as mathematical models. For systematic evaluation, we introduce the Industrial Process Control Benchmark (IPC-Bench), a novel multimodal dataset of 50 canonical scenarios requiring joint reasoning over text and process diagrams. Through comprehensive automated structural assessments and double-blind human evaluation, little m substantially outperforms state-of-the-art LLMs, generating semantically correct models. These evaluations assess formulation quality rather than solver feasibility, formal physical validity, or closed-loop industrial performance. The implementation of little m and the IPC-Bench dataset are available at https://github.com/yeyongchao/process-modeling-benchmark.

Astrocytes are non-neuronal glial cells that are receiving widespread attention due to their emerging role in neural computation. In this paper, we propose and study dynamical mechanisms by which astrocytes may augment the ability of neural networks to infer context in reinforcement learning (RL) settings. We construct a biologically inspired, two-level dynamical neural-astrocyte network with distinct spatial and temporal organization. We train this model on a hierarchical multi-context task that requires the agent to infer changes in latent task rules based on derived rewards. We find that in this setting, astrocytes enable evidence accumulation of changes in context and subsequent context-specific modulation of neural dynamics. We show that these functions are implemented via two dynamical mechanisms: (i) reward-induced bifurcations that relocate an asymptotically stable attractor into different, context-specific regions of state space, and (ii) the relative shallowness of these attractors, mediated by the entropy of the environment, giving rise to behavioral stickiness. Together, these mechanisms amount to a hybrid automaton, in which uncertainty accumulates until, eventually, the neural dynamics are switched to a new context. This model provides a neuro-dynamic schema, compatible with neural-astrocyte biology and prior empirical observations, for how astrocytes may integrate information from the periphery and drive contextual changes in neural circuits.

The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.

Pretrained world models, learned simulators that encode an observation into a latent state and predict how it evolves under actions, are beginning to be reused as off-the-shelf dynamics backbones for control, like pretrained encoders and language models are reused today. We show that this reuse opens a supply-chain backdoor: an adversary who controls only a released checkpoint can hijack the downstream controller, even though the victim trains and evaluates entirely on clean data and never sees the trigger. The attack encodes no explicit trigger-to-action rule. Instead, the poisoned model routes trigger-bearing observations into a chosen latent region and reshapes the local dynamics there, so that the victim's own optimization (Dreamer-style actor training in imagination, or MPC/CEM planning over predicted futures) re-discovers the attacker's target action on its own. Across several control tasks and trigger families, the trigger steers the controller's action toward the attacker's target, controlling every action dimension and hijacking 100% of triggered steps on the strongest settings. The checkpoint still passes the clean-data diagnostics a victim would run before deployment, with clean-task success retaining at least $\sim$75%. The effect is temporally gated: it appears only while the trigger is present and disappears when the trigger is removed. Trigger-blind repair is budget-dependent: moderate clean fine-tuning can preserve clean utility while leaving the triggered failure intact, whereas sufficiently aggressive adaptation can remove it only after substantially degrading clean control. The world-model backbone itself is therefore an emerging and underexamined attack surface for control. The full code and artifacts are available in our repository.

The deployment of a geoengineering program to cool Earth's climate may be imminent. It is crucial that tools be developed to ensure that such a program would achieve its objectives while minimizing disruption. Here we exploit recently developed differentiable atmospheric models to demonstrate a novel geoengineering control strategy. In the differentiable primitive-equation atmospheric model JAX-GCM we impose a uniform $+4$,K ocean warming and ask what pattern of sea-surface temperature cooling -- in five ocean-masked zonal bands of prescribed SST forcings whose amplitudes are free -- returns land near-surface air temperature closest to the model's own unwarmed climatology. This idealized set-up represents a cooling pattern that could be delivered physically either by marine cloud brightening or stratospheric aerosol injection. Gradients through chaotic dynamics decorrelate from the true sensitivity beyond the Lyapunov horizon, so we optimize greedily over segments of 8 to 14 days, following receding-horizon control. The learned strategy removes $92.3 \pm 0.4\%$ of the realized land warming across a ten-member ensemble of two-year rollouts, and a three-year run sustains it. If we use the spatial pattern of land temperature as the optimization objective, the distributions of precipitation, evaporation, and specific humidity over land are restored as well, even though they are not included in the objective function. The learned strategy from JAX-GCM replayed in the AI emulators LUCIE and NeuralGCM without re-optimization is successful, suggesting robustness. These promising results demonstrate a strategy for designing optimal climate interventions that can be applied broadly for geoengineering scenarios under consideration.

Reactive synthesis is a powerful tool for generating correct-by-construction controllers from formal specifications. GR(1) is an assume-guarantee specification framework that enables efficient synthesis, allowing synthesised controllers to be used in a wide array of applications. The limitation of such controllers is that, should they encounter environment behaviour unspecified in the assumptions of the specification, the specified system guarantees are no longer ensured. Our work proposes an approach based on oracle-guided inductive synthesis to adapt the specification to be consistent with the observed assumption violation, while degrading system guarantees as little as possible to maintain realisability. Our methodology discovers multiple potential solutions, so we propose a preference criteria, based on the ability of the specification to enable robustness under adaptation. Although our approach is capable of degrading the entire specification, for our case studies we successfully discover degradations that preserve the entire set of original guarantees.

Hydrogen supply chains are expected to play a central role in future low-carbon energy systems by enabling renewable energy integration, long-duration storage, and decarbonization of industrial and transportation sectors. However, their operation is challenged by renewable generation variability, electricity price fluctuations, uncertain hydrogen demand, and engineering constraints associated with electrolyzers, energy storage, and grid interaction. As hydrogen infrastructure expands toward commercial deployment, operational strategies must balance economic performance, reliability, and sustainability under dynamic and uncertain conditions. This paper investigates and compares four control approaches for a renewable-powered hydrogen supply chain: a rule-based controller (RBC), model predictive control (MPC), reinforcement learning without forecasts (RL-NF), and reinforcement learning with forecast-augmented observations (RL-F). All methods are evaluated within a unified, physically realistic framework incorporating electrolyzer minimum-load and ramp-rate constraints, battery and hydrogen storage dynamics, grid import limits, and consistent economic assumptions, enabling a fair comparison under identical operating conditions. Simulation results show that MPC achieves the highest economic performance by exploiting short-term forecasts to coordinate storage, reduce grid dependence, and improve efficiency. RL-NF demonstrates robust and competitive performance without future information, highlighting the capability of learning-based methods to discover effective policies from experience. RL-F does not consistently outperform its no-forecast counterpart, suggesting that forecast uncertainty and increased state complexity can limit forecast-augmented learning. The results provide guidance for selecting operational control strategies in future hydrogen energy systems.

We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz. For the Moreau-smoothed target $\pi_\lambda$ and the MYULA invariant law $\widehat\pi_{\lambda,h}$, we prove $$\sqrt m\,W_2(\pi_\lambda,\widehat\pi_{\lambda,h}) =O(h)+\widetilde O(h^{3/4})$$ under $0<h(L_f+\lambda^{-1})\le c$, with only logarithmic dependence on $\lambda^{-1}$ in the error coefficients. Combining this estimate with the Moreau approximation bias yields $\widetilde O(\varepsilon^{-4/3})$ iterations to achieve $\sqrt m\,W_2(\mu_N,\pi)\le\varepsilon$, for fixed model parameters and initialization. The proof combines a discrete Poisson corrector with active-trace estimates and a shared-noise bound for the exact--Euler two-point curvature.

We study loss-based filtering for finite-sum optimization with a subset of corrupted component functions whose gradients may be highly unreliable. Motivated by minimum-loss-based SGD (min-$k$-loss) and quantile-based methods for corrupted linear systems, we propose and analyze a general loss-filtering framework -- Quantile-$k$-Loss SGD (Q$k$L-SGD) -- that samples $k$ component losses at each iteration and updates using an index chosen uniformly from the lower empirical $q$-quantile. We prove linear convergence of this family of methods under standard convexity assumptions, requiring the sample size to scale with the number of corruptions and a subset strong-convexity threshold. For the cases when large enough sampling is impossible or undesirable, we give a complementary small-sample probabilistic analysis that covers any sample size $k$ and the convergence behavior depends on the probability of selecting an outlier and on the curvature of the selected good step. Experiments on polynomial regression, regularized logistic regression, and regularized hinge loss show that intermediate quantiles often outperform both standard SGD and min-$k$-loss SGD. In particular, min-$k$ often stalls by repeatedly selecting nearly solved components, while intermediate quantiles retain robustness and produce more informative updates.

The deployment of Federated Learning (FL) in multi-center clinical networks faces the challenge of "knowledge dominance," where high-volume hubs naturally overwhelm minority community nodes, implicitly treating the distinct clinical patterns of smaller cohorts as outliers. Existing geometric defenses provide a security baseline but leave this efficiency-fairness dilemma unresolved. To bridge this gap, we propose Fed-Equilibrium, a framework that advances the paradigm from simple defense to topological equilibrium. Unlike traditional aggregators, Fed-Equilibrium implements a sequential architectural synergy. It utilizes a two-stage gradient control cascade: Stage I (geometric quality assurance) enforces directional consistency via a cosine similarity funnel to filter malicious noise, creating a stabilized manifold; Stage II (topological Pareto control) then actively modulates verified contributions by identifying the optimal Pareto knee point. We validated this framework on a bi-national simulation integrating Canadian (CNODES) and U.S. (SyntheticMass) registries. Experimental results demonstrate that the system simultaneously secures the network against adversarial divergence while accommodating underrepresented signals. Notably, the minority U.S. spoke (representing less than 3% of data volume) achieved deep convergence comparable to the data-rich Canadian hub. This confirms that Fed-Equilibrium effectively counters "knowledge dominance," establishing a true "knowledge commons" where global generalizability does not come at the cost of local clinical representation.

This paper presents a Model Predictive Control-based motion planning and control pipeline for autonomous car racing capable of adapting to different driving contexts, such as overtaking, nominal driving, and countersteering. A Cost Blending state machine manages the identification of different driving contexts and the selection of their predefined weights to be applied to the Model Predictive Planning (MPP) and Control (MPC) modules. The two optimization-based solutions share the same problem formulation and model, differing only in horizon length, rate, tuning, and in their open-loop versus closed-loop approach to maximize the effectiveness of their interaction. The work is validated on the fully autonomous open-wheel racecar Superformula EAV-25, with a lap time achieved that is within 2% of the best human driver reference. The results demonstrate the capability of the solution in driving at the limit of handling, smoothly executing overtaking maneuvers, and quickly reacting to high oversteering conditions to recover the vehicle stability.

As the number of autonomous robots continues to grow, safety becomes increasingly important. Control barrier functions (CBFs) provide a theoretically grounded framework for ensuring safety, but existing design methods often face limitations in effectiveness, scalability, or interpretability, and may result in overly conservative safe sets. In this paper, we propose \emph{VertexCBF}, a framework for learning neural CBFs in a scalable, systematic, and explainable way. We approximate the stationary Hamilton--Jacobi value function using a neural network trained via a combination of physics-informed and sparsely supervised learning. By exploiting control-affine dynamics and a convex polytope control set, under which the Hamiltonian is maximized at the control vertices, we efficiently generate supervision points via GPU-parallel vertex-restricted tree search, while a residual architecture guarantees that the learned CBF is never larger than the specified constraint function. We evaluate the method on 15 systems and compare it against relevant baselines, showing that it reliably recovers large safe sets where the baselines are conservative or fail completely. In addition, we perform a hardware experiment in which a mobile robot safely avoids pedestrians using a neural CBF trained with our method.

Functional integration is a growing trend in vehicle control, often involving the coordination of multiple controllers to achieve various objectives simultaneously. The need for flexibility and reliability has led to a "plug-and-play" approach in control system design, which presents challenges for traditional integrated model predictive control (MPC). Agent-based model predictive control (AMPC) has recently emerged as a distributed solution that treats controllers as agents, creating a collaborative framework among them to reach a common goal. However, this approach struggles to manage distributed conflicting objectives when agents are coupled or interdependent. To address this, we propose a novel, practical distributed control scheme called multi-objective AMPC, which adapts the alternating direction method of multipliers (ADMM) into a general control strategy that approximates global optimization while decoupling objectives. We systematically develop three formulations that maintain convergence while addressing control regularization and inequality constraints, applying them to complex vehicle control systems for the first time. The proposed method has been tested on two vehicle control scenarios with a multi-objective topology. Different formulations are compared through simulations, and the most computationally efficient one was implemented on an electric vehicle for real-world evaluations. The results demonstrate that the proposed multi-objective AMPC can converge approximately to the same global optimum as integrated MPC with greater flexibility and the potential to reduce computational costs.

Robotic bioprinting and Direct Ink Writing (DIW) are being explored towards the treatment of Volumetric Muscle Loss (VML). While previous studies have shown the importance of proper parameter selection on the print outcome, existing approaches often rely on time- and material-intensive design of experiments methods, or require large, well-curated datasets for training machine learning models. In this paper, we propose a physics-based closed-loop robotic bioprinting system capable of near real-time parameter adaptation. The system integrates a 3D point cloud camera and fully autonomous vision-based algorithms to provide quantitative evaluation of printed constructs. This evaluation is fed into a controller that adjusts printing parameters to achieve a desired bead thickness. To assess the framework's performance, four experimental configurations were tested, each repeated three times. In these tests, printing began from an arbitrary initial parameter value, and the controller was tasked with adjusting the parameters to reach the desired thickness. The system converged in all trials, achieving a tracking error below 0.5 mm within an average of 5.2 seconds from the start of printing. The low standard deviation of the converged pressure over different tests (0.04 bar on average) demonstrates robustness and repeatability. Additional experiments were conducted with the controller turned off, enabling direct comparison with open-loop DIW bioprinting, further confirming the effectiveness of the proposed closed-loop framework in achieving the desired bead geometry.

Agent-based model predictive control (AMPC) has recently been proposed for vehicle systems with various controllers, such as differential braking and torque vectoring, where controllers are regarded as distributed agents contributing to the same objective. However, this scheme is challenging in handling multiple conflicting objectives with coupled agents. A common approach for such tasks is the integrated MPC, where all objectives and agents are stacked together in one optimization. Nevertheless, as more agents and objectives are involved, the integrated MPC will face challenges like computational burdens and maintenance difficulties in practice. To this end, this paper proposes a learning multi-objective AMPC that can improve design flexibility and computing efficiency. First, under the assumption of information exchange, a multi-objective AMPC tailored from the alternating direction method of multipliers (ADMM) is proposed to decouple the system and achieve the same performance as the integrated scheme iteratively. Second, a learning-based method for initializing iterations is proposed to accelerate convergence. In addition, a data management method is proposed for real-time efficiency, and an authentication module is designed for learning reliability. We compare the proposed scheme against the integrated scheme via a combined path-tracking simulation for autonomous vehicles with various controllers. The proposed scheme achieves the same control performance as the integrated one while reducing the computational time by 43.5%. Furthermore, the learning-based method saves 88.6% more computational time than without learning, making it suitable for real-time implementation.

This work enhances global path planning via a pure-pursuit controller with multi-model kinematic switching that sustains plan fidelity across diverse terrains. The system includes a traversability graph for terrain analysis, a Heading-Aware A* algorithm for generating feasible paths, and a multi-model Pure Pursuit controller for dynamic tracking. A core innovation is adaptive kinematic modeling, enabling real-time switching between kinematic models based on terrain features and robot states. This adaptability optimizes path efficiency and energy use in challenging scenarios. We validate the approach in simulation on different platforms, namely the Artaban quadruped and the X3 quadrotor drone, showcasing improved performance, robustness, and adaptability over standard baselines.

We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schr"{o}dinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.

We study continuous-time and possibly high-dimensional stochastic control problems where drift coefficients and running reward functions are unknown. Due to these missing model primitives, we take the exploratory, reinforcement learning (RL) framework of Wang, Zariphopoulou, and Zhou(2020) with relaxed controls and entropy regularization. The objective is to develop theoretically grounded, efficient and scalable RL algorithms to learn both the optimal value functions (which also solve the exploratory HJB equation) and optimal exploratory feedback control policies. When the diffusion coefficients do not contain control, we employ probabilistic representations of both the optimal value function and its gradient based on an auxiliary state process depending only on the diffusion part of the original dynamics. With a delicate analysis on some properly defined mappings and their fixed points, this leads to the introduction of our policy iteration algorithms and their convergence. We demonstrate the performance of our algorithms through various numerical examples. Finally, we study a special control-dependent diffusion case where probability representation of the Hessian is called for.

Multi-robot Control Barrier Function (CBF) safety filters can become infeasible, but a failed quadratic program (QP) does not indicate why the conflict occurred or how to resolve it. To address this, we develop an exact feasibility certificate for multi-agent CBF filters with heterogeneous control-affine dynamics and convex input sets. The certificate quantifies a feasibility reserve by separating the demand imposed by safety constraints from the available actuator supply. This decomposition shows when CBF gain tuning or increased actuation can and cannot resolve infeasibility, and identifies the agents and interactions responsible for the conflict. We further propose an algorithm to optimally allocate shared safety constraints by maximizing the worst local feasibility margin, yielding a linear program for polyhedral input sets. In $320$ paired closed-loop simulations, the proposed allocation reduces infeasible control steps from roughly $50\%$ to $6.2\%$, and reduces safety-violating runs from $118/160$ to $24/160$. In addition, across $52$ infeasibility events, the certificate identifies an interaction whose relaxation restores feasibility in $94\%$ of cases.

Real-world reinforcement learning (RL) offers a promising route to dexterous manipulation policies that can adapt directly from physical interaction, but learning is hindered by inefficient early exploration and costly failures. We propose a framework that uses sampling-based model predictive control (MPC) as scaffolding for real-world dexterous RL, providing structured prior experience and task-directed guidance during learning without human demonstrations or corrective actions. A small set of MPC trajectories is first used to populate an offline replay buffer and to pretrain the actor and critic. During online learning, MPC intermittently guides data collection while an off-policy Soft Actor-Critic learner trains from both prior MPC experience and newly collected physical interaction, with control gradually transitioning to the learned policy. On continuous in-hand rotation with a 16-DoF Allegro hand, initialized from 20 MPC trajectories collected in 12 minutes on hardware, the policy reaches 100% success after 7 minutes of online RL, with about three object drops on average during training. After 20 minutes of online learning, the policy achieves more than five times the rotation speed of the MPC controller and completes 1000 consecutive rotations without a drop. Ablations show complementary benefits from MPC-based pretraining, retained MPC experience, and online MPC guidance, while additional experiments demonstrate rapid adaptation to new object geometries and successful goal-conditioned reorientation.

We present a primitive-informed sampling-based model predictive control (MPC) framework for multi-fingered dexterous manipulation. Sampling-based MPC evaluates candidate control trajectories through forward simulation without requiring gradients through complex contact dynamics. However, directly sampling these trajectories in the high-dimensional joint space of a dexterous hand is inefficient and makes performance strongly dependent on the sampling distribution. Our framework biases sampling using low-dimensional manipulation primitives that encode coordinated finger motions, while simultaneously optimizing joint-level residuals to adapt these motions to the current hand-object configuration. Task-related rollout constraints reject infeasible trajectories during forward simulation, improving the effective use of the sampling budget. We evaluate the approach on a 16 DoF Allegro hand using a synchronized MuJoCo digital twin. Ablations show that both the primitive and residual are necessary for reliable continuous in-hand rotation, that increasing the sampling budget alone does not recover this coordination, and that rollout constraints substantially improve success rate. A primitive extracted for one object size transfers to other sizes and remains effective under model mismatch. The framework further supports grasping, object reorientation, and coordinated arm-hand manipulation, using primitives extracted from both a simulation-trained policy and human hand-motion data.

We propose a decentralized privacy-preserving learning algorithm in which each agent holds a single private sample and a shared model. Samples are learned sequentially, and each update must preserve the endpoint mappings at previously learned samples while protecting private data. This gives each agent three roles: (i) a learner that updates the model parameters, (ii) a teacher whose sample is learned at the current iteration, and (iii) a protected agent whose sample has already been learned. We build on Tuning without Forgetting (TwF) method to preserve previously learned mappings and show that TwF provides an indistinguishability guarantee for the learner whenever the set of protected agents contains another sample with the same label. For the teacher, we formulate a minimax optimal control problem that models the differential privacy noise as a worst-case disturbance to prevent performance loss while maintaining the same level of privacy for the gradient. For the protected agents, we compute the projections locally and aggregate them using a private push-sum gossip protocol. We prove geometric convergence of the decentralized gossip algorithm and of the distributed projection for TwF.

In urban search and rescue, articulated tracked robots (ATRs) must traverse structured but contact-rich environments such as stairwells and cluttered building interiors. Reliable autonomy remains challenging because robot-terrain interaction (RTI) is hybrid and discontinuous, and effective flipper-track coordination is difficult to model analytically. We present ASTRIL-MPC, a language-guided neural kinematics model predictive control (MPC) framework for autonomous traversal. A learned kinematics model predicts short-horizon task-state increments from a height sequence and recent trajectories; NMPC plans with multi-objective costs and strict feasibility constraints; and a large language model (LLM) proposes bounded updates to selected weights and bounds through a safety-checked interface with range clipping, rate limiting, and consistency checks. The compiled predictor enables a full control cycle within 100 ms. Across three traversal tasks and a multi-height generalization setting, ASTRIL-MPC improves an aggregate traversal-quality score by up to 71% over a non-adaptive NMPC and by 67% over a PPO baseline, while eliminating measurable collision impacts during descent. These results indicate that combining terrain-conditioned neural kinematics, optimization-based planning, and language-guided adaptation yields data-efficient and robust autonomy for articulated tracked robots. Real-robot trials over four indoor obstacles further demonstrate transfer to contact-rich physical traversal.

While offering significant promise for diverse applications, pattern-oriented swarms encounter multifaceted challenges in geometric control, self-organization, and safe navigation through dynamic environments. In this paper, we present a GRF-based stochastic optimal control framework to address these challenges within a unified probabilistic architecture. By extending the GRF into the temporal domain, the proposed framework casts collective coordination as a Bayesian inference task, enabling swarms to accommodate environmental uncertainty, satisfy non-convex constraints, and reconcile heterogeneous dynamics across diverse platforms. We develop an uncertainty- and safety-aware collision avoidance module for navigation in the presence of stochastic obstacle motion. The unscented transform is employed to propagate state uncertainty for both dynamic obstacles and neighboring agents, yielding principled confidence bounds for collision avoidance. In addition, density-guided pattern control is introduced, which encodes geometric patterns as implicit density fields. This representation decouples pattern specification from explicit agent-to-target assignments, thereby facilitating intrinsic self-healing and elastic reconfiguration in a distributed manner. The proposed framework is extensively evaluated through Monte Carlo simulations across diverse scenarios. Its model-agnostic nature is demonstrated on both quadrotor and fixed-wing UAV swarms, highlighting its generalizability across platforms with heterogeneous dynamics. Finally, the efficacy and robustness of the proposed method are validated through indoor experiments with a 15-quadrotor swarm and outdoor deployments involving 4 custom-built autonomous quadrotors. These experiments substantiate the proposed framework's capacity to maintain reliable geometric pattern transitions and safety-aware navigation within real-world environments.

The widespread adoption of data-driven, energy-efficient model predictive control (MPC) in buildings remains hindered by substantial effort to collect data and train models for individual buildings. Transfer learning (TL) has consequently gained increasing attention for target building modeling, as it reduces data requirements and modeling effort by reusing pretrained source models. However, these TL models are typically evaluated only on prediction accuracy in the target, without testing downstream control performance. To address this gap, we apply a state-of-the-art TL approach - pretraining a generalized model on multiple source buildings using standard operational data - within an MPC setup in a target building. We show that this approach is insufficient to achieve satisfactory control performance. As a solution, we introduce generalized models pretrained on excitation-based operational source data - purposefully probed inputs that explore the building's state-action space. For evaluation, we apply the generalized models via zero-shot (i.e., without fine-tuning) to 32 simulated target buildings and assess MPC performance. Our results show that excitation-based generalized models achieve the strongest control performance among all benchmarks, outperforming an online linear model-based MPC and a PI controller by 6.4% and 36.9%, respectively. By combining strong control performance with the ability to generalize across multiple buildings, without requiring any target-specific data, our approach reduces MPC setup cost and simplifies its widespread deployment in the building sector.

Closed kinematic chains complicate modular modeling by coupling active and passive coordinates through nonlinear closure constraints. This paper presents a Path-Assembled Closure Differential Mapping (PACDM) framework for modular closure resolution and kinematic reduction. Each closure element compares two ordered transformation paths with common endpoints, with their mismatch expressed through the logarithm on SE(3) and the corresponding Jacobian assembled from local transformation derivatives. Multi-path modules are constructed from a minimal set of pairwise closure elements, while rank-revealing analysis selects locally independent scalar constraints. A defect homotopy recovers closure-consistent passive coordinates from approximate estimates along a feasible and regular continuation path. At regular configurations, implicit differentiation yields the local active-to-passive differential mapping, which is subsequently used in a predictor-corrector continuation procedure for prescribed motion. The framework is evaluated on a seven-degree-of-freedom heavy-duty manipulator containing two-path and three-path closed-chain modules. Comparison with Simscape Multibody yields trajectory root-mean-square errors below 8.5 x 10^-10 rad, while predictor-corrector continuation is approximately 45.8 times faster than applying defect homotopy at every trajectory sample.

We present a robust contact-aware control framework for aerial writing on an underactuated platform. The framework combines nonlinear model predictive control (NMPC) for accurate end-effector position and normal-force tracking at small reference penetration depths, with consistent performance across controller tunings, with whole-body incremental nonlinear dynamic inversion (INDI) for robustness to frictional and aerodynamic disturbances during contact. The proposed controllers are validated on a quadrotor-based aerial manipulator with a rigid, single-link, one-degree-of-freedom (DoF) arm in simulation and real-world experiments. The aerial writing experiments span vertical and inclined surfaces, multiple reference forces, different friction conditions, and wind disturbances. The results demonstrate that robust simultaneous five-DoF end-effector pose and contact-force tracking is achievable on a standard underactuated quadrotor with a simple, rigid, single-link arm, without requiring a fully actuated platform, a complex arm, or dedicated force/torque sensing.

Agent-based model predictive control (AMPC) has recently been proposed as a distributed scheme that collaborates with all agents to achieve optimal holistic performance. However, its optimality highly depends on the prediction accuracy that requires all agents or their contributions to be known, which is too idealistic for actual implementation. This research proposes a novel practical hybrid control scheme - learning agent-based MPC (LAMPC), combining the model-based AMPC approach and data-based learning methods to improve the holistic vehicle performance for multi-agent systems. The Gaussian process regression (GPR) enhanced by an online data management strategy serves as the learning core to predict unknown contributions. A novel multi-step prediction mechanism leverages the GPR learning potential along the horizon. The predicted mean, representing the learned unknown contributions, completes the system model in the MPC for more accurate control. Meanwhile, a stochastic framework is formulated to guarantee control safety and feasibility using soft chance constraints based on the prediction variance. Both simulations and experiments show that, with the learning capability, LAMPC outperforms the traditional AMPC. LAMPC can achieve higher tracking performance in well-learned scenarios and always guarantee constraint satisfaction even in less-learned scenarios. Moreover, the proposed hybrid control scheme is efficient for real-time implementation and is flexible to any control agent topology.

This work considers adaptive shared human-robot control for nonlinear control-affine systems, where the assumption of a fully rational human is relaxed and the robot adapts its assistance to observed boundedly rational human behavior. We use a level-k bounded-rationality model of the two-player game to construct a finite bank of candidate human and robot policies through alternating best-response computations, with the associated value functions and policies approximated using adaptive dynamic programming. During the shared-control interaction, state-transition residuals compare the measured system evolution with the trajectories predicted by the candidate human policies. The residuals are accumulated using a forgetting factor and mapped to a probabilistic human-behavior model over the finite candidate bank. Rather than selecting a single candidate or averaging stored robot policies, the robot computes a distribution-aware one-step best response by minimizing an expected cooperative cost over the complete estimated human behavior distribution. For a quadratic terminal-value approximation and Euler state propagation, this response admits a closed-form solution expressed in terms of the expected human input. The proposed methods are evaluated in simulations of a benchmark nonlinear system stabilization task, and of a planar manipulator shared control setup. The reported results show decreasing Kullback-Leibler divergence between the estimated and simulated human behavior distributions, and a lower accumulated running cost for the robot agent over the shared control interaction period, than the maximum-probability and probability-weighted alternative policies baseline.

Reinforcement learning has produced capable controllers across a broad range of legged-robot tasks, but a subset of these tasks fail to converge under standard training: those for which most exploration trajectories terminate before producing useful gradient signal. To address such tasks we introduce the \emph{Actuator Dynamics Curriculum}, a procedure that initializes joint stiffness at a high value and anneals it toward the system-identified value as completed episode lengths grow. Using a cart-pole system as a representative example, we show that higher closed-loop joint natural frequency under critical damping enlarges the viability kernel of the underlying Markov Decision Process, increasing the fraction of initial states from which the task is feasible. We validate the kernel monotonicity on the cart-pole and apply the curriculum to a quadrupedal-to-handstand transition on the Boston Dynamics Spot, a narrow-viability task where training under fixed identified stiffness plateaus at a policy that never completes the transition. The trained policy executes the transition in simulation across 10 seeds and transfers to hardware. More broadly, our results suggest that simulated actuator dynamics is a useful axis along which to design curricula for tasks in which exploration is bottlenecked by termination conditions rather than by reward signal.

This paper addresses safety-critical coordination for scalar agents whose distributed commands are implemented through constrained physical-input dynamics. Agents communicate over a fixed weighted digraph with a directed spanning tree, while their outputs must remain inside a common moving safety corridor and their realized inputs must satisfy heterogeneous asymmetric bounds. We propose a networked Admissibility-Preserving Control (APC) architecture in which an Admissibility-Preserving Input Realization (APIR) governs physical inputs and a logarithmic barrier coordinate represents the safety corridor. The synthesis yields an exact cascade in which exponentially decaying realization errors drive nonsymmetric consensus dynamics. For every compatible compact initial set, the closed-loop system admits a unique complete solution, renders the moving corridor and actuator intervals forward invariant with uniform margins, keeps commands bounded, and achieves exponential consensus. We derive direction-specific sufficient conditions under which positive and negative control demands remain within their corresponding actuator limits. The analysis yields a closed-form barrier-coordinate limit determined by the left Perron vector and initial APIR mismatch. Under strong connectivity and the stated gain and compatibility conditions, partial pinning propagates a constant barrier reference from a nonempty informed subset and assigns the induced safety corridor trajectory. A non-weight-balanced example illustrates the directional certificate and predicted collective motion.

Unlocking the potential of tiny aerial robots requires order of magnitude improvements in the performance of embedded edge control. In particular, although recent cached model predictive control (MPC) solvers can handle the fast system dynamics and complex constraints required for agile drone flight, their computational demands remain prohibitive for resource-constrained robots, forcing prior implementations to operate at reduced control rates. AccelMPC overcomes this challenge through an end-to-end co-design approach that jointly optimizes the solver algorithm, numerical representation, hardware mapping, and physical integration. AccelMPC pairs a co-designed FPGA-accelerated alternating direction method of multipliers (ADMM)-based MPC solver with a custom 6g PCB, providing high-bandwidth communication for deployment on a 35g Crazyflie. Hardware experiments demonstrate 1 kHz onboard constrained MPC with dynamic obstacles, up to 15.6x faster solve times and 195.4x improvement in energy-delay product over state-of-the-art embedded microcontroller-based solvers, all while scaling to optimization problems with over 20,000 optimization variables and a comparable number of constraints. We release our PCB design files, firmware, and FPGA solver code open source.

Sampling-Based Model-Predictive Control (MPC) algorithms are a flexible class of controllers used for navigation on a wide range of robotic systems. Historically, such approaches have lacked hard safety guarantees, a shortcoming which we remedy in this work by computing guaranteed reachable-set overapproximations online with a fast, interval-based pipeline. We show that our method achieves similar performance to a state-of-the-art reachability-based planner without the need for the expensive pre-computation step, and can be scaled to systems that are infeasible using existing approaches. Finally, we demonstrate that our technique reduces safety violations by over 99% in a racing simulation and successfully controls a model racecar on real hardware experiments without crashes.

Tensegrity robots offer lightweight, compliant mobility over challenging terrain but remain difficult to model and control due to complex contact-rich dynamics and partial observability. This work presents a model predictive path integral (MPPI) controller for a three-bar tensegrity robot driven by a learned graph neural network (GNN) dynamics model. This work first extends prior GNN-based models with a differentiable contact detection module. The extension allows the dynamics model to reason over non-horizontal planar terrains, obstacles, as well as self-collisions. Then, the learned dynamics model and the MPPI controller operate in a closed data-collection loop, iteratively improving model accuracy and control performance. This work further introduces a hybrid MPPI strategy that combines MPPI with turning motion primitives to improve maneuverability. Experiments are performed in MuJoCo across five navigation tasks, which include, wall obstacles, inclines, narrow corridors, low-clearance structures, and a composite 3D obstacle course. The experiments demonstrate that the hybrid MPPI controller operating over the learned GNN dynamics model improves predictive accuracy over a flat-ground baseline model and achieves superior navigation performance compared to $A^*$-based re-planning and MPPI-only variants. Results show that the contact-aware learned dynamics combined with the sampling-based model predictive control enable robust tensegrity navigation in complex, contact-rich environments.

Flying humanoids are expected to perform tasks in diverse environments, while their existing locomotion is mainly limited to aerial flight and ground walking. The capability to move in complex three-dimensional space can greatly expand their application range. For such walking motion on ceilings and similar anti-gravity environments, whole-body MPC is effective. However, the discontinuous changes in dynamic structure accompanying contact switching during walking can induce thrust spikes, resulting in control instability. Therefore, in this work, we propose and implement a real-time whole-body MPC framework for anti-gravity bipedal walking. First, we formulate whole-body MPC using the time derivative of thrust, namely thrust-rate, as the control input. This formulation guarantees continuity of the thrust trajectory during contact switching while preserving the sparse structure of the optimal control problem for fast computation. Second, we address the lack of natural support forces in anti-gravity environments. We introduce lower bounds on the foot-normal component of the contact force, and smoothly transfer them during the doublesupport phase. Finally, we implement the proposed framework and demonstrate anti-gravity walking by a flying humanoid through simulation and a hardware experiment. To the best of our knowledge, this is the first demonstration of multi-contact whole-body MPC for a transformable aerial robot and walking by a flying humanoid beyond the ground.

Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.