Online System Identification

In this paper, we tackle the problem of jointly estimating the system states and partially unknown dynamics within distributed sensor-equipped networks, particularly in scenarios where only partial state observations are available. To address this issue, we propose an observer-based dynamic cooperative learning framework incorporating online distributed Gaussian Process (GP) regression, which enables accurate estimation despite incomplete in measurements and deficient GP models. In addition, a novel data collection strategy is introduced, with theoretical conditions ensuring feasible data acquisition. Moreover, we also derive an error upper bound encompassing state estimation and model estimation, leveraging the deterministic error bounds of GPs. Empirical simulations demonstrate the superiority of our approach compared to existing distributed GP-based methods.

Off-road mobility requires autonomous mobile robots to generalize across heterogeneous vehicle fleets and continuously changing terrain conditions. Existing cross-vehicle adaptation approaches generally assume flat terrain, while terrain-aware kinodynamic models often require platform-specific data collection and retraining. To this end, we propose VertiAKD, a unified framework for transferring and adapting off-road kinodynamic knowledge across diverse vehicles on geometrically and semantically complex terrain simultaneously. VertiAKD learns a shared mobility representation that jointly encodes vehicle configurations, trajectory transitions, and local elevation and semantic terrain features. Given limited data from a novel vehicle operating on unseen terrain, VertiAKD identifies the most relevant mobility descriptors and transfers their knowledge to initialize a terrain-aware kinodynamic model via function encoders, which is then periodically refined online from streaming observations without gradient-based retraining. We evaluate VertiAKD in the Verti-Bench simulator, built on the Chrono multi-physics engine, and on five physical configurations of the Verti-4-Wheeler platform. With only one minute of new trajectory data and associated terrain features, VertiAKD reduces long-horizon prediction error by up to 34.52% over direct mobility descriptor transfer across diverse unseen vehicle configurations and 94.43% over competing baselines. We further demonstrate robust closed-loop trajectory tracking in both simulation and physical experiments, highlighting the effectiveness of terrain-aware cross-vehicle knowledge transfer for accurate modeling and reliable off-road navigation.

Recent advances in deep-learning-based nonlinear system identification have led to encoder-based estimation of neural state-space (ANN-SS) models that achieve state-of-the-art performance in offline settings by estimating initial model states from past input-output data. These methods are typically used in multiple-shooting-based offline identification, and online learning of these models remains largely unexplored. This paper presents a batch-wise learning pipeline and a direct recursive identification algorithm for subspace encoder-based ANN-SS models. We provide convergence analysis of the recursive formulation and validate its performance through extensive simulation studies. The results demonstrate that the proposed approach enables computationally efficient online adaptation with high model accuracy.

Motivated by the challenge of stabilizing a general unknown linear dynamical system (LDS) from observations, we study the natural prerequisite of online prediction. Our goal is to achieve sublinear regret with a memory footprint that adapts to the intrinsic complexity of the dynamics rather than the full hidden-state dimension. We focus on the practically central regime of systems with low instability complexity -- eigenvalues outside the real stable interval that do not decay rapidly, together with non-semisimple modes -- potentially embedded in an otherwise stable real spectrum of much higher dimension; we write $k$ for this count. This regime is the primary setting in which stabilization is plausible: we show that many systems with high instability complexity cannot be stabilized without exponentially large controls. Thus, prediction is meaningful for stabilization precisely when the instability complexity is small. Within this regime, we introduce a unified online algorithm that handles every LDS (including non-diagonalizable systems with complex or exploding modes) with a learnable parameter count of $\widetilde{O}(k)$. Finally, we prove a lower bound showing that $k$ is a valid complexity measure: any filter-based predictor needs at least $k$ filters. Experiments corroborate our theory: on a high-dimensional system, our predictor sharply outperforms prior methods at an equal parameter budget.

Offline models for autonomous robots often fail under time-varying dynamics outside their training distribution. Koopman operator theory offers a linear representation of nonlinear dynamics via lifting, but its transition to real-time recursive estimation may suffer numerical vulnerabilities: covariance windup under low excitation when using exponential forgetting, and vanishing gain without forgetting. This paper introduces a Covariance-Regulated Recursive Koopman Learning (CR-RKL) framework with two complementary strategies--error dead-zone gating and constant-trace normalization--each independently capable of preventing covariance explosion and parameter freezing, with the latter additionally preserving the geometric structure of uncertainty. Validated on a non-holonomic differential-drive robot with wheel slip and Stribeck friction and on a 26-gram butterfly-inspired flapping-wing micro aerial vehicle, CR-RKL achieves numerically stable and accurate online modeling, and when embedded in model predictive control, it maintains reliable tracking performance under uncertain, time-varying dynamics.

Nonlinear dynamics and the strong couplings that arise between multiple effectors undermine the assumptions behind conventional, linear control allocation techniques. When flight enters regimes where nonlinear effects dominate, linear allocators exhibit reduced accuracy due to increased model mismatch, which subsequently degrades performance and robustness of the flight control system. High fidelity onboard models and black box data driven approaches can recover accuracy across the flight envelope, but respectively impose computational burdens prohibitive for real time allocation and sacrifice the interpretability required for verification and fault diagnosis. This paper addresses these limitations by learning an explicit, physics constrained analytical model of the control effectiveness mapping from representative flight data using Sparse Identification of Nonlinear Dynamics. The resulting mapping is compact, interpretable, and admits analytical derivatives, enabling efficient computation within nonlinear solvers that additionally incorporate actuator dynamics, without requiring an onboard model. An online adaptation mechanism monitors prediction residuals and refreshes the model when significant plant changes are detected, providing graceful reconfiguration under actuator failures and varying operating conditions. The methodology is evaluated on a high fidelity nonlinear benchmark aircraft across a range of aggressive maneuvers, achieving accuracy comparable to a full nonlinear onboard model while substantially reducing computational cost relative to established baselines.

Dexterous manipulation with multi-finger hands can be sensitive to physical parameters such as object shape, pose, and friction coefficients. While simulation enables large-scale data collection with known parameter values, simulation-trained policies must still handle uncertainty at deployment, where the true parameters and therefore the true dynamics are unknown. Standard domain randomization strategies may be insufficient for precise tasks like screwdriver turning, as manipulation strategies may need to change depending on specific parameter values. To address this, we propose Probabilistic Latent Unified world Modeling and parameter Estimation (PLUME), a world model that jointly learns to evolve a belief over parameter values as well as the system dynamics conditioned on those parameters. We learn a latent space to jointly represent multiple qualitatively different physical parameters along with rewards, themselves functions of partially-observable variables, to inform planning. Our novel learning framework leads to efficient alignment of the world model to true dynamics through online parameter inference as opposed to re-training or fine-tuning. We evaluate our method on simulated screwdriver turning, valve turning, bucket lifting, and disk flicking tasks, as well as a hardware screwdriver turning task, where we achieve successful zero-shot transfer of our simulation-trained policy and outperform state-of-the-art offline reinforcement learning and world-model-augmented behavior cloning baselines. Please see our website at https://plume-world-model.github.io for videos.

Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.

This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input delay changes degrade model performance, and the trade-off among accuracy, robustness, and memory usage arises when using multiple small models for each time-series pattern. To address these issues, this paper presents an online framework/method that treats streaming time series as dynamic mixtures of time-delay systems. This framework maintains robustness of model tracking and reduces memory usage by summarizing past regimes using a fixed-length representation that captures both the system dynamics and input-output delays. Concretely, this approach constructs a summary system tensor using the system's Markov parameter series, capturing both dynamic behavior and delay characteristics. If necessary, a tensor decomposition algorithm extracts relevant past models from the tensor and helps select the system that best fits the current regime. This method enables rapid adaptation to environmental changes and is computationally efficient. Tests on real datasets show that DelayMix consistently outperforms other methods, achieving superior forecast accuracy and faster adaptation to delays, especially for highly non-stationary data.

Recent advances in learning-based model predictive control (MPC) have leveraged neural networks for online model learning, achieving strong performance when nonstationary system dynamics deviate from nominal models. However, existing approaches primarily address specific or relatively structured forms of dynamical variation, leaving more general, unknown, and unpredictable time-varying dynamics insufficiently handled. To tackle this challenge, we propose T2S-MPC, a framework that adaptively learns a residual dynamics model online and integrates it with the nominal model within the MPC framework to enable fast-evolving online planning. To make the model time-aware, we explicitly encode temporal information through a structured time embedding and employ a two-timescale update scheme, allowing the controller to capture nonstationary dynamics while balancing rapid adaptation with stable learning. We evaluate the proposed method on a 2D quadrotor across stabilization and trajectory tracking tasks under diverse time-varying disturbances, including linear drifting and periodic perturbations. Experimental results show that T2S-MPC consistently outperforms classical MPC, neural MPC, and ablated variants in control performance, while also demonstrating strong robustness across a wide range of disturbance conditions without additional tuning. The source code is publicly available at https://github.com/Zeyuu0920/T2S_MPC

Executable world models can be read, edited, executed, and reused for planning, but only if the program captures the environment's transition law rather than semantic shortcuts in its surface vocabulary. We study online executable world-model learning under prior misalignment, where an agent must induce state-dependent dynamics from interaction evidence alone, without rule descriptions, reward signals, or trustworthy lexical priors. We introduce Alice, a closed-loop system that treats failed candidate updates as structural signal: when a candidate explains a new transition but loses previously explained ones, the preservation conflict reveals dynamics that the current program had conflated. Alice refines these conflicts into hypothesis classes that both provide compact, class-stratified preservation counterexamples for update and guide frontier exploration toward transitions that are novel and underrepresented with respect to the current program. We evaluate Alice on Baba in Wonderland, a prior-misaligned variant of Baba Is You that preserves simulator dynamics while replacing semantically meaningful rule-property labels with unrelated words. Experiments show that Alice substantially improves executable world-model learning under prior misalignment, and ablations show that both class refinement and class-aware exploration contribute.

Accurate dynamics models are critical for aerial manipulators operating under complex tasks such as payload transport. However, modeling these systems remains fundamentally challenging due to strong quadrotor-manipulator coupling, delayed aerodynamic interactions, and regime-dependent dynamics variations arising from payload changes and manipulator reconfiguration. These effects produce residual dynamics that are simultaneously cross-coupled, history-dependent, and nonstationary, causing both analytical models and purely offline learned models to degrade during deployment. To address these challenges, we propose a structured encoder-decoder framework for adaptive residual dynamics learning in aerial manipulators. The proposed nonlinear latent encoder captures cross-variable coupling and temporal dependencies from state-input histories, while a lightweight linear latent decoder enables online adaptation under regime-dependent nonstationary dynamics. The linear-in-parameter decoder structure permits closed-form Bayesian adaptation together with consistency-driven covariance inflation, enabling rapid and stable adaptation to both transient and slowly varying dynamics changes while remaining compatible with real-time model predictive control (MPC). Experimental results on a real aerial manipulation platform demonstrate improved residual prediction accuracy, faster adaptation under changing operating conditions, and enhanced MPC-based trajectory tracking performance. These results highlight the importance of jointly modeling coupled temporal dynamics and deployment-time nonstationarity for reliable aerial manipulation.

Autonomous driving in off-road environments presents significant challenges due to the dynamic and unpredictable nature of unstructured terrain. Traditional kinodynamic models often struggle to generalize across diverse geometric and semantic terrain types, underscoring the need for real-time adaptation to ensure safe and reliable navigation. We propose VertiAdaptor (VA), a novel online adaptation framework that efficiently integrates elevation with semantic embeddings to enable terrain-aware kinodynamic modeling and planning via function encoders. VA learns a kinodynamic space spanned by a set of neural ordinary differential equation basis functions, capturing complex vehicle-terrain interactions across varied environments. After offline training, the proposed approach can rapidly adapt to new, unseen environments by identifying kinodynamics in the learned space through a computationally efficient least-squares calculation. We evaluate VA within the Verti-Bench simulator, built on the Chrono multi-physics engine, and validate its performance both in simulation and on a physical Verti-4-Wheeler platform. Our results demonstrate that VA improves prediction accuracy by up to 23.9% and achieves a 5X faster adaptation time, advancing the robustness and reliability of autonomous robots in complex and evolving off-road environments.

Model-based control can achieve reliable task performance, but its effectiveness depends on the accuracy of the underlying model. Robots operating under model uncertainty must often adapt to previously unseen payloads, objects, and interaction dynamics to complete a task successfully. Conventional approaches typically rely on a dedicated task- and control-agnostic excitation phase for estimating physics parameters, delaying task execution and collecting potentially irrelevant data. In this paper, we instead consider zero-shot task execution under parametric uncertainty, where online model learning and control proceed concurrently during task execution. Our approach formulates reference generation within a dual control framework to produce task-relevant, informative trajectories that reduce parameter uncertainty in directions critical to task success. We predefine a feedback policy with an explicit parameter adaptation law and optimize the reference through the resulting adaptive closed-loop dynamics. We propose two formulations: 1) minimizing expected task cost under parameter uncertainty, and 2) minimizing optimality loss, which quantifies the degradation in task performance caused by planning with an incorrect parameter estimate. By actively optimizing for informative trajectories via a natural Fisher information measure, we tightly approach a lower bound on task-relevant parameter uncertainty while simultaneously achieving reliable task execution. Across diverse tasks, controllers, and adaptation laws, targeted exploration enables the identification required for successful task execution, allowing robots to learn relevant physical parameters while completing the task in a single attempt.