Kinematics

Imitation Learning from monocular video demonstrations provides a scalable approach for teaching complex skills to humanoid robots. However, translating human motion to humanoids requires overcoming significant morphological mismatches. Standard approaches rely on Geometric Retargeting or Indirect Dynamic Retargeting pipelines. We identify that these intermediate kinematic projections introduce a geometric bias, restricting the search space and yielding suboptimal dynamic behaviors. In this paper, we propose Direct Dynamic Retargeting (DDR), a novel single-stage framework that generates high-fidelity, dynamically feasible trajectories directly from expert videos. By formulating the problem in the task space and leveraging a sampling-based Model Predictive Control solver within a physics simulator, DDR natively optimizes over complex contact sequences while mitigating input drift. Our experiments demonstrate that bypassing the geometric bias allows DDR to outperform state-of-the-art baselines in demonstration tracking accuracy. Furthermore, we establish that providing such physically viable references to RL agents accelerates training convergence and enhances the final execution of agile and balancing behaviors. Source code will be made publicly available.

Mobile imitation learning on portable demonstration interfaces faces two coupled bottlenecks: locomotion-contaminated action labels and inference-induced execution latency on a continuously moving base. Recent wrist-mounted interfaces lower the cost of tabletop data collection, yet a single wrist view does not capture the global context required for base navigation. Adding a body-mounted camera entangles human walking with hand motion. Meanwhile, generative policies introduce hundreds of milliseconds of inference latency, during which the base advances past predicted waypoints, forcing backward corrections at action splices. This paper presents Mobile UMI, a hardware-free demonstration framework that addresses both gaps through three components. First, a dual-camera capture system records chest-centric global context and wrist-centric local interaction without any robot present. Second, a one-shot ChArUco-based spatial anchor unifies the chest and hand visual-inertial frames; the hand pose is then re-expressed relative to the chest to extract decoupled SE(3) manipulation and SE(2) base trajectories. Third, an asynchronous receding-horizon executor performs online state matching: each generated action chunk is realigned with the current physical pose so that expired waypoints are discarded before execution. The full system is evaluated on four long-horizon household tasks, achieving an average success rate of 83.8% over 100 trials per task. Controlled comparisons against ACT and Diffusion Policy show that the chest-relative label alone closes much of the gap; online state matching closes the remainder. These results indicate that, for mobile imitation learning under the tested conditions, explicit kinematic factorization combined with state-level latency alignment provides an effective solution without requiring architectural changes to the underlying policy class.

Developing dynamic models for tendon-driven continuum robots is challenging due to their nonlinear, high-dimensional, and friction-dominated dynamics. This paper presents a comparative study of data-driven system identification methods, including N4SID, ARX, and SINDYc, for modeling a tendon-actuated continuum robot with rolling joints developed at CERN. Despite the high number of joints of the robot, experimental analysis reveals that a two-degree-of-freedom dynamic model can accurately capture the system dynamics, owing to strong kinematic dependencies between the joints. The models are validated against experimental data, and used in the design of a model predictive controller, demonstrating their feasibility for real-time control.

Retrieving the 3D kinematics of articulated objects from monocular video is a fundamental challenge in computer vision. Existing methods rely on complex video setups or cues such as long-term point tracking or wide-baseline matching, but are frequently brittle under severe occlusions, rapid camera ego-motion, or weak local features. Learning-based methods, meanwhile, struggle to generalize beyond their training categories. We propose a category-agnostic optimization framework that treats articulated object understanding as a primitive-fitting problem. Geometric primitives serve as a proxy representation that avoids the pitfalls of unstable point tracks; a novel mechanism organizes them into coherent parts constrained by revolute and prismatic joints. Our formulation jointly optimizes part segmentation and joint parameters, recovering complex kinematics from a single casually captured video. A visibility-aware procedure handles partial observations and occlusions inherent to real-world data. We also propose the AiP-synth and AiP-real benchmarks, featuring significant camera motion and heavy occlusions, and outperform existing methods. Project page: https://aartykov.github.io/Articulation-in-Prime/

Robotic assembly in architectural construction faces a persistent bottleneck: existing planners are either highly specialized, requiring prohibitive retraining for every new geometric design, or operationally inefficient, treating structural sequencing and kinematic motion as disjoint processes. We present EUPHORIA, a unified framework that achieves universal few-shot adaptability and dynamic efficiency through a hybrid optimization strategy. To overcome the retraining bottleneck, we propose a Meta-Geometric Encoder based on Graph Hypernetworks: unlike standard contrastive learning, which performs only feature-level recognition, our hypernetwork dynamically generates policy parameters from a minimal support set, enabling parameter-level adaptation to complex topologies (e.g., domes, arches) without gradient-based retraining. For structural reasoning, we introduce a Physics-Informed Graph Transformer trained via Soft Actor-Critic (SAC), with a Physics-Bias Attention mechanism that modulates attention scores using contact forces from Discrete Element Model (DEM) simulations, guiding the planner toward structurally critical connections. We further ensure operational efficiency through Kinematics-Aware Sequencing, where the SAC objective penalizes high-energy transitions. Finally, we bridge the Sim2Real gap via Residual Stability Correction, a differentiable optimization layer that fine-tunes coarse assembly actions by minimizing a joint energy-stability cost prior to execution. Experiments show that EUPHORIA significantly reduces energy consumption over decoupled baselines and achieves state-of-the-art success rates on unseen, non-standard geometries with minimal few-shot examples, fusing meta-learning, physics-informed attention, and residual optimization into a cohesive, generalized planner.

This paper presents a quadratic unconstrained binary optimization-based formulation framework for robot design optimization using kinematic structure-level evaluation metrics. In the proposed framework, classical computation is used to evaluate design-dependent metrics while the resulting combinatorial selection problem is formulated in a structure compatible with quantum annealing-based optimization. A robotic hand is adopted as a representative case study, as its performance is determined by both the individual kinematic characteristics of each finger and interaction terms. The proposed formulation incorporates individual design rewards, overlap workspace interactions, one-hot constraint, and structural dependency penalties into a unified quadratic model. A 27-variable robotic hand design problem is constructed, and simulated annealing is used as a classical baseline to verify the feasibility of the formulation. Quantum annealing is further performed to examine the applicability of the proposed formulation to annealing-based hardware execution. The results show that feasible design combinations satisfying both one-hot selection and pairwise constraints can be obtained, with the observed objective-value range becoming narrower as the number of reads increases. In addition, the formulation process is discussed for other robotic systems. The proposed framework provides a generalized approach for transforming kinematic structure-based robot design problems into combinatorial optimization problems.

Explicit dynamic finite element (FE) simulations are widely used for large deformation engineering analysis, but repeated simulations remain costly during design space exploration and optimisation. In explicit FE analysis, nodal kinematics and element level deformation measures evolve through coupled node element updates. This motivates graph learned simulators that approximate one step FE state transitions and roll them out autoregressively. However, many mesh based graph surrogates are node centred, which makes element level variables and native nodal elemental exchange less direct to represent. This work proposes CAttBiGNN, a cross attention based bipartite graph neural network for coupled nodal elemental learning. The graph represents FE mesh nodes and elements as distinct entities linked by directed node element edges, enabling nodal displacement increments and element level deformation states to be predicted on their native discretisation domains. An edge aware cross attention processor uses geometric edge embeddings to modulate directional node element message passing. For larger graphs, CAttBiUGNN combines the bipartite processor with graph downsampling and upsampling to improve long-range information propagation. The method is evaluated on dome shaped cold forming and corner shaped hot forming benchmarks. Comparisons with node centred baselines and bipartite and attention ablations show improved accuracy and balance in nodal displacement and elemental thinning prediction during autoregressive rollout. The results indicate that the proposed finite element inspired learned simulator can support manufacturability oriented field prediction and efficient design space exploration in large deformation sheet material forming.

Text- and image-conditioned video generation models have achieved strong visual fidelity and temporal coherence, but they often fail to generate motion governed by kinematic and geometric constraints. In these settings, object parts must remain rigid, maintain contact or coupling with neighboring components, and transfer motion consistently across connected parts. These requirements are especially explicit in articulated mechanical assemblies, where motion is constrained by rigid-link geometry, contact/coupling relations, and transmission through kinematic chains. A generated video may therefore appear plausible while violating the intended mechanism, such as rotating a part that should translate, deforming a rigid component, breaking coupling between parts, or failing to move downstream components. To evaluate this gap, We introduce MechVerse, a benchmark for mechanically consistent image-to-video generation. MechVerse contains 21,156 synthetic clips from 1,357 mechanical assemblies across 141 categories, organized into three tiers of increasing kinematic complexity: independent articulation, pairwise coupling, and densely coupled multi-part mechanisms. Each clip is paired with a structured prompt describing part identities, stationary supports, moving components, motion primitives, direction, speed/extent, and inter-part dependencies. We evaluate proprietary, open-source, and fine-tuned image-to-video models using standard video metrics, instruction-following scores, and human judgments of motion correctness and kinematic coupling. Results show that current models can preserve appearance and smoothness while failing to generate mechanically admissible motion, with errors increasing as coupling complexity grows. MechVerse provides a benchmark for measuring and improving mechanism-aware video generation from image and language inputs.

Kinematic monitoring plays a critical role in long-term rehabilitation for patients with spinal cord injury (SCI), where multi-view markerless motion capture methods have shown significant potential. However, owing to the reliance on calibration and the difficulty of achieving multi-view synchronization, their deployment in patient self-deployed environments remains challenging. In this work, we propose an agentic pipeline for self-synchronized multi-view joint angle monitoring in uncalibrated environments using two cameras without hardware triggers. The Multimodal large language models enable automatic video synchronization and agent-driven self-verification. State-of-the-art monocular 2D pose estimation models are employed to extract candidate poses, where an agent-based selection mechanism is then applied to automatically identify and track the target subject, thereby producing consistent 2D poses in the presence of multiple individuals and occlusions. Such 2D poses are optimized to estimate joint angles from uncalibrated multi-view pose sequences, ensuring interpretability through explicit geometric modeling. Validation against Vicon system demonstrated the strong performance, achieving an MAE of $5.97^\circ \pm 2.36^\circ$ and a Pearson correlation coefficient of $0.962 \pm 0.014$. The proposed method is expected to provide a practical, patient self-deployable system to perform daily kinematic monitoring in uncalibrated home environments.

This paper presents a kinematics-aware deep reinforcement learning framework based on Rainbow Deep Q-Networks (DQN) for cooperative peg-in-hole manipulation by a Delta parallel robot and a 3-RRS (Revolute--Revolute--Spherical) parallel manipulator. A key contribution is the integration of a geometric design-optimization stage that precedes learning: the 3-RRS geometry is tuned to maximize the singularity-free workspace and improve conditioning, which in turn enlarges the safe region in which the reinforcement learning policy can explore. Together the two manipulators expose a 6~degree-of-freedom (DoF) controllable subspace (three Delta translations, two 3-RRS rotations, and one 3-RRS vertical translation); the peg-in-hole task is invariant to rotation about the peg axis, so the task-relevant manifold is five dimensional. The cooperative insertion problem is cast as a Markov Decision Process with a 12-dimensional state vector and a discrete action set containing $6 \times 2 = 12$ incremental commands (one positive and one negative per controlled DoF). A shaped reward combines dense proximity guidance, penalties for kinematic and workspace violations, and sparse bonuses for successful insertions. The Rainbow DQN -- integrating double Q-learning, dueling architecture, prioritized replay, multi-step returns, noisy linear layers for exploration, and a distributional value head -- is trained with a two-stage curriculum. The co-designed framework is validated in a high-fidelity kinematic simulator, where it achieves stable policy convergence, reliable insertions, and reduced constraint violations compared against a vanilla DQN agent and a classical sampling-based planner.

Discrete-time joint acceleration constraints are widely used to enforce position and velocity limits. However, under voltage-constrained electric actuators, kinematically admissible accelerations may be physically unrealizable, exposing a missing execution-level abstraction. We propose Voltage-Realizable Acceleration (VRA), a joint-level acceleration interface that grounds kinematic acceleration in voltage-constrained actuator physics by restricting commanded accelerations to voltage-realizable constraints. Hardware experiments on electric actuators and a wheel-legged quadruped show that VRA removes unrealizable accelerations, restores consistent near-constraint execution, and reduces constraint-induced oscillations.

Predicting the shape of tendon driven continuum robots (TDCRs) at steady state from actuation remains challenging due to continuous deformation, complex tendon routing, compliance, friction, and fabrication variability. In this paper, we address this problem as kinematic self modeling conditioned on action. We present a lightweight 3D printed TDCR hardware platform and an RGB-D data collection pipeline with multiple cameras, and we learn a point cloud flow matching model that maps motor actuation states to the robot's settled 3D geometry. The model is trained from randomly sampled quasi static configurations and evaluated on test motor commands within the same TDCR design family and actuation range. We compare against prior 3D deformable object and robot self modeling approaches in both MuJoCo simulation and real hardware experiments. Experiments on simulated 2-, 3-, and 5-module TDCRs and real 2- and 3-module robots show improved shape prediction accuracy under CD and EMD metrics. We further show in simulation that the same conditional formulation generalizes to tip payload as a conditioning input, enabling payload conditioned steady-state shape prediction. These results demonstrate a data driven self modeling framework for quasi static TDCR geometry prediction.

Reconstructing dynamic 3D scenes from blurry monocular videos is challenging as motion-induced blur entangles object motion and geometry, hindering geometric consistency. We present Kinematics-GS, a kinematics-aware framework that models blur as motion-aligned deformation and introduces a kinematic prior to reparameterize Gaussian shapes along motion trajectories, thereby mitigating degenerate shape collapse without auxiliary motion supervision. To stabilize optimization, we decompose scenes into dynamic and static components using temporal deformation variance and employ a coarse-to-fine deformation strategy to capture both global motion and fine-grained details. We also introduce a challenging real-world dataset of deformable and elastic objects exhibiting non-rigid motion with spatially non-uniform motion blur that obscures geometric cues. Extensive experiments on real-world benchmarks with realistic motion blur demonstrate that Kinematics-GS outperforms prior methods by a clear margin in monocular dynamic scene reconstruction, highlighting its effectiveness in handling complex and non-rigid motion scenarios.

The ability to derive precise spatial and physical insights is a cornerstone of vision-language models (VLMs), yet their poor performances in related spatial intelligence tasks such as physical reasoning remain a fundamental barrier. The community critically lacks a scientific analysis revealing whether VLMs faithfully reach answers or plausibly make guesses. This work aims to provide a fundamental understanding of how VLMs perceive the physical world, and utilize physical laws, while assessing the reliability of model confidence. We propose NICE and FACT, a dual-diagnostic paradigm that explicitly decomposes quantitative reasoning for kinematic physics: FACT diagnoses visual fidelity, physical law comprehension, and temporal grounding. NICE studies our novel neighborhood-informed calibration method and novel metrics to evaluate and calibrate confidence reliability. Evaluated across 6 latest state-of-the-art VLMs, we uncover that models fail to identify visual preconditions or utilize necessary physical laws to reach answers. This work highlights and establishes a standardized diagnostic paradigm to guide the development of faithful, physically-grounded VLMs.

Gap-closing rate and visual looming swap discriminative dominance depending on deceleration intensity - a finding that reconciles a long-standing conflict in the car-following literature and challenges spacing-centered assumptions in traditional driver behavior models. This study presents a two-stage analytical framework that distinguishes between information availability (kinematic variables measurable in the environment) and information utilization (variables that demonstrably separate driver behavioral patterns), applied to 1,060,119 valid car-following observations from the NGSIM trajectory dataset (2,932 vehicles). Six kinematic features are extracted, and deceleration events are detected under two threshold conditions (-0.5 m/s^2 and -0.3 m/s^2). K-means clustering identifies behavioral modes, and one-way ANOVA with eta-squared effect sizes ranks each feature's discriminative power. Three key findings emerge: (1) threshold selection fundamentally shapes behavioral inference - the stricter threshold yields three interpretable modes while the permissive threshold collapses these to two; (2) hard braking prioritizes gap-closing rate (eta^2 = 0.715) while moderate braking emphasizes visual looming (eta^2 = 0.574); and (3) spacing headway is negligible (eta^2 <= 0.014) across both thresholds. These findings provide empirically grounded candidates for perceptual cue prioritization and have direct implications for ADAS warning system design and autonomous vehicle control.

Continuous estimation of high-dimensional finger kinematics from forearm surface electromyography (EMG) could enable natural control for hand prostheses, AR/XR interfaces, and teleoperation. However, the complexity of human hand gestures and the entanglement of forearm muscles make accurate recognition intrinsically challenging. Existing approaches typically reduce task complexity by relying on classification-based machine learning, limiting the controllable degrees of freedom and compromising on natural interaction. We present an end-to-end framework for continuous EMG-to-kinematics regression using only consumer-grade hardware. The framework combines an 8-channel EMG armband, a single webcam, and an automatic synchronization procedure, enabling the collection of the EMG Finger-Kinematics dataset (EMG-FK), a 10-h dataset of synchronized EMG and 15 finger joint angles from 20 participants performing rich, unconstrained right-hand motions. We also introduce the Temporal Riemannian Regressor (TRR), a lightweight GRU-based model that uses sequences of multi-band Riemannian covariance features to decode finger motion. Across EMG-FK and the public emg2pose benchmark, TRR outperforms state-of-the-art methods in both intra- and cross-subject evaluation. On EMG-FK, it reaches an average absolute error of $9.79 °\pm 1.48$ in intra-subject and $16.71 °\pm 3.97$ in cross-subject. Finally, we demonstrate real-time deployment on a Raspberry Pi 5 and intuitive control of a robotic hand; TRR runs at nearly 10 predictions/s and is roughly an order of magnitude faster than state-of-the-art approaches. Together, these contributions lower the barrier to reproducible, real-time EMG-based decoding of high-dimensional finger motion, and pave the way toward more natural and intuitive control of embedded EMG-based systems.

This study investigates the kinematic role of palm degrees of freedom (DoF) in enhancing thumb opposability in a five-finger robotic hand. A hand model consisting of a five DoF thumb and four fingers with three to four DoF is analyzed, where palm motion is introduced between adjacent fingers. To quantitatively evaluate thumb-finger interaction, the overlap workspace volume is defined based on voxelized fingertip reachable regions. Seven cases are considered, including configurations with increased total DoF and configurations in which the total DoF is maintained by redistributing DoF from the fingers to the palm. The results show that palm DoF significantly improves opposability, particularly for the ring and little fingers, by repositioning their base locations rather than simply extending their reachable range. However, when the total DoF is constrained, redistributing DoF to the palm leads to trade-offs between overlap workspace expansion and kinematic redundancy. These findings indicate that palm DoF and finger DoF play distinct roles in hand kinematics and should be considered jointly in design. This study provides a quantitative framework for evaluating palm-induced opposability without relying on object or contact models and offers practical design guidelines for incorporating palm motion in robotic hands.

Evaluating the pinch capability of a robotic hand is important for understanding its functional dexterity. However, many existing grasp evaluation methods rely on object geometry or contact force models, which limits their applicability during the early stages of robotic hand design. This study proposes a kinematic evaluation method for analyzing pinch configurations of robotic hands based on interactions between fingertip workspaces. First, the reachable workspace of each fingertip is computed from the joint configurations of the fingers. Then, feasible pinch configurations are detected by evaluating the relationships between fingertip pairs. Since the proposed method does not require information about object geometry or contact force models, the pinch capability of a robotic hand can be evaluated solely based on its kinematic structure. In addition, analyses are performed on four different kinematic structures of the hand to investigate their impact on the pinch configurations. The proposed evaluation framework can serve as a useful tool for comparing different robotic hand designs and analyzing pinch capability during the design stage.

In the design stage of robotic hands, it is not straightforward to quantitatively evaluate the effect of phalanx length ratios on dexterity without defining specific objects or manipulation tasks. Therefore, this study presents a framework for optimizing the phalanx length ratios of a five-finger robotic hand based on potential dexterity within a kinematic structure. The proposed method employs global manipulability, workspace volume, overlap workspace volume, and fingertip sensitivity as evaluation metrics, and identifies optimal design configurations using a weighted objective function under given constraints. The reachable workspace is discretized using a voxel-based representation, and joint motions are discretized at uniform intervals for evaluation. The optimization is performed over design sets for both the thumb and the other fingers, and design combinations that do not generate overlap workspace are excluded. The results show that each phalanx does not contribute equally to the overall dexterity, and the factors influencing each phalanx are identified. In addition, it is observed that the selection of weighting coefficients does not necessarily lead to the direct maximization of individual performance metrics, due to the non-uniform distribution of evaluation measures within the design space. The proposed framework provides a systematic approach to analyze the trade-offs among reachability, dexterity, and controllability, and can serve as a practical guideline for the kinematic design of multi-fingered robotic hands.

Kinematic rigs provide a structured interface for articulating 3D meshes but lack any associated pose space, i.e., an explicit representation of the plausible manifold of joint configurations for a given mesh. Without such a pose space, stochastic sampling or manual manipulation of raw rig parameters easily results in semantic and/or geometric violations, such as anatomical hyperextension and non-physical self-intersections. We propose Video-informed Pose Spaces (ViPS), a feedforward framework that discovers the latent distribution of valid articulations for auto-rigged meshes by distilling motion priors from a pretrained video diffusion model. Unlike existing methods that rely on scarce, artist-authored 4D datasets, or focus on reconstructing instances of individual motions, ViPS transfers generative video model priors into a universal distribution over the given rig parameterization. Differentiable geometric validators applied to the skinned mesh enforce shape-specific integrity without requiring manual regularizers. Our feedforward model reveals a smooth, compact, and controllable pose space. This, in turn, supports sampling for diverse shape variations, manifold projection for inverse kinematics, and temporally coherent trajectories for animation and keyframing. Further, the distilled 3D pose samples serve as semantic proxies to guide video diffusion, effectively closing the loop between generative 2D priors and structured 3D kinematic control. Our evaluations show that ViPS, trained solely using video priors, matches the performance of state-of-the-art models trained on synthetic artist-created 4D data in both plausibility and diversity. Additionally, as a universal model, ViPS exhibits robust zero-shot generalization to out-of-distribution species and unseen skeletal topologies.

Road traffic accidents are a leading cause of fatalities worldwide. In the US, human error causes 94% of crashes, resulting in excess of 7,000 pedestrian fatalities and $500 billion in costs annually. Autonomous Vehicles (AVs) with emergency collision avoidance systems that operate at the limits of vehicle dynamics at a high frequency, a dual constraint of nonlinear kinodynamic accuracy and computational efficiency, further enhance safety benefits during adverse weather and cybersecurity breaches, and to evade dangerous human driving when AVs and human drivers share roads. This paper parameterizes a Deep Reinforcement Learning (DRL) collision avoidance policy Out-Of-Distribution (OOD) utilizing race car overtaking, without explicit geometric mimicry reference trajectory guidance, in simulation, with a physics-informed, simulator exploit-aware reward to encode nonlinear vehicle kinodynamics. Two policies are evaluated, a default uni-direction and a reversed heading variant that navigates in the opposite direction to other cars, which both consistently outperform a Model Predictive Control and Artificial Potential Function (MPC-APF) baseline, with zero-shot transfer to proportionally scaled hardware, across three intersection collision scenarios, at 31x fewer Floating Point Operations (FLOPS) and 64x lower inference latency. The reversed heading policy outperforms the default racing overtaking policy in head-to-head collisions by 30% and the baseline by 50%, and matches the former in side collisions, where both DRL policies evade 10% greater than numerical optimal control.

Reconstructing the shape of continuum manipulators from sparse, noisy sensor data is a challenging task, owing to the infinite-dimensional nature of such systems. Existing approaches broadly trade off between parametric methods that yield compact state representations but lack probabilistic structure, and Cosserat rod inference on factor graphs, which provides principled uncertainty quantification at the cost of a state dimension that grows with the spatial discretization. This letter combines the strength of both paradigms by estimating the coefficients of a low-dimensional Geometric Variable Strain (GVS) parameterization within a factor graph framework. A novel kinematic factor, derived from the Magnus expansion of the strain field, encodes the closed-form rod geometry as a prior constraint linking the GVS strain coefficients to the backbone pose variables. The resulting formulation yields a compact state vector directly amenable to model-based control, while retaining the modularity, probabilistic treatment and computational efficiency of factor graph inference. The proposed method is evaluated in simulation on a 0.4 m long tendon-driven continuum robot under three measurement configurations, achieving mean position errors below 2 mm for all three scenarios and demonstrating a sixfold reduction in orientation error compared to a Gaussian process regression baseline when only position measurements are available.

Kalman filter-based algorithms are fundamental for mobile robots, as they provide a computationally efficient solution to the challenging problem of state estimation. However, they rely on two main assumptions that are difficult to satisfy in practice: (a) the system dynamics must be linear with Gaussian process noise, and (b) the measurement model must also be linear with Gaussian measurement noise. Previous works have extended assumption (a) to nonlinear spaces through the Invariant Extended Kalman Filter (IEKF), showing that it retains properties similar to those of the classical Kalman filter when the system dynamics are group-affine on a Lie group. More recently, the counterpart of assumption (b) for the same nonlinear setting was addressed in [1]. By means of the proposed Iterated Invariant Extended Kalman Filter (IterIEKF), the authors of that work demonstrated that the update step exhibits several compatibility properties of the classical linear Kalman filter. In this work, we introduce a novel open-source state estimation algorithm for legged robots based on the IterIEKF. The update step of the proposed filter relies solely on proprioceptive measurements, exploiting kinematic constraints on foot velocity during contact and base-frame velocity, making it inherently robust to environmental conditions. Through extensive numerical simulations and evaluation on real-world datasets, we demonstrate that the IterIEKF outperforms the vanilla IEKF, the SO(3)-based Kalman Filter, and its iterated variant in terms of both accuracy and consistency.

Skeleton-based action recognition is widely applied in sensor-based systems, including human-computer interaction and intelligent surveillance. However, typical sensors produce sparse and discrete joint coordinates, often leading to the loss of fine-grained spatiotemporal information during dynamic movements. Furthermore, predefined physical topologies restrict modeling potential long-range dependencies. To address these challenges, we propose KGS-GCN, which integrates kinematics-driven Gaussian splatting and probabilistic topology within a graph convolutional network. A Gaussian splatting module constructs anisotropic covariance matrices by extracting instantaneous joint velocity vectors, rendering sparse skeleton sequences into multi-view continuous heatmaps rich in spatiotemporal semantics. Additionally, a probabilistic topology construction strategy transcends physical connectivity limitations by utilizing the Bhattacharyya distance to quantify statistical correlations between joint Gaussian distributions, generating an adaptive prior adjacency matrix. Finally, the lightweight multi-view rendering branch and topological GCN backbone are unified through a visual context gating mechanism, enabling seamless fusion of continuous dynamic cues with structural priors while maintaining high computational efficiency, requiring only 1.4M parameters and 1.3 GFLOPs. Extensive experiments on multiple benchmark datasets demonstrate that KGS-GCN significantly enhances the modeling of complex spatiotemporal dynamics and achieves competitive performance at low computational cost, establishing an efficient paradigm for improving the perceptual robustness of low-fidelity sensor data.

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.

Accurate relative localization is critical for multi-robot cooperation. In robot groups, measurements from different robots arrive asynchronously and with clock time-offsets. Although Continuous-Time (CT) formulations have proved effective for handling asynchronous measurements in single-robot SLAM and calibration, extending CT methods to multi-robot settings faces great challenges in achieving high-accuracy, low-latency, and high-frequency performance. In particular, existing CT methods suffer from the inherent query-time delay of unclamped B-splines and high optimization latency. This paper proposes CT-RIO, a novel Continuous-Time Relative-Inertial Odometry framework. We adopt Clamped Non-Uniform B-splines (C-NUBS) to represent states, eliminating the query-time delay. We further augment C-NUBS with closed-form extension and shrinkage operations that preserve the spline shape, making it suitable for online estimation and enabling flexible knot management. This flexibility leads to the concept of a knot-keyknot strategy, which supports spline extension at high frequency while retaining sparse keyknots for adaptive relative motion modeling. We then formulate a reference-centric sliding-window relative localization problem that operates purely on relative kinematics and inter-robot constraints. To enable low-latency and high-frequency estimation, we decompose the tightly coupled optimization into robot-wise subproblems and solve them in parallel using asynchronous block coordinate descent. Extensive experiments show that CT-RIO converges from time-offsets as large as 264 ms to sub-millisecond within 3 s, and achieves RMSEs of 0.046 m and 1.8 degree. It consistently outperforms evaluated published methods, with improvements of up to 60% under high-speed motion.

Articulation modeling enables robots to learn joint parameters of articulated objects for effective manipulation which can then be used downstream for skill learning or planning. Existing approaches often rely on prior knowledge about the objects, such as the number or type of joints. Some of these approaches also fail to recover occluded joints that are only revealed during interaction. Others require large numbers of multi-view images for every object, which is impractical in real-world settings. Furthermore, prior works neglect the order of manipulations, which is essential for many multi-DoF objects where one joint must be operated before another, such as a dishwasher. We introduce PokeNet, an end-to-end framework that estimates articulation models from a single human demonstration without prior object knowledge. Given a sequence of point cloud observations of a human manipulating an unknown object, PokeNet predicts joint parameters, infers manipulation order, and tracks joint states over time. PokeNet outperforms existing state-of-the-art methods, improving joint axis and state estimation accuracy by an average of over 27% across diverse objects, including novel and unseen categories. We demonstrate these gains in both simulation and real-world environments.

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed.

Text-driven motion editing and intra-structural retargeting, where skeletons share topology but may differ in bone lengths and rest pose, are traditionally handled by fragmented pipelines with incompatible inputs and representations: editing relies on specialized generative steering, while retargeting is deferred to geometric post-processing. We present a unified conditional-flow framework that casts generation, semantic editing, and intra-structural retargeting as condition-modulated transport within one text- and skeleton-conditioned rectified-flow model. Under this formulation, editing changes the semantic condition while preserving skeletal structure, whereas retargeting changes the skeletal condition while preserving motion semantics. This makes FlowEdit-style transport a unified inference rule for motion manipulation rather than a task-specific editor. To instantiate this for articulated 3D motion, we develop a text- and skeleton-conditioned rectified-flow transformer. The model uses per-joint tokenization and explicit joint self-attention to capture spatial kinematic dependencies. We further inject text conditions at both joint and frame levels, while residual multi-condition classifier-free guidance balances text adherence and skeletal conformity. Experiments on SnapMoGen and a multi-character Mixamo subset show that one trained model supports text-to-motion generation, zero-shot editing, and zero-shot intra-structural retargeting without task-specific fine-tuning. This unified framework replaces separate pipelines with a single conditional motion transport model while keeping the same-topology retargeting scope explicit.