Inverse Kinematics

This paper presents the kinematic and dynamic modeling, trajectory generation, and stability analysis of an 8-degree-of-freedom (DOF) biped robot walking on flat and inclined terrain. Denavit-Hartenberg (DH) parameters and homogeneous transformations are used to derive the forward kinematics, while closed-form inverse kinematics maps the desired hip and swing-foot Cartesian trajectories, generated with cubic splines, to joint angles. Joint torques are computed using the Newton-Euler iterative algorithm, and dynamic stability is evaluated using the zero moment point (ZMP) criterion. A genetic algorithm (GA) optimizes the hip height, maximum swing-foot lift, and frontal-plane tilt angle by minimizing the work done by the joints subject to a ZMP feasibility penalty. Simulation results in MATLAB show that the nominal 8-DOF model remains ZMP-stable for step completion times down to 0.5 s and for slope inclinations up to 22.5 degrees with the given foot geometry. Beyond these limits, the ZMP leaves the support polygon, and either the foot dimensions or the trajectory parameters must be modified. The results also show that ZMP stability is governed by the mass distribution among the links rather than the total mass of the robot.

Human-to-humanoid retargeting has largely been studied on legged platforms, while comparatively few wheeled-humanoid systems support coupled locomotion and manipulation from general human motion. Building on GMR's configurable general-motion retargeting and BeyondMimic's physically simulated R1 Pro learning framework, we present a reproducible pipeline that converts multi-dataset SMPLX motion into executable loco-manipulation behavior for the Galaxea R1 Pro wheeled humanoid. The robot has a planar three-wheel base, a serial torso, and two arms but no leg joints, so human lower-body motion must be redistributed across base motion and torso posture without sacrificing manipulation-relevant arm geometry. Our pipeline combines canonical body-shape preprocessing, planar-base normalization, morphology-aware differential inverse kinematics, shoulder-rooted hierarchical arm retargeting, and continuous torso substitution for bending and squatting. A reference-twist-driven planning layer then decodes planar base motion into continuous three-wheel steering and rolling commands subject to hysteresis, kinematic continuity, acceleration, and actuator-rate limits. Finally, a 21-dimensional BaseDecode policy is trained in Isaac Lab with directional joint-limit scaling, focused upper-body tracking, and a staged wheel-contact reward. The resulting system provides a complete bridge from human motion data to physically trackable wheeled-humanoid loco-manipulation rather than a visualization-only retargeter; quantitative policy comparisons remain scheduled for a later revision.

Planning trajectories for robot manipulators under kinematic equality constraints restricts feasible motions to a measure-zero submanifold of the configuration space, requiring special algorithmic treatment. A promising strategy is parametrizing the set of feasible configurations using analytic inverse kinematics (IK). Bespoke analytic IK functions can be written to be differentiable, a necessary property for gradient-based trajectory optimization. But the vast majority of IK functions are computed by automated meta-solvers like IKFast, and are difficult to modify for differentiability. We present a new approach for computing gradients of analytic IK parameterizations: we leverage the inverse function theorem to recover the desired gradients from the ordinary forward kinematic Jacobian. Furthermore, we present a least-squares domain extension and an optimization-amenable description of the reachability constraint, which preserves gradient signal outside the reachable workspace. We demonstrate the efficacy of our approach through numerical experiments and downstream tasks, including a hardware demonstration of an RB-Y1 picking up a box and placing it on a table. Project website: https://cohnt.github.io/inverse-function-theorem-parameterization/

We present the PccDiffuser, a conditional diffusion framework for continuum robots that learns a multimodal distribution over complete configuration-space paths and samples multiple candidate solutions in parallel, which are subsequently converted into an executable trajectory by time allocation considering actuator constraints. Under the piecewise constant-curvature model, we use exponential co-ordinates to describe the robot kinematics, and use graph neural network to encode a variable number of environment obstacles. Analytical differential kinematics is incorporated in the denoising process to improve terminal accuracy and whole-body clearance. On a mixed test set comprising workspace with zero to four obstacles, PccDiffuser achieved a success rate of 91%. Compared with existing sampling- and optimisation-based benchmarks, it delivered both a higher success rate and greater computational efficiency, with the latter advantage becoming more substantial when sampling more candidate solutions. Experiments on a three-section tendon-driven continuum robot further demonstrate consecutive planning, multi-solution planning, and whole-body obstacle avoidance.

Surface coverage with task-redundant manipulators is challenging because each surface point may admit multiple inverse kinematics (IK) solutions, and configuration choices strongly affect motion quality. This paper extends the classical Spanning Tree Coverage (STC) method to redundant manipulators through offline and online Joint Spanning Tree Coverage (JSTC) algorithms. Offline JSTC samples multiple Inverse Kinematics (IK) solutions per grid cell and formulates the problem as a Generalized Minimum Spanning Tree (GMST), selecting one configuration per cell and tracing the resulting tree to obtain a non-revisiting coverage path. Online JSTC incrementally expands and backtracks a spanning tree with feasibility and cost evaluation while handling dynamic grid updates. Simulation results show that offline JSTC reduces computation time, reconfigurations, and joint motion compared to other methods, while online JSTC achieves fast per-step planning in dynamic scenarios.

The kinematic analysis of a generic 3R robot has been investigated with multiple approaches in the past. The algebraic approaches have established concrete results but are unfortunately limited to special classes or architectural simplifications. Geometric approaches on the other hand have extended the analysis to generic robots while also providing an intuitive understanding of their kinematic properties. We use the best of both approaches to present the kinematic analysis of a generic 3R robot, using the inverse kinematic model inherited from a method based on conformal geometric algebra. The paper discusses a generic framework to study the conditions for a 3R robot to have four inverse kinematic solutions (IKS) and allows to study the distribution of IKS as seen in workspace. The necessary and sufficient conditions for a class of orthogonal robots are presented using the proposed approach.

The inverse kinematics of generic 3R robots has been investigated through multiple approaches, mainly algebraic methods involving the solution of certain equation sets. Previous geometric interpretations of the solution, characterized as the intersection of a pair of conics have been confined to the joint-space domain. In this article, we study the Inverse Kinematic Model (IKM) of 3R robots, using the advantages of Conformal Geometric Algebra (CGA) to provide further insights on its kinematic properties. Our approach directly yields a univariate polynomial in terms of theta_2 without the need to eliminate theta_1 and theta_3 by reframing the problem as the intersection of two circles, which are fundamental elements within this algebraic framework.

Robotic manipulation policies trained via imitation learning, such as Action Chunking with Transformers (ACT), can achieve strong performance under ideal conditions but often remain sensitive to small execution errors and distribution shifts. Correcting these failures typically requires dataset aggregation and full-policy retraining, which is computationally expensive and unsuitable for real-time deployment. In this work, we propose Online Residual Policy Adaptation (ORPA), a framework that enables immediate, feedback-driven correction of robot actions without modifying the underlying policy parameters. ORPA augments a pretrained control policy with a lightweight, feedback-conditioned module that predicts residual adjustments directly in joint space, allowing the system to adapt its behavior at runtime. We evaluate ORPA on a set of precision-sensitive manipulation tasks using the ALOHA platform, demonstrating improvements in success rate and recovery from small perturbations compared to baseline control policies and rule-based inverse kinematics corrections.

We propose a workspace-fibered decomposition framework for motion planning in nR planar redundant manipulators operating in cluttered environments. Rather than planning directly in the full n-dimensional configuration space, the method incrementally constructs obstacle-constrained reachable workspaces of lower-dimensional non-redundant sub-chains and recursively lifts them through redundant orientation fibers. This yields a sequence of reduced planning manifolds that preserve branch-consistent reachability structure while avoiding explicit construction of the full configuration-space obstacle geometry. We first establish that, for planar position-only manipulators, the obstacle-constrained reachable workspace induced by the minimal non-redundant sub-chain provides an exact characterization of feasibility with respect to the connected component of the start configuration, enabling early infeasibility detection prior to introducing redundant degrees of freedom (DOF). We then introduce an incremental fiber-lifting procedure that propagates reachable workspace structure through successive redundant links while enforcing local inverse-kinematic branch consistency using Jacobian determinant continuity constraints. The resulting representation admits efficient reduced-space planning directly on recursively-constructed workspace-fiber manifolds. Experimental results on redundant nR planar manipulators demonstrate that the proposed construction preserves collision-free connectivity structure across successive lifting stages while substantially reducing collision checking complexity relative to direct configuration space reasoning.

Articulated portrait mesh estimation is fundamental to 3D understanding, avatar generation, and immersive interaction. Existing approaches primarily rely on 3D Morphable Models (3DMMs). However, face-centric models suffer from the "floating head" assumption, conflating head pose with global rotation due to the lack of neck kinematics. Conversely, body-centric models lack high-fidelity facial expression capabilities. Furthermore, current methods struggle to disentangle jaw articulation from expression blendshapes, often over-relying on expressions for mouth opening. These limitations make monocular portrait recovery difficult across representation, supervision, and anatomical parameter estimation. To address these limitations, we introduce GRAPE(Graduated Routing for Articulated Portrait mesh Estimation). We build a Portrait Parametric Model (PPM) with an explicit torso-to-head kinematic chain and a canonical injection step to merge FLAME and the SMPL-X torso. We propose a Progressive Anatomical Alignment (PAA) network, which is composed of a pretrained portrait encoder, a Graduated-Mask Router, and coarse-to-fine experts that follow the portrait anatomical prior. We then train this network with multi-source supervision that combines sparse anatomical keypoints, feature distillation, foreground mask constraints, and relative geometry constraints. Experiments show that GRAPE improves portrait mesh recovery quality, pose alignment, and jaw--expression disentanglement over prior methods. We also demonstrate that our method can benefit the downstream tasks of audio-driven talking-head generation and 3D portrait generation.

Learned manipulation policies increasingly predict motions for abstract "hands" and are attractive in practice because they rely on easily collected demonstrations and transfer across robot platforms. Executing these trajectories on multi-arm robots, however, is not trivial. Multi-hand policy outputs must be assigned to physical arms, each arm must realize a configuration-space motion that tracks its prescribed end-effector trajectory, and all arms must respect kinematic limits and avoid collisions. In the absence of algorithms that directly address this problem, practitioners typically extend single-arm inverse-kinematics (IK) pipelines in an ad hoc way, with no guarantees of feasibility or safety. In this work, we close this execution gap with a search-based framework that is theoretically complete for grounding policy-generated multi-hand trajectories onto physical multi-arm systems. Building on Conflict-Based Search, our method explicitly searches over both the discrete assignment of trajectories to arms and the continuous Jacobian null spaces of redundant manipulators, using redundancy to avoid inter-arm collisions while tracking the prescribed motions. This unified treatment of assignment and null-space motion yields a practically efficient planner that safely realizes coordinated manipulation-policy outputs on multi-arm robots. See omcbsa.github.io for more.

This paper introduces a twist decomposition framework for serial manipulators performing lower mobility tasks. Rather than relying on Jacobian null-space projections, the method separates the end-effector twist into task and redundant components using geometrically defined twist projectors. This formulation provides a direct and intuitive distinction between task-relevant and task-irrelevant motions in operational space, enabling a compact inverse kinematics scheme that naturally handles both manipulator and task redundancy.

Long-reach drilling booms must reach successive poses without self-collision. Moving from operator-supervised control toward autonomy requires collision-aware motion planning and execution. For the Sandvik SB60, this study adapts established methods by integrating pose-parameterized planning with a capsule-based control barrier function quadratic program (CBF-QP) in measured-state inverse kinematics (IK). A fixed task-specific parameter set within each task generates waypoints, detours, timed references, and chained motion without target-specific retuning. The offline detour planner screens candidate waypoints using 23 selected rod-segment-to-body-region distances, whereas the online CBF-QP filters joint velocities using 14 configured capsule-pair constraints from a nine-primitive whole-body capsule model. Evaluation considers two drilling tasks in a manufacturer-developed SB60 Simscape Multibody model: a five-target restricted-orientation tour and a three-target full-pose tour. Across several hundred thousand samples, the method produced zero IK failures, generated several detour waypoints, achieved millimetre-level mean final-position error, and recorded no sampled CBF margins below the reported thresholds.

Real-time collision avoidance for robotic manipulators requires fast reactions to unexpected obstacle motion and lookahead to avoid becoming trapped by near-future constraints. Full model predictive control can provide this foresight, but its online cost may grow quickly with horizon length, model fidelity, and the number of active geometric constraints. Conversely, horizon-free reactive methods are computationally efficient but can be short-sighted in dynamic clutter. We present a task-space receding-horizon controller that uses a short contact-consistent rollout to generate a terminal kinematic reference satisfying internal non-penetration constraints, then computes only the first input of a smooth minimum-acceleration transition toward that reference. Starting from a closed-loop inverse-kinematics regulation law, the rollout is performed with an iterative dynamics solver operating on inflated convex robot and obstacle geometries, so that robot-obstacle contacts, dynamic obstacle motion, and self-collisions can shape the terminal reference without requiring full constrained trajectory optimization. We analyze the contact-inactive closed loop and show local exponential task-space regulation under standard regularity assumptions. For contacts activated inside the rollout, we characterize the corresponding discrete updates and bound the effect of moving obstacles on regular operating sets. Simulations on a 40-DOF multi-chain system show that intermediate horizons balance anticipation, responsiveness, and computational cost. Hardware experiments on a 6-DOF platform demonstrate consistent sim-to-real behavior without accurate inertial parameter estimation, and comparisons against dynamic optimization fabrics and model predictive control (MPC) baselines show improved success rates in dynamic clutter while preserving solve times compatible with real-time execution in the tested regimes.

High-speed off-road autonomy requires precise closed-loop control for a target vehicle while remaining robust across changing terrains. Recent forward kinodynamic (FKD) prediction foundation models suggest a promising path, starting from a generalist model and specializing it to the target platform. However, effective specialization remains challenging, as it often requires substantial real-world data, and models adapted to one setting can still overfit to specific terrains or driving regimes. We present OptCar (Optimized Car), a recipe for bridging the gap from generalist to specialist FKD models that preserves cross-terrain generalization while optimizing performance for a specific vehicle. $\texttt{OptCar}$ introduces a history-conditioned dynamics adaptation module that encodes recent state-action observations into a dynamics context token, and then fine-tunes the generalist model using limited real-world data together with targeted synthetic rollouts from environment-specific system identification. In closed-loop model predictive control (MPC) experiments across three terrains and an out-of-distribution cart-pulling task, the largest gains appear at 6m/s, the highest speed evaluated and the regime in which slip dominates tracking error. On vegetation and dirt, the most slip-diverse terrain, OptCar reduces 6m/s trajectory tracking error by roughly 55% relative to a fine-tuned AnyCar baseline, and remains the most accurate even when an unseen cart payload changes the dynamics. With only 5 minutes of real data per terrain, OptCar is competitive on road with a specialist trained on 30 minutes of road data, and substantially outperforms it once the terrain changes.

Continuum robots provide intrinsic compliance, high dexterity, and safe physical interaction, enabling navigation and manipulation in confined and unstructured environments. Despite recent advances in sensing and control, heightening the need for precise motion generation, most widely used planning libraries are grounded in rigid-body assumptions, creating a critical gap for fast and practical tools for continuum robots. To address this, we present CR-Solver, a two-stage, optimization-based solver for the motion generation of tendon-driven continuum robots. Our method unifies inverse kinematics, path following, and trajectory planning within a single constrained nonlinear optimization framework. Leveraging GPU-accelerated parallel optimization, CR-Solver delivers fast, accurate, and constraint-aware solutions. We validate our approach on three tasks, demonstrating significant speedups over traditional CPU-based solvers while achieving a consistently high success rate above 95% and millimeter-level accuracy. The solver is implemented in pure Python, reducing the barrier to adoption and offering a practical, extensible foundation for continuum robots' high-performance motion planning.

Dexterous grasp generation across robot hands is challenging because hands differ in kinematic topology, actuation dimensions, and native command spaces. We introduce GraspGraphNet, a topology-aware grasp generation framework that represents each hand as a URDF-derived kinematic graph and directly generates executable palm poses and joint configurations. GraspGraphNet combines hierarchical object surface encoding, differentiable forward kinematics, and dynamic world-edge message passing to model evolving robot-object interactions. It applies conditional flow matching directly in executable palm-pose and joint-state space, avoiding post-processing optimization, inverse kinematics, and retargeting. Using a shared model trained on Barrett Hand, Allegro Hand, and Shadow Hand, GraspGraphNet achieves an average success rate of 83.48% with 40ms inference time per grasp on a 40-object benchmark. Without retraining, the same model achieves 72.70% success on controlled finger-removal variants, demonstrating robustness to hand-topology variations. These results suggest that graph-structured hand representations can effectively support dexterous grasp generation across robot hands with different kinematic structures. Project: https://lysees.github.io/graspgraphnet-page

In many real-world systems, including articulated robots and biomechanical models, rotations are defined in joint space and naturally parameterized by Euler angles with bounded ranges. Yet regressing Euler angles remains challenging, as their discontinuities and singularities often destabilize training. In this work, we revisit Euler-angle regression and show that its effectiveness depends critically on the interaction between rotation representation, regression architecture, and domain constraints. We introduce a new framework that combines range-aware Euler modeling with Kolmogorov-Arnold Networks (KAN), which replace fixed node-wise activations with learnable univariate functions on edges. We further provide theoretical analysis indicating that bounded Euler ranges motivate a near-additive structure in the regression function, which favors the additive functional form of KAN, and we confirm this trend empirically. Extensive experiments on controlled rotation regression, object pose estimation, and robotic and human inverse kinematics demonstrate consistent improvements in accuracy, convergence, and efficiency. The code will be publicly available.

Recent studies suggest that diffusion models can recover geometric structure in the data manifolds they are trained on, yet the supporting evidence has so far come mostly from natural-image data, where the underlying geometry itself is unknown. We study this question in a setting where the geometry is analytically tractable: constrained inverse kinematics (IK). Each task-space constraint defines a configuration-space manifold with known intrinsic dimension, giving direct ground truth for evaluating the geometry learned by the model. For each of the 6-DoF UR5 and 7-DoF Franka, we train a single conditional diffusion model across seven constraint families, spanning solution manifolds from discrete IK branches to self-motion manifolds. Our empirical results reveal that the intrinsic dimension recovered from the model's score function matches the analytical degrees of freedom of the corresponding constraint manifold across both robots. Moreover, linear interpolation in the latent space leads to generated solutions that remain close to the appropriate constraint manifold, indicating that the learned representation further captures geometric structure of the constraint family beyond intrinsic dimension alone. Constrained IK therefore offers a controlled setting for studying the intrinsic geometry learned by diffusion models.

We present a unified framework that turns a set of 6-DoF inspection viewpoints into a time-optimal, collision-free route for a 9-DoF robotic system. Unlike modular pipelines that fix a single inverse-kinematics (IK) configuration per viewpoint, build an all-pairs travel-time map, and then route, our method jointly optimizes the visiting order and the per-viewpoint configuration in a single global search. The three-dimensional self-motion manifold of each viewpoint is parameterized in closed form so that the pose constraint holds by construction, the rest-to-rest travel time is approximated by a closed-form admissible double-integrator surrogate, and the tour is encoded by random keys. A derivative-free optimizer (CMA-ES) minimizes a cheap penalized objective over order and configuration, after which direct-collocation trajectory optimization is applied only to the edges of the selected route to certify dynamic feasibility and torque limits, and to return exact timings. This reduces the trajectory solves from quadratic to linear in the number of viewpoints and removes the decoupling that prevents modular pipelines from being globally time-optimal. Simulations and real-robot experiments on a KUKA LBR iiwa with a 2-DoF linear stage validate feasibility, smooth execution, and reduced end-to-end inspection time relative to modular and naive distance-based baselines.

Markerless, single-RGB-D-camera motion capture provides a low-cost and non-invasive alternative to conventional marker-based systems for robot teleoperation; however, depth estimation often degrades in the presence of self-occlusion, particularly during upper-limb motion. This paper presents an Arm Kinematic Correction (AKC) method that improves depth estimation by enforcing geometric constraints based on constant arm lengths. The proposed approach reconstructs occluded joint depths by leveraging wrist positions and predefined arm lengths via a deterministic formulation based on the Pythagorean theorem, thereby avoiding the need for complex probabilistic modeling or parameter tuning. Experimental validation against a Vicon reference system demonstrates reliable performance for both static and dynamic joint motions, evaluated using root-mean-square error (RMSE) and Pearson correlation. Furthermore, motion-mapping teleoperation is successfully demonstrated in both simulated and physical robot environments. The results show that AKC enhances robustness and preserves anatomical consistency under long-duration, severe self-occlusion, even when paired with less reliable temporal filters, highlighting its practicality for real-time applications such as robot teleoperation and human-robot interaction.

Inverse kinematics (IK) remains a critical bottleneck for real-time robot manipulation. Classical numerical solvers achieve high geometric precision but often suffer from discontinuous branch switching and unstable behavior near kinematic singularities during closed-loop deployment. Meanwhile, learned IK approaches frequently struggle to balance spatial accuracy, motion smoothness, and real-time efficiency, particularly when trained on noisy human teleoperation data. We present \textbf{MimicIK}, a real-time generative inverse kinematics framework that learns smooth and robust joint-space motion priors from teleoperation demonstrations through conditional flow matching. Given the current joint configuration and a target end-effector pose, MimicIK predicts continuous delta-joint commands using an efficient two-step iterative refinement process based on a Minimal Iterative Policy (MIP) backbone. To enforce physical consistency, we further introduce an FK consistency loss, a differentiable forward-kinematics regularization that penalizes task-space deviations from the target pose during training. We evaluate MimicIK on a real-world 6-DOF robot dataset containing 8,848 teleoperation demonstrations. MimicIK achieves a mean position error of 4.65 mm, a 10 mm success rate of 92.01%, and a trajectory spike rate of only 7.99%. Compared with a UNet diffusion baseline, our method improves both spatial accuracy and motion smoothness while reducing inference latency from 21.66 ms to 6.74 ms. Furthermore, unlike deterministic MLP baselines that catastrophically diverge under out-of-distribution deployment, MimicIK remains stable near singular configurations and enables robust 20 Hz real-time control on deployment hardware.

Most learned dexterous grasp generators relegate contact forces to a downstream verification step, so a kinematically-plausible pose can still violate the conditions for a stable physical grasp. We address this with EquiDexFlow, an SE(3)-equivariant flow-matching model that jointly predicts wrist pose, joint angles, fingertip contacts, surface normals, and contact forces from an object point cloud. Our architecture projects contacts onto the object surface and forces into the Coulomb friction cone by construction, so placement and friction compliance hold without loss penalties. We prove end-to-end SE(3) equivariance and verify it empirically over 200 rotations, with wrist residuals below $0.04^\circ$ and exactly zero joint deviation. Trained on 8,100 force-closure grasps across 81 objects for the 16-DoF Allegro Hand, our model achieves zero friction violations, the best composite score, and the lowest wrench residual among all ablation variants. We retarget decoded fingertip contacts to a 16-DoF LEAP Hand via per-finger inverse kinematics, and our hardware-feasible refinement places every joint at least 5% inside its actuator envelope while preserving wrench balance. On the physical robot, retargeted EquiDexFlow-decoded grasps complete open-loop pick-and-hold trials on all six test objects, with every asymmetric object succeeding at both the canonical pose and a $120^\circ$ co-rotation. Videos, code, and checkpoints are available at https://equidexflow.github.io.

This paper proposes actuator-aware inverse kinematics for torque-controlled redundant robots under joint-limit constraints. In the considered architecture, the inverse-kinematic output is not merely a purely kinematic joint-velocity command; it is the required joint velocity supplied to a downstream torque-level controller. Therefore, a small commanded task residual may not necessarily improve realized motion. The proposed method formulates a convex quadratic programming problem whose decision variable is the joint-level required velocity. Control barrier function style bounds impose reference-level joint-limit admissibility, while the task equation is handled through a penalized slack variable. Redundancy is resolved using a controller-compatibility objective that accounts for previous-command consistency and actuator torque-capacity weighting. The method is independent of the particular torque-level controller and can serve as an intermediate IK layer between an endpoint trajectory and a redundant robot controller. Experiments on a virtual-decomposition-controlled seven-degree-of-freedom upper-limb exoskeleton compare the method with standard inverse-kinematic baselines and a constrained task-preserving quadratic programming baseline. The results indicate lower limit-pushing commands, bounded admissible required velocities, and improved realized task behavior in the tested trajectory, without modifying the downstream controller.

Inverse kinematics (IK) is a fundamental problem in robotics, requiring the generation of joint configurations that satisfy target end-effector poses. Existing approaches often struggle to generalize across diverse robot morphologies and to effectively model the multi-modal nature of IK, particularly in articulated systems with multiple kinematic branches. In this work, we propose GraphDiff-IK, a structure-aware graph diffusion framework for inverse kinematics. Specifically, we represent the robot as a kinematic graph constructed from the robot URDF, where nodes correspond to actuated joints and edges encode kinematic dependencies. Building upon this representation, we formulate IK as a conditional graph diffusion process that directly generates joint configurations on the robot graph. To better capture structural dependencies in articulated systems, we further introduce a structure-aware graph reasoning framework with hierarchical stage-wise message passing and torso-aware conditioning for multi-branch robots. In addition, we incorporate noisy forward kinematics feedback and task-space supervision to improve geometric consistency during denoising. The proposed framework provides a unified formulation that naturally supports single-arm robots, dual-arm systems, and articulated robots with torso or waist structures. Extensive experiments on diverse robotic platforms demonstrate that the proposed method achieves accurate and stable IK performance while preserving the ability to generate multiple feasible solutions for redundant robotic systems.

Inverse Kinematics (IK) plays a critical role in robotic motion planning and control. The IK solutions of a robot manipulator could be done by conventional ways such as geometric, algebraic, or Jacobian methods, which have drawbacks. The Artificial Neural Networks (ANNs) have become a promising alternative for approximating IK solutions due to their generalization ability and computational efficiency. This approach basically trains only a few samples of the end effector that are recorded for the solution of the IK problem. However, a fundamental question remains: how many training samples are sufficient to achieve reliable and accurate IK predictions? This study investigates the mathematical framework of relating the size of training datasets and the accuracy of ANN-based IK solvers. Using an articulated robotic manipulator, we generate varying amounts of joint-position pairs to train feedforward neural networks and assess their accuracy, convergence, and generalization capability. The results reveal more training samples than 125 did not contribute to the improvement of the model efficiency that the comparable measure dealing with the approximation accuracy over the sampling size, offering valuable insight into data efficiency. This work provides practical guidance for optimizing the data sizing of ANN solutions, balancing computational cost and model accuracy for real-world robotic applications.

Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in isolation, failing to exploit their combined potential. This paper introduces cross-space symmetry compositions, a framework for learning robot policies that are jointly equivariant to multiple symmetries across configuration and task spaces. Leveraging the differential-geometric structure of the forward kinematics map, we both descend symmetries from configuration to task space and lift symmetries from task to configuration space, enabling their composition within a unified representation space. We validate our framework on simulated and real-world experiments on a dual-arm robot, demonstrating that jointly leveraging multiple symmetries yields improved generalization.

Existing Driving VLAs predict trajectories while largely ignoring their visual tokens -- a phenomenon we trace not to insufficient training but to a structurally ill-posed task formulation. We show that trajectory recovery, when viewed through the lens of inverse kinematics, requires both a current and a future visual state as boundary conditions; existing VLAs supply only the former, which encourages the model to shortcut through ego status and text commands alone. To address this, we re-design Driving VLA in the style of an inverse kinematics solver. First, a next visual state prediction objective that requires the LLM to predict the future visual scene provides dense visual supervision and suppresses shortcut paths. Second, a separate Inverse Kinematics Network (a cross-attention-based conditional diffusion model) that takes only the current and future visual states as input is designed to suppress reliance on ego status and textual shortcuts during trajectory decoding. With this simple prescription alone, our 0.5B-scale model recovers visual grounding and reaches trajectory planning performance comparable to 7B--8B VLAs more than an order of magnitude larger, on both the closed-loop NAVSIM-v2 and the nuScenes benchmarks. Extensive analysis further shows that this improvement stems from a recovered ability to exploit visual features, with the effect being most pronounced in dynamic driving situations such as turning.

arly identification of motor impairment in infancy relies on expert visual assessment of spontaneous movement, motivating the development of automated, objective alternatives. One promising approach is using computer vision, which benefits from high quality pose estimation from video. In this study, we systematically evaluated three state-of-the-art pose estimation frameworks (MeTRAbs-ACAE, SAM 3D Body, and Sapiens) on 100 videos over 13 sessions of 8 infants recorded with a multi-view markerless motion capture system. We quantified keypoint detection accuracy using reprojection error, geometric consistency, and Procrustes-aligned 3D position error, and demonstrated proof-of-concept for fitting an inverse kinematic framework to infant data. While Sapiens achieved the lowest reprojection error and highest geometric consistency of the methods evaluated (22.8 pixels and 0.82, respectively), SAM 3D Body provided the most comprehensive 3D information for kinematic reconstruction with Procrustes-aligned position errors of 19 to 28 mm. We demonstrate in a case comparison example that biomechanical models fit to SAM 3D estimates distinguish representative movement patterns in infants related to motor development, as identified by a clinical expert. Together, these findings highlight both the promise and current limitations of 3D pose estimation for infant biomechanics and establish preliminary groundwork for scalable, video-based assessment of early motor development.

Accurate hand and finger tracking from video has significant clinical applications for monitoring activities of daily living and measuring range of motion, yet monocular video approaches for obtaining hand biomechanics remain under-developed. We present a method that combines the SAM 3D Body foundation model with inverse kinematics optimization in a full-body biomechanical model to extract anatomically-constrained finger joint angles from single-view video. We port SAM 3D Body from PyTorch to JAX for integration with MuJoCo-MJX, enabling GPU-accelerated optimization, and develop a novel mapping between the Momentum Human Rig (MHR) outputs and biomechanical model markers. Validation against 8-camera multiview reconstruction on 4,590 frames from 7 participants performing a variety of hand poses and object manipulation tasks shows finger joint angle errors of approximately 10 degrees and hand position errors of approximately 6 mm, after Procrustes alignment. Results were consistent across camera viewpoints and robust to different methods for producing reference values from multiview video. This work extends monocular biomechanical analysis to detailed finger tracking, expanding access to quantitative characterization of hand movement from readily available video.

This paper presents a subsystem-based adaptive control framework for serial flexible manipulators with an arbitrary number of links, in which the elastic deformation PDE of each link is carried through the entire control design without spatial discretization or modal truncation. All dynamic quantities -- rigid-body motion, elastic deformation, and inter-link constraint forces -- are expressed uniformly as body-fixed twists and wrenches within the se3 Lie-algebraic structure. A controllable form of the per-link dynamics is derived by substituting the strain-based deformation PDE into the dynamic equation, eliminating distributed elastic acceleration and yielding a model governed by the body-fixed twist acceleration and deformation field. Desired subsystem twist trajectories are generated via a deflection-compensating inverse kinematics procedure. A nominal per-link controller is proven to produce exponential twist error decay via a per-subsystem Lyapunov function. An adaptive modification replaces exact physical parameters with online estimates governed by a projection-based law, augmenting with a parameter estimation error term. Upon summing over all links, the interaction power terms telescope to zero by Newton's third law and the frame invariance of the natural power pairing on se3se(3), establishing exponential convergence of all twist errors and bounded elastic deformation under both nominal and adaptive controllers. The screw-theoretic structure renders interaction term cancellation exact, making the stability certificate modular and scalable to chains of arbitrary length. The framework is validated numerically on a two-link flexible manipulator in three-dimensional motion.

This paper investigates singular configurations of planar 3-RPR parallel manipulators, which result from applying the averaging technique to solution pairs of their direct kinematic problem. Without computing the zeros of the corresponding degree 6 polynomial we parametrize the input pairs and determine their relative orientation in a way that the flexion order of the averaged configurations increases. Moreover, the obtained results are visualized for concrete examples. The presented methodology can also be used for studying the spherical and spatial analogues of planar 3-RPR parallel manipulators.

Inverse kinematics (IK) is a core operation in animation, robotics, and biomechanics: given Cartesian constraints, recover joint rotations under a known kinematic tree. In many real-time human avatar pipelines, the available signal per frame is a sparse set of tracked 3D joint positions, whereas animation systems require joint orientations to drive skinning. Recovering full orientations from positions is underconstrained, most notably because twist about bone axes is ambiguous, and classical IK solvers typically rely on iterative optimization that can be slow and sensitive to noisy inputs. We introduce IK-GAT, a lightweight graph-attention network that reconstructs full-body joint orientations from 3D joint positions in a single forward pass. The model performs message passing over the skeletal parent-child graph to exploit kinematic structure during rotation inference. To simplify learning, IK-GAT predicts rotations in a bone-aligned world-frame representation anchored to rest-pose bone frames. This parameterization makes the twist axis explicit and is exactly invertible to standard parent-relative local rotations given the kinematic tree and rest pose. The network uses a continuous 6D rotation representation and is trained with a geodesic loss on SO(3) together with an optional forward-kinematics consistency regularizer. IK-GAT produces animation-ready local rotations that can directly drive a rigged avatar or be converted to pose parameters of SMPL-like body models for real-time and online applications. With 374K parameters and over 650 FPS on CPU, IK-GAT outperforms VPoser-based per-frame iterative optimization without warm-start at significantly lower cost, and is robust to initial pose and input noise

Underground mining robots are increasingly modeled for planning, operator training, and digital-twin workflows, where reliable actuator-level kinematics is needed to reduce hazardous in situ trials. Unlike typical open-chain industrial manipulators, representative mining machines are often linear-actuator-driven closed-chain mechanisms with planar four-bar linkages, making reusable kinematic modeling and real-time FK/IK solving challenging. We present \textit{\hl{MineRobot}}, an actuator-centered framework for modeling and solving the kinematics of this representative mechanism class. MineRobot introduces the Mining Robot Description Format (MRDF), a domain-specific representation that parameterizes mining-robot kinematics with native semantics for actuators and loop closures. It then contracts planar four-bar substructures into generalized joints and extracts, for each actuator, an Independent Topologically Equivalent Path (ITEP) classified into four canonical types. Based on this decomposition, per-type solvers are composed into a sequential forward-kinematics (FK) pipeline, while inverse kinematics (IK) is formulated as a bound-constrained actuator-length optimization solved by a Gauss--Seidel-style update scheme. By converting coupled closed-chain kinematics into small topology-aware solves, MineRobot reduces robot-specific hand derivations and supports efficient repeated FK/IK computation without treating each query as a full coupled constraint-solving problem. Experiments on representative underground mining robots demonstrate real-time FK performance and robust IK convergence within the tested operating ranges, supporting the use of MineRobot as an actuator-centered kinematic layer for planning, training, and digital-twin workflows.

Reconstructing biomechanically realistic 3D human motion - recovering both kinematics (motion) and kinetics (forces) - is a critical challenge. While marker-based systems are lab-bound and slow, popular monocular methods use oversimplified, anatomically inaccurate models (e.g., SMPL) and ignore physics, fundamentally limiting their biomechanical fidelity. In this work, we introduce MonoMSK, a hybrid framework that bridges data-driven learning and physics-based simulation for biomechanically realistic 3D human motion estimation from monocular video. MonoMSK jointly recovers both kinematics (motions) and kinetics (forces and torques) through an anatomically accurate musculoskeletal model. By integrating transformer-based inverse dynamics with differentiable forward kinematics and dynamics layers governed by ODE-based simulation, MonoMSK establishes a physics-regulated inverse-forward loop that enforces biomechanical causality and physical plausibility. A novel forward-inverse consistency loss further aligns motion reconstruction with the underlying kinetic reasoning. Experiments on BML-MoVi, BEDLAM, and OpenCap show that MonoMSK significantly outperforms state-of-the-art methods in kinematic accuracy, while for the first time enabling precise monocular kinetics estimation.

Inverse Kinematics (IK) is a core problem in robotics, in which joint configurations are found to achieve a (collision-free) desired end-effector pose. Modern IK solvers face a fundamental trade-off: analytical methods are fast but lack generality, while numerical optimization-based methods are broadly applicable but prone to local minima and high computational costs. To overcome this challenge, we introduce HJCD-IK, a GPU-accelerated, sampling-based hybrid solver. By pairing a novel orientation-aware greedy coordinate descent initialization with Jacobian-based polishing and a parallel collision filter, our method achieves up to order-of-magnitude gains in speed and accuracy over state-of-the-art solvers, consistently finding collision-free solutions on the accuracy-latency Pareto frontier, while producing a diverse distribution of high-quality samples. We validate our solver on a physical Franka manipulator and release our code open-source.