Actuator-Aware Inverse Kinematics with Joint-Limit Admissibility for Torque-Controlled Redundant Robots

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) 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.

Robots working in unstructured or partially unobservable environments must combine accurate motion with physical compliance that can passively correct contact misalignment. Soft robots provide this compliance but have struggled to precisely control their tip compliance and position. This paper presents a robot architecture designed around that control problem: a 7-link arm whose six articulated joints provide twelve independently driven revolute axes, each actuated by an antagonistic pair of pneumatic muscles, so that every axis can simultaneously change its angle and linearly adjust its stiffness. The rigid articulated backbone makes the tip compliance and position of the arm predictable enough to be commanded quantitatively in real time. The robot employs a unified iterative inverse-kinematics and inverse-compliance controller to achieve simultaneous, quantitative control of both compliance and position. The task-space compliance and kinematics models and the control law are derived and verified on both the physical arm and a matched simulation. Simulation is then used to study how the same framework extends to other arm morphologies. Finally, the arm demonstrates tasks that have been difficult for both rigid and soft arms: rejecting disturbances while writing on a moving whiteboard, and passively correcting hidden misalignment during a key-insertion and drawer-opening task. That these tasks succeed under so straightforward a controller is evidence for the advantage of this algorithm-informed structural design.