Abstract--Industrial automation with six-axis robotic arms is critical for many manufacturing tasks, including welding and additive manufacturing applications; however, many of these operations are functionally redundant due to the symmetrical tool axis, which effectively makes the operation a five-axis task. Exploiting this redundancy is crucial for achieving the desired workspace and dexterity required for the feasibility and optimisation of toolpath planning. Inverse kinematics algorithms can solve this in a fast, reactive framework, but these techniques are underutilised over the more computationally expensive offline planning methods. We propose a novel algorithm to solve functionally redundant inverse kinematics for robotic manipulation utilising a task space decomposition approach, the damped least-squares method and Halley's method to achieve fast and robust solutions with reduced joint motion. We evaluate our methodology in the case of toolpath optimisation in a cold spray coating application on a non-planar surface. The functionally redundant inverse kinematics algorithm can quickly solve motion plans that minimise joint motion, expanding the feasible operating space of the complex toolpath.

Virtual reality (VR) teleoperation has emerged as a promising approach for controlling humanoid robots in complex manipulation tasks. However, traditional tele-operation systems rely on inverse kinematics (IK) solvers and hand-tuned PD controllers, which struggle to handle external forces, adapt to different users, and produce natural motions under dynamic conditions. In this work, we propose a learning-based neural teleoperation framework that replaces the conventional IK+PD pipeline with learned policies trained via reinforcement learning. Our approach learns to directly map VR controller inputs to robot joint commands while implicitly handling force disturbances, producing smooth trajectories, and adapting to user preferences. We train our policies in simulation using demonstrations collected from IK-based teleoperation as initialization, then fine-tune them with force randomization and trajectory smoothness rewards. Experiments on the Unitree G1 humanoid robot demonstrate that our learned policies achieve 34% lower tracking error, 45% smoother motions, and superior force adaptation compared to the IK baseline, while maintaining real-time performance (50Hz control frequency). We validate our approach on manipulation tasks including object pick-and-place, door opening, and bimanual coordination. These results suggest that learning-based approaches can significantly improve the naturalness and robustness of humanoid teleoperation systems.

Each column illustrates four failure modes: joint violation, floating, penetration, and skating. Humanoid-X (Mao et al., 2025) (top row) often exhibits these issues due to direct video-to-motion conversion, while PHUMA (bottom row) mitigates those violations through careful data curation and physically grounded retargeting. Motion imitation is a promising approach for humanoid locomotion, enabling agents to acquire humanlike behaviors. Existing methods typically rely on high-quality motion capture datasets such as AMASS, but these are scarce and expensive, limiting scalability and diversity. Recent studies attempt to scale data collection by converting large-scale internet videos, exemplified by Humanoid-X. However, they often introduce physical artifacts such as floating, penetration, and foot skating, which hinder stable imitation. In response, we introduce PHUMA, a Physically-grounded HUMAnoid locomotion dataset that leverages human video at scale, while addressing physical artifacts through careful data curation and physics-constrained retargeting. PHUMA enforces joint limits, ensures ground contact, and eliminates foot skating, producing motions that are both large-scale and physically reliable. We evaluated PHUMA in two sets of conditions: (i) imitation of unseen motion from self-recorded test videos and (ii) path following with pelvis-only guidance. In both cases, PHUMA-trained policies outperform Humanoid-X and AMASS, achieving significant gains in imitating diverse motions. The code is available at https://davian-robotics.github.io/PHUMA. Humanoid robots are central to the pursuit of general-purpose embodied AI, but their deployment in real-world first requires locomotion that is both stable and humanlike.

Researchers have studied Stewart-Gough platforms, also known as Gough-Stewart platforms or hexapod platforms extensively for their inherent fine control characteristics. Their studies led to the potential deployment opportunities of Stewart-Gough Platforms in many critical applications such as the medical field, engineering machines, space research, electronic chip manufacturing, automobile manufacturing, etc. Some of these applications need micro and nano-level movement control in 3D space for the motions to be precise, complicated, and repeatable; a Stewart-Gough platform fulfills these challenges smartly. For this, the platform must be more accurate than the specified application accuracy level and thus proper calibration for a parallel robot is crucial. Forward kinematics-based calibration for these hexapod machines becomes unnecessarily complex and inverse kinematics complete this task with much ease. To experiment with different calibration techniques, various calibration approaches were implemented by using external instruments, constraining one or more motions of the system, and using extra sensors for auto or self-calibration. This survey paid attention to those key methodologies, their outcome, and important details related to inverse kinematic-based parallel robot calibrations. It was observed during this study that the researchers focused on improving the accuracy of the platform position and orientation considering the errors contributed by one source or multiple sources. The error sources considered are mainly kinematic and structural, in some cases, environmental factors also are reviewed, however, those calibrations are done under no-load conditions. This study aims to review the present state of the art in this field and highlight the processes and errors considered for the calibration of Stewart-Gough platforms.

This paper presents a method to generate feasible, unique forward-kinematic solutions for a general Stewart platform. This is done by using inverse kinematics to obtain valid workspace data and corresponding actuator lengths for the moving platform. For parallel kinematic machines, such as the Stewart Platform, inverse kinematics are straight forward, but the forward kinematics are complex and generates multiple solutions due to the closed loop structure of the kinematic links. In this research, a simple iterative algorithm has been used employing modified Denavit-Hartenberg convention. The outcome is encouraging as this method generates a single feasible forward kinematic solution for each valid pose with the solved DH parameters and unlike earlier forward kinematics solutions, this unique solution does not need to be manually verified. Therefore, the forward kinematic solutions can be used directly for further calculations without the need for manual pose verification. This capability is essential for the six degree of freedom materials testing system developed by the authors in their laboratory. The developed system is aimed at characterizing additively manufactured materials under complex combined multiple loading conditions. The material characterization is done by enabling high precision force control on the moving platform via in situ calibration of the as-built kinematics of the Stewart Gough Platform.

Stewart platform-based Parallel Kinematic (PKM) Machines have been extensively studied by researchers due to their inherent finer control characteristics. This has opened its potential deployment opportunities in versatile critical applications like the medical field, engineering machines, space research, electronic chip manufacturing, automobile manufacturing, etc. All these precise, complicated, and repeatable motion applications require micro and nano-scale movement control in 3D space; a 6-DOF PKM can take this challenge smartly. For this, the PKM must be more accurate than the desired application accuracy level and thus proper calibration for a PKM robot is essential. Forward kinematics-based calibration for such hexapod machines becomes unnecessarily complex and inverse kinematics complete this task with much ease. To analyze different techniques, an external instrument-based, constraint-based, and auto or self-calibration-based approaches have been used for calibration. This survey has been done by reviewing these key methodologies, their outcome, and important points related to inverse kinematic-based PKM calibrations in general. It is observed in this study that the researchers focused on improving the accuracy of the platform position and orientation considering the errors contributed by a single source or multiple sources. The error sources considered are mainly structural, in some cases, environmental factors are also considered, however, these calibrations are done under no-load conditions. This study aims to understand the current state of the art in this field and to expand the scope for other researchers in further exploration in a specific area.

Inverse Kinematics (IK) is a core problem in robotics, in which joint configurations are found to achieve a desired end-effector pose. Although analytical solvers are fast and efficient, they are limited to systems with low degrees-of-freedom and specific topological structures. Numerical optimization-based approaches are more general, but suffer from high computational costs and frequent convergence to spurious local minima. Recent efforts have explored the use of GPUs to combine sampling and optimization to enhance both the accuracy and speed of IK solvers. We build on this recent literature and introduce HJCD-IK, a GPU-accelerated, sampling-based hybrid solver that combines an orientation-aware greedy coordinate descent initialization scheme with a Jacobian-based polishing routine. This design enables our solver to improve both convergence speed and overall accuracy as compared to the state-of-the-art, consistently finding solutions along the accuracy-latency Pareto frontier and often achieving order-of-magnitude gains. In addition, our method produces a broad distribution of high-quality samples, yielding the lowest maximum mean discrepancy. We release our code open-source for the benefit of the community.

Although robotic manipulators are used in an ever-growing range of applications, robot manufacturers typically follow a ``one-fits-all'' philosophy, employing identical manipulators in various settings. This often leads to suboptimal performance, as general-purpose designs fail to exploit particularities of tasks. The development of custom, task-tailored robots is hindered by long, cost-intensive development cycles and the high cost of customized hardware. Recently, various computational design methods have been devised to overcome the bottleneck of human engineering. In addition, a surge of modular robots allows quick and economical adaptation to changing industrial settings. This work proposes an approach to automatically designing and optimizing robot morphologies tailored to a specific environment. To this end, we learn the inverse kinematics for a wide range of different manipulators. A fully differentiable framework realizes gradient-based fine-tuning of designed robots and inverse kinematics solutions. Our generative approach accelerates the generation of specialized designs from hours with optimization-based methods to seconds, serving as a design co-pilot that enables instant adaptation and effective human-AI collaboration. Numerical experiments show that our approach finds robots that can navigate cluttered environments, manipulators that perform well across a specified workspace, and can be adapted to different hardware constraints. Finally, we demonstrate the real-world applicability of our method by setting up a modular robot designed in simulation that successfully moves through an obstacle course.