We introduce a real-time system for tracking hand pose using 6- axis inertial measurement units (IMUs) without requiring magnetometers or external sensors. Accurate hand pose tracking with only 6-axis IMUs is known to be fundamentally challenging due to the absence of a shared heading reference, leading to severe drift and inter-sensor misalignment. To overcome these limitations, we propose a hybrid method that combines a learning-based pose estimation approach followed by a late-stage Extended Kalman Filter (EKF). The learning-based model estimates noisy yet reasonable hand poses and is trained with drift-insensitive features like gravity vectors and wrist-relative gyroscope signals. On the other hand the EKF can appropriately filter the noise from pose estimates leading to robust tracking. Evaluated on a 12-hour dataset spanning 23 interaction tasks across 10 participants, our system improves joint angle accuracy by 40% over an EKF-only baseline and by 18% over a learning-only approach, achieving a mean joint error below 10°. The resulting framework enables real-time hand tracking invariant to magnetic perturbations, occlusion, or lighting changes, and is well suited for robotics, human–robot interaction (HRI), and human-computer interaction (HCI) applications.

Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities greater than cubic $O(n^3)$ with respect to rotation space discretization and lack extensive evaluation under significant outlier contamination. To this end, we propose a rotation estimation algorithm between two spherical patterns with linear time complexity $O(n)$. Unlike existing spherical-function-based methods, we explicitly represent spherical patterns as discrete 3D point sets on the unit sphere, reformulating rotation estimation as a spherical point-set alignment (i.e., Wahba problem for 3D unit vectors). Given the geometric nature of our formulation, our spherical pattern alignment algorithm naturally aligns with the Wahba problem framework for 3D unit vectors. Specifically, we introduce three novel algorithms: (1) SPMC (Spherical Pattern Matching by Correlation), (2) FRS (Fast Rotation Search), and (3) a hybrid approach (SPMC+FRS) that combines the advantages of the previous two methods. Our experiments demonstrate that in the $\mathbb{S}^2$ domain and in correspondence-free settings, our algorithms are over 10x faster and over 10x more accurate than current state-of-the-art methods for the Wahba problem with outliers. We validate our approach through extensive simulations on a new dataset of spherical patterns, the ``Robust Vector Alignment Dataset. "Furthermore, we adapt our methods to two real-world tasks: (i) Point Cloud Registration (PCR) and (ii) rotation estimation for spherical images.

Robot motion is controlled in the joint space whereas the robots have to perform tasks in their task space. Many tasks like carrying a glass of liquid, pouring liquid, opening a drawer requires constraints on the end-effector during the motion. The forward and inverse kinematic mappings between joint space and task space are highly nonlinear and multi-valued (for IK). Consequently, modeling task space constraints like keeping the orientation of the end-effector fixed while changing its position (which is required for carrying a cup of liquid without dropping it) is quite complex in the joint space. In this paper, we show that the use of screw linear interpolation to plan motions in the task space combined with resolved motion rate control to compute the corresponding joint space path, allows one to satisfy many common task space motion constraints in motion planning, without explicitly modeling them. In particular, any motion constraint that forms a subgroup of the group of rigid body motions can be incorporated in our planning scheme, without explicit modeling. We present simulation and experimental results on Baxter robot for different tasks with task space constraints that demonstrates the usefulness of our approach.