Unmanned Aerial Vehicles (UAVs), particularly multi-rotor platforms, have rapidly advanced in research and applications due to their unique capabilities, including vertical takeoff and landing (VTOL), hovering, and high maneuverability. These features make them ideal for complex environments and have driven their adoption in fields such as environmental monitoring, precision agriculture, infrastructure inspection, and emergency response, among others. A key area of recent interest is the control and coordination of multiple UAVs in formation. Formation control enables groups of UAVs to maintain specific geometric arrangements while performing tasks, offering advantages such as enhanced coverage, efficiency, and redundancy [24]. These benefits are critical for applications ranging from search and rescue to cooperative tasks like cargo transport and aerial cinematography.

-- Object handover is an important skill that we use daily when interacting with other humans. T o deploy robots in collaborative setting, like houses, being able to receive and handing over objects safely and efficiently becomes a crucial skill. In this work, we demonstrate the use of Reinforcement Learning (RL) for dexterous object handover between two multi-finger hands. Key to this task is the use of a novel reward function based on dual quaternions to minimize the rotation distance, which outperforms other rotation representations such as Euler and rotation matrices. The robustness of the trained policy is experimentally evaluated by testing w.r .t. objects that are not included in the training distribution, and perturbations during the handover process. The results demonstrate that the trained policy successfully perform this task, achieving a total success rate of 94% in the best-case scenario after 100 experiments, thereby showing the robustness of our policy with novel objects. In addition, the best-case performance of the trained policy decreases by only 13.8% when the other robot moves during the handover, proving that our policy is also robust to this type of perturbation, which is common in real-world object handovers. Code and videos can be found here. With the recent focus on humanoid robots, service robots, and human-robot collaboration, several efforts have been made to teach robots how to perform dexterous manipulation tasks, such as collaborative assembly, package manipulation in logistics, and household chores.

Integrated Navigation (IN) techniques have emerged as a promising solution by combining multiple sensor measurements, such as those obtained from Inertial Measurement Units (IMU), Global Navigation Satellite Systems (GNSS), and vision-based sensors. IN approaches offer significant advantages, including robustness, improved accuracy, and the ability to overcome the limitations of individual sensors. Among the various mathematical tools employed in IN, quaternions have garnered considerable attention for estimating a vehicle's attitude (orientation). Quaternions provide an elegant and compact representation of orientation, avoiding the limitations of traditional Euler angles, such as singularities and ambiguity.

This paper investigates optimal fiducial marker placement on the surface of a satellite performing relative proximity operations with an observer satellite. The absolute and relative translation and attitude equations of motion for the satellite pair are modeled using dual quaternions. The observability of the relative dual quaternion system is analyzed using empirical observability Gramian methods. The optimal placement of a fiducial marker set, in which each marker gives simultaneous optical range and attitude measurements, is determined for the pair of satellites. A geostationary flyby between the observing body (chaser) and desired (target) satellites is numerically simulated and the optimal fiducial placement sets of five and ten on the surface of the desired satellite are solved. It is shown that the optimal solution maximizes the distance between fiducial markers and selects marker locations that are most sensitive to measuring changes in the state during the nonlinear trajectory, despite being visible for less time than other candidate marker locations. Definitions and properties of quaternions and dual quaternions, and parallels between the two, are presented alongside the relative motion model.

Relative pose (position and orientation) estimation is an essential component of many robotics applications. Fiducial markers, such as the AprilTag visual fiducial system, yield a relative pose measurement from a single marker detection and provide a powerful tool for pose estimation. In this paper, we perform a Lie algebraic nonlinear observability analysis on a nonlinear dual quaternion system that is composed of a relative pose measurement model and a relative motion model. We prove that many common dual quaternion expressions yield Jacobian matrices with advantageous block structures and rank properties that are beneficial for analysis. We show that using a dual quaternion representation yields an observability matrix with a simple block triangular structure and satisfies the necessary full rank condition.

This paper reports on a novel method for LiDAR odometry estimation, which completely parameterizes the system with dual quaternions. To accomplish this, the features derived from the point cloud, including edges, surfaces, and Stable Triangle Descriptor (STD), along with the optimization problem, are expressed in the dual quaternion set. This approach enables the direct combination of translation and orientation errors via dual quaternion operations, greatly enhancing pose estimation, as demonstrated in comparative experiments against other state-of-the-art methods. Our approach reduced drift error compared to other LiDAR-only-odometry methods, especially in scenarios with sharp curves and aggressive movements with large angular displacement. DualQuat-LOAM is benchmarked against several public datasets. In the KITTI dataset it has a translation and rotation error of 0.79% and 0.0039{\deg}/m, with an average run time of 53 ms.

This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree-of-freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for performing smooth equidistant travel of the tool is provided by applying arc-length reparameterization. This general approach can be applied to one-DoF mechanisms with four to seven joints characterized by a rational motion, without any additional geometrical analysis. An experiment was performed to demonstrate the usage in a laboratory setup.

Single-loop N-bar linkages are closed kinematic chains that connect a number of rigid bars via revolute or prismatic joints in one loop. Over-constrained mechanisms are a special class of such linkages. In this class, the Grübler-Kutzbach-Chebyshev formula, computing the degrees-of-freedom (DoF) of the mechanism, fails and the causes of this failure are special geometric properties of the design parameters of the mechanism. Because of the low number of DoFs, single-loop linkages can be synthesized as simple single-purpose devices for specific tasks, such as pick-and-place operations. This can be advantageous compared to serial robots, because they can perform complicated motions following space-curves of higher degree with a low number of active joints.

A common prerequisite for evaluating a visual(-inertial) odometry (VO/VIO) algorithm is to align the timestamps and the reference frame of its estimated trajectory with a reference ground-truth derived from a system of superior precision, such as a motion capture system. The trajectory-based alignment, typically modeled as a classic hand-eye calibration, significantly influences the accuracy of evaluation metrics. However, traditional calibration methods are susceptible to the quality of the input poses. Few studies have taken this into account when evaluating VO/VIO trajectories that usually suffer from noise and drift. To fill this gap, we propose a novel spatiotemporal hand-eye calibration algorithm that fully leverages multiple constraints from screw theory for enhanced accuracy and robustness. Experimental results show that our algorithm has better performance and is less noise-prone than state-of-the-art methods.

Modeling the kinematics and dynamics of robotics systems with suspended loads using dual quaternions has not been explored so far. This paper introduces a new innovative control strategy using dual quaternions for UAVs with cable-suspended loads, focusing on the sling load lifting and tracking problems. By utilizing the mathematical efficiency and compactness of dual quaternions, a unified representation of the UAV and its suspended load's dynamics and kinematics is achieved, facilitating the realization of load lifting and trajectory tracking. The simulation results have tested the proposed strategy's accuracy, efficiency, and robustness. This study makes a substantial contribution to present this novel control strategy that harnesses the benefits of dual quaternions for cargo UAVs. Our work also holds promise for inspiring future innovations in under-actuated systems control using dual quaternions.