Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics.

Transformer-based autoregressive models have emerged as a unifying paradigm across modalities such as text and images, but their extension to 3D molecule generation remains underexplored. The gap stems from two fundamental challenges: (1) tokenizing molecules into a canonical 1D sequence of tokens that is invariant to both SE(3) transformations and atom index permutations, and (2) designing an architecture capable of modeling hybrid atom-based tokens that couple discrete atom types with continuous 3D coordinates. To address these challenges, we introduce InertialAR. InertialAR devises a canonical tokenization that aligns molecules to their inertial frames and reorders atoms to ensure SE(3) and permutation invariance. Moreover, InertialAR equips the attention mechanism with geometric awareness via geometric rotary positional encoding (GeoRoPE). In addition, it utilizes a hierarchical autoregressive paradigm to predict the next atom-based token, predicting the atom type first and then its 3D coordinates via Diffusion loss. Experimentally, InertialAR achieves state-of-the-art performance on 7 of the 10 evaluation metrics for unconditional molecule generation across QM9, GEOM-Drugs, and B3LYP. Moreover, it significantly outperforms strong baselines in controllable generation for targeted chemical functionality, attaining state-of-the-art results across all 5 metrics.

Department of Ships and Ocean Structures, SINTEF Ocean, Trondheim, Norway Abstract: In this paper, we present a Newton-Euler formulation of the equations of motion for underwater vehicles with an interntal moving mass actuator. Furthermore, the moving mass dynamics are expressed as an extension to the manoeuvring model for underwater vehicles, originally introduced by Fossen (1991). The influence of the moving mass is described in body-frame and included as states in both an additional kinematic equation and as part of the coupled rigid-body kinetics of the underwater vehicle. The Coriolis-centripetal effects are derived from Kirchhoff's equations and the hydrostatics are derived using first principals. The proposed Newton-Euler model is validated through simulation and compared with the traditional Hamiltonian internal moving mass actuator formulation.

Galilean symmetry is the natural symmetry of inertial motion that underpins Newtonian physics. Although rigid-body symmetry is one of the most established and fundamental tools in robotics, there appears to be no comparable treatment of Galilean symmetry for a robotics audience. In this paper, we present a robotics-tailored exposition of Galilean symmetry that leverages the community's familiarity with and understanding of rigid-body transformations and pose representations. Our approach contrasts with common treatments in the physics literature that introduce Galilean symmetry as a stepping stone to Einstein's relativity. A key insight is that the Galilean matrix Lie group can be used to describe two different pose representations, Galilean frames, that use inertial velocity in the state definition, and extended poses, that use coordinate velocity. We provide three examples where applying the Galilean matrix Lie-group algebra to robotics problems is straightforward and yields significant insights: inertial navigation above the rotating Earth, manipulator kinematics, and sensor data fusion under temporal uncertainty. We believe that the time is right for the robotics community to benefit from rediscovering and extending this classical material and applying it to modern problems.

Achieving precise lateral motion modeling and decoupled control in hover remains a significant challenge for tail-sitter Unmanned Aerial Vehicles (UAVs), primarily due to complex aerodynamic couplings and the absence of welldefined lateral dynamics. This paper presents a novel modeling and control strategy that enhances yaw authority and lateral motion by introducing a sideslip force model derived from differential propeller slipstream effects acting on the fuselage under differential thrust. The resulting lateral force along the body y-axis enables yaw-based lateral position control without inducing roll coupling. The control framework employs a YXZ Euler rotation formulation to accurately represent attitude and incorporate gravitational components while directly controlling yaw in the yaxis, thereby improving lateral dynamic behavior and avoiding singularities. The proposed approach is validated through trajectory-tracking simulations conducted in a Unity-based environment. Tests on both rectangular and circular paths in hover mode demonstrate stable performance, with low mean absolute position errors and yaw deviations constrained within 5.688 degrees. These results confirm the effectiveness of the proposed lateral force generation model and provide a foundation for the development of agile, hover-capable tail-sitter UAVs.

The control of robotic systems in complex, shared collaborative workspaces presents significant challenges in achieving robust performance and safety when learning from experienced or simulated data is employed in the pipeline. A primary bottleneck is the reliance on coordinate-dependent models, which leads to profound data inefficiency by failing to generalize physical interactions across different frames of reference. This forces learning algorithms to rediscover fundamental physical principles in every new orientation, artificially inflating the complexity of the learning task. This paper introduces a novel framework that synergizes a coordinate-free, unreduced multibody dynamics and kinematics model based on tensor mechanics with a Data-Assisted Control (DAC) architecture. A non-recursive, closed-form Newton-Euler model in an augmented matrix form is derived that is optimized for tensor-based control design. This structure enables a principled decomposition of the system into a structurally certain, physically grounded part and an uncertain, empirical, and interaction-focused part, mediated by a virtual port variable. Then, a complete, end-to-end tensor-invariant pipeline for modeling, control, and learning is proposed. The coordinate-free control laws for the structurally certain part provide a stable and abstract command interface, proven via Lyapunov analysis. Eventually, the model and closed-loop system are validated through simulations. This work provides a naturally ideal input for data-efficient, frame-invariant learning algorithms, such as equivariant learning, designed to learn the uncertain interaction. The synergy directly addresses the data-inefficiency problem, increases explainability and interpretability, and paves the way for more robust and generalizable robotic control in interactive environments.

This paper presents a novel cascaded observer architecture that combines optical flow and IMU measurements to perform continuous monocular visual-inertial odometry (VIO). The proposed solution estimates body-frame velocity and gravity direction simultaneously by fusing velocity direction information from optical flow measurements with gyro and accelerometer data. This fusion is achieved using a globally exponentially stable Riccati observer, which operates under persistently exciting translational motion conditions. The estimated gravity direction in the body frame is then employed, along with an optional magnetometer measurement, to design a complementary observer on $\mathbf{SO}(3)$ for attitude estimation. The resulting interconnected observer architecture is shown to be almost globally asymptotically stable. To extract the velocity direction from sparse optical flow data, a gradient descent algorithm is developed to solve a constrained minimization problem on the unit sphere. The effectiveness of the proposed algorithms is validated through simulation results.

-- This work demonstrates an airflow inertial based odometry system with multi-sensor data fusion, including thermal anemometer, IMU, ESC, and barometer . This goal is challenging because low-cost IMUs and barometers have significant bias, and anemometer measurements are very susceptible to interference from spinning propellers and ground effects. We employ a GRU-based deep neural network to estimate relative air speed from noisy and disturbed anemometer measurements, and an observer with bias model to fuse the sensor data and thus estimate the state of aerial vehicle. A complete flight data, including takeoff and landing on the ground, shows that the approach is able to decouple the downwash induced wind speed caused by propellers and the ground effect, and accurately estimate the flight speed in a wind-free indoor environment. IMU, and barometer bias are effectively estimated, which significantly reduces the position integration drift, which is only 5.7m for 203s manual random flight. The open source is available on https://github.com/

This work investigates the manufacturing of complex shapes parts with wire arc additive manufacturing (WAAM). In order to guarantee the integrity and quality of each deposited layer that composes the final piece, the deposition process is usually carried out in a flat position. However, for complex geometry parts with non-flat surfaces, this strategy causes unsupported overhangs and staircase effect, which contribute to a poor surface finishing. Generally, the build direction is not constant for every deposited section or layer in complex geometry parts. As a result, there is an additional concern to ensure the build direction is aligned with gravity, thus improving the quality of the final part. This paper proposes an algorithm to control the torch motion with respect to a deposition substrate as well as the torch orientation with respect to an inertial frame. The control scheme is based on task augmentation applied to an extended kinematic chain composed by two robots, which constitutes a coordinated control problem, and allows the deposition trajectory to be planned with respect to the deposition substrate coordinate frame while aligning each layer buildup direction with gravity (or any other direction defined for an inertial frame). Parts with complex geometry aspects have been produced in a WAAM cell composed by two robots (a manipulator with a welding torch and a positioning table holding the workpiece) in order to validate the proposed approach.

This work is motivated by the development of cooperative teams of small, soft underwater robots designed to accomplish complex tasks through collective behavior. These robots take inspiration from biology: salps are gelatinous, jellyfish-like marine animals that utilize jet propulsion for maneuvering and can physically connect to form dynamic chains of arbitrary shape and size. The primary contributions of this research are twofold: first, we adapt a planar nonlinear multi-link snake robot model to model a planar multi-link salp-inspired system by removing joint actuators, introducing link thrusters, and allowing for non-uniform link lengths, masses, and moments of inertia. Second, we conduct a nonlinear observability analysis of the multi-link system with link thrusters, showing that the link angles, angular velocities, masses, and moments of inertia are locally observable when equipped with inertial measurement units and operating under specific thruster conditions. This research provides a theoretical foundation for modeling and estimating both the state and intrinsic parameters of a multi-link system with link thrusters, which are essential for effective controller design and performance.