Reduced-order models (ROMs) can efficiently simulate high-dimensional physical systems but lack robust uncertainty quantification methods. Existing approaches are frequently architecture- or training-specific, which limits flexibility and generalization. We introduce a post hoc, model-agnostic framework for predictive uncertainty quantification in latent space ROMs that requires no modification to the underlying architecture or training procedure. Using conformal prediction, our approach estimates statistical prediction intervals for multiple components of the ROM pipeline: latent dynamics, reconstruction, and end-to-end predictions. We demonstrate the method on a latent space dynamical model for cloud microphysics, where it accurately predicts the evolution of droplet-size distributions and quantifies uncertainty across the ROM pipeline.

Then the time derivative of z (t) is d dt x d x dt ... d Single phase space trajectories can feed into themselves representing periodic motion. Effectively an additional dimension is added to phase space, which is time. This maintains generality and allows NODEs to be used as a component of a larger model. These are the same equations that were derived by Chen et al. The gradients from the positional part and the velocity part are found separately and added.

The problem of interpolating a rigid body motion is to find a spatial trajectory between a prescribed initial and terminal pose. Two variants of this interpolation problem are addressed. The first is to find a solution that satisfies initial conditions on the k-1 derivatives of the rigid body twist. This is called the kth-order initial value trajectory interpolation problem (k-IV-TIP). The second is to find a solution that satisfies conditions on the rigid body twist and its k-1 derivatives at the initial and terminal pose. This is called the kth-order boundary value trajectory interpolation problem (k-BV-TIP). Solutions to the k-IV-TIP for k=1,...,4, i.e. the initial twist and up to the 4th time derivative are prescribed. Further, a solution to the 1-IV-TBP is presented, i.e. the initial and terminal twist are prescribed. The latter is a novel cubic interpolation between two spatial configurations with given initial and terminal twist. This interpolation is automatically identical to the minimum acceleration curve when the twists are set to zero. The general approach to derive higher-order solutions is presented. Numerical results are shown for two examples.

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 is achieved e.g. if a constant fraction of all samples lies on the point Theorem 3.3 by reformulating lines 190-191 as follows: "Furthermore, consider an infinite data stream of observations ". Making Theorem 3.3 quantitative as suggested by Reviewer #2 Although unbounded, they grow slow enough to allow the proof of Theorem 3.3 such that the main We will add a brief discussion on this in the updated paper. Reviewer #1 pointed out, that Assumption 3.1. Therefore, Assumption 3.1 is valid for our experimental setup. We will include the given reasoning in the updated paper.

Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory control of parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element for this is the computationally efficient evaluation of the second time derivative of the inverse dynamics solution. This has not been presented in the literature, and is addressed in the present paper for the first time. The special topology of PKM is exploited reusing the recursive algorithms for evaluating the inverse dynamics of serial robots. A Lie group formulation is used and all relations are derived within this framework. Numerical results are presented for a 6-DOF Gough-Stewart platform (as part of an exoskeleton), and for a planar PKM when a flatness-based control scheme is applied.

Derivatives of equations of motion(EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.