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Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…

In this paper, we propose an approach to learn stable dynamical systems evolving on Riemannian manifolds. The approach leverages a data-efficient procedure to learn a diffeomorphic transformation that maps simple stable dynamical systems…

Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a…

The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many…

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded…

Modern robotic manipulation primarily relies on visual observations in a 2D color space for skill learning but suffers from poor generalization. In contrast, humans, living in a 3D world, depend more on physical properties-such as distance,…

Spectral submanifolds (SSMs) have recently been shown to provide exact and unique reduced-order models for nonlinear unforced mechanical vibrations. Here we extend these results to periodically or quasiperiodically forced mechanical…

Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. Although direct trajectory optimization is widely applied to solve this problem, inappropriate parameterizations of rigid body dynamics often…

In many robot control problems, factors such as stiffness and damping matrices and manipulability ellipsoids are naturally represented as symmetric positive definite (SPD) matrices, which capture the specific geometric characteristics of…

Diagrammatic Teaching is a paradigm for robots to acquire novel skills, whereby the user provides 2D sketches over images of the scene to shape the robot's motion. In this work, we tackle the problem of teaching a robot to approach a…

Dynamical systems (DSs) provide a framework for high flexibility, robustness, and control reliability and are widely used in motion planning and physical human-robot interaction. The properties of the DS directly determine the robot's…

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to…

In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive…

In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…

Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…

Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…

We introduce a method for constructing reduced-order models directly from videos of dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user-selected part in the video of an autonomous dynamical system. In…

Robots operating in dynamic environments face significant challenges due to the presence of moving agents and displaced objects. Traditional SLAM systems typically assume a static world or treat dynamic as outliers, discarding their…

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…

Continuum robots exhibit high-dimensional, nonlinear dynamics which are often coupled with their actuation mechanism. Spectral submanifold (SSM) reduction has emerged as a leading method for reducing high-dimensional nonlinear dynamical…