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Arne Sachtler
TITLE: Riding the Dynamics: Geometric Motion Structures for Control of a Weakly Actuated Robot
ABSTRACT: What can a robot do when its motors can barely hold a few percent of its own gravity torque? Quite a lot, if control exploits the dynamics instead of fighting them. This talk centers on what we call natural motion manifolds: two-dimensional invariant submanifolds of the state space, swept out by continuous, energy-parametrized families of periodic orbits. We first show why conservative mechanical structure makes such families the rule rather than the exception, how nonlinear normal modes arise as a special case, and how the families terminate or bifurcate at equilibria, homoclinic orbits, folds, and branch points. We then turn this geometry into control: on a two-degree-of-freedom robot with severely limited torque, a controller combining manifold stabilization with limit-aware energy injection excites swing-up, oscillation, and acrobatic maneuvers that would be unreachable by tracking physically uninformed reference trajectories. We close with open questions on identifying and representing these physics-given structures with learning-based methods.
Jake Welde
TITLE: Symmetry and Beyond: Efficient, Generalizable Learning for Low-Level Control of Aerial and Space Robots
ABSTRACT: To perform useful, interactive work, aerial and space robots must evolve beyond simple, single-body designs (e.g., quadrotors) towards high-dimensional, articulated morphologies. However, explicit analytical controllers for such systems are not easily crafted, and numerical optimal control algorithms quickly overwhelm the lightweight processors available onboard. Reinforcement learning frontloads these burdens to offline training, typically employing vast computational resources to run brittle training pipelines fine-tuned to particular tasks. To mitigate these downsides, we exploit the natural symmetries of robotic systems to efficiently learn high-performance, generalizable policies for low-level robot control. In particular, we develop a theory of symmetry reduction for tracking control problems, proving that a tracking controller trained in a reduced setting will perform equally well on the original system while also generalizing automatically to unseen trajectories. However, the classical notion of symmetry is too rigid to apply to many practical systems, which may enjoy only a very small symmetry group. We thus propose a relaxed notion of symmetry (termed “weak invariance”) that balances structure with generality, enabling us to factor out a much larger symmetry group while still attaining the same performance guarantees, greatly expanding the applicability and impact of these methods.
Rodrigo Pérez-Dattari
KTH Royal Institute of Technology
TITLE: Robot Learning with Dynamical Systems Priors
ABSTRACT: Dynamical systems have been used for decades to embed structure into learning models. By combining ideas from control theory, physics, and differential geometry, they provide a principled framework for designing inductive biases in robot policy learning, with the potential to improve generalization, safety, and data efficiency. In this talk, we will discuss recent methods that bring these ideas into the deep learning and generative modeling era. In particular, we will explore how modern tools such as flow matching can be combined with dynamical systems principles to obtain robot policies that are not only expressive, but also structured and reliable, making them better suited for deployment in real-world robotic systems.
Thomas Cohn
Massachusetts Institute of Technology
TITLE: Motion Planning in Minimal Coordinates for Kinematically-Constrained Systems
ABSTRACT: Motion planning algorithms often model a robot's configuration space as a Euclidean space. But this simple model breaks down when the robot must respect certain equality constraints, like carrying an object with two hands or keeping both feet fixed on the ground. We propose charting the manifold of feasible configurations, eliminating the nonlinear equality constraints. Analytic IK is used to construct the chart, ensuring speed and well-definedness, and differentiating through the mapping enables gradient-based optimization. This intrinsic formulation makes it easier for optimizers to find feasible solutions for challenging robotic planning problems.
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