Universität Ulm

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arXiv Nov 5, 2026
Neural reachability now errs on the safe side: ConDR pushes the learned value below the true one and gives the lowest closed-loop collision rates
DeepReach replaces the grid in Hamilton–Jacobi reachability with a neural value function but penalizes both sides of the residual equally, so the learned value can sit above the true one and unsafe states get labeled safe. ConDR instead trains toward a subsolution of the HJI variational inequality: the obstacle branch and terminal condition hold by construction, a one-sided loss pushes the differential residual below a safety margin, and a complementarity term blocks the degenerate all-unsafe solution. On Air3D, Air6D, a 9D multi-vehicle system and a 13D quadrotor, ConDR reports the lowest false-negative rate and the lowest closed-loop collision rates, with at most a small rise in intervention.
DeepReach replaces the grid in Hamilton–Jacobi reachability with a neural value function but penalizes both sides of the residual equally, so the learned value can sit above the true one and unsafe states get labeled safe. ConDR instead trains toward a subsolution of the HJI variational inequality: the obstacle branch and terminal condition hold by construction, a one-sided loss pushes the differential residual below a safety margin, and a complementarity term blocks the degenerate all-unsafe solution. On Air3D, Air6D, a 9D multi-vehicle system and a 13D quadrotor, ConDR reports the lowest false-negative rate and the lowest closed-loop collision rates, with at most a small rise in intervention.
Vanderbilt University Universität Ulm
Kendra Givens（First author）
ConDR Hamilton-Jacobi Reachability Safety-Critical Control
arXiv Sep 27, 2026
TUM team surveys 329 works on physics-embedded robot learning: 71% encode physics in architectures, only 4% combine multiple embedding routes
This survey systematically reviews methods that embed physics priors into robot learning and proposes a unified taxonomy classifying existing work by where physics is embedded—physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training losses—then reviews methods for robot dynamics learning, trajectory planning and prediction, control, and estimation together with the open-source software ecosystem, reporting that physics-encoded architectures account for 71% of surveyed methods, physics-guided 16%, and physics-informed 13%, while only 4% combine more than one embedding route.
This survey systematically reviews methods that embed physics priors into robot learning and proposes a unified taxonomy classifying existing work by where physics is embedded—physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training losses—then reviews methods for robot dynamics learning, trajectory planning and prediction, control, and estimation together with the open-source software ecosystem, reporting that physics-encoded architectures account for 71% of surveyed methods, physics-guided 16%, and physics-informed 13%, while only 4% combine more than one embedding route.
Technical University of Munich Universität Ulm Technische Hochschule Ulm Technische Universität Darmstadt University of Trento
Mattia Piccinini（First author）
Diffusion Model Trajectory Tracking Control Variational Autoencoder Physics-Informed Neural Network Robot Manipulation

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Neural reachability now errs on the safe side: ConDR pushes the learned value below the true one and gives the lowest closed-loop collision rates

TUM team surveys 329 works on physics-embedded robot learning: 71% encode physics in architectures, only 4% combine multiple embedding routes