Andrea Patrizi | Searcharxiv

arXiv2026

ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI

We introduce ODYN, a novel all-shifted primal-dual non-interior-point quadratic programming (QP) solver designed to efficiently handle challenging dense and sparse QPs. ODYN combines all-shifted nonlinear complementarity problem (NCP) functions with proximal method of multipliers to robustly address ill-conditioned and degenerate problems, without requiring linear independence of the constraints. It exhibits strong warm-start performance and is well suited to both general-purpose optimization, and robotics and AI applications, including model-based control, estimation, and kernel-based learning methods. We provide an open-source implementation and benchmark ODYN on the Maros-Mészáros test set, demonstrating state-of-the-art convergence performance in small-to-high-scale problems. The results highlight ODYN's superior warm-starting capabilities, which are critical in sequential and real-time settings common in robotics and AI. These advantages are further demonstrated by deploying ODYN as the backend of an SQP-based predictive control framework (OdynSQP), as the implicitly differentiable optimization layer for deep learning (ODYNLayer), and the optimizer of a contact-dynamics simulation (ODYNSim).

cs.RO↗

arXiv2026

RL-Augmented MPC for Non-Gaited Legged and Hybrid Locomotion

We propose a contact-explicit hierarchical architecture coupling Reinforcement Learning (RL) and Model Predictive Control (MPC), where a high-level RL agent provides gait and navigation commands to a low-level locomotion MPC. This offloads the combinatorial burden of contact timing from the MPC by learning acyclic gaits through trial and error in simulation. We show that only a minimal set of rewards and limited tuning are required to obtain effective policies. We validate the architecture in simulation across robotic platforms spanning 50 kg to 120 kg and different MPC implementations, observing the emergence of acyclic gaits and timing adaptations in flat-terrain legged and hybrid locomotion, and further demonstrating extensibility to non-flat terrains. Across all platforms, we achieve zero-shot sim-to-sim transfer without domain randomization, and we further demonstrate zero-shot sim-to-real transfer without domain randomization on Centauro, our 120 kg wheeled-legged humanoid robot. We make our software framework and evaluation results publicly available at https://github.com/AndrePatri/AugMPC.

cs.RO↗