Odyn and ELASTIC ODYN: Non-Interior-Point Optimization for Robotics and AI

Modern robotics and AI systems rely heavily on quadratic programming (QP) to power model predictive control, trajectory optimization, contact simulation, and differentiable learning. However, in real-world applications such as robotic legged locomotion, QP subproblems are frequently ill-conditioned, warm-started, or even infeasible due to conflicting tasks, contact degeneracies, or modeling errors. In such regimes, classical interior-point and active-set solvers can become unstable or fail to recover feasibility. In this talk, I present Odyn, a non-interior-point QP solver designed for robustness in challenging real-time settings. Odyn exhibits strong warm-start performance and serves as the backend of an SQP-based trajectory optimization framework for highly constrained robotic systems. I then introduce ELASTIC ODYN, which explicitly handles infeasible QPs through smooth elastic relaxations, enabling stable restoration phases within SQP and reliable gradient propagation in differentiable optimization layers. Together, these methods provide a unified, warm-start-friendly, and differentiable optimization framework that bridges augmented Lagrangian and interior-point methods, enabling robust trajectory optimization, contact simulation, model predictive control, and learning in challenging real-world scenarios.