Robotics: Science and Systems XVIII 2022
DOI: 10.15607/rss.2022.xviii.040
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PROX-QP: Yet another Quadratic Programming Solver for Robotics and beyond

Abstract: Quadratic programming (QP) has become a core modelling component in the modern engineering toolkit. This is particularly true for simulation, planning and control in robotics. Yet, modern numerical solvers have not reached the level of efficiency and reliability required in practical applications where speed, robustness, and accuracy are all necessary. In this work, we introduce a few variations of the well-established augmented Lagrangian method, specifically for solving QPs, which include heuristics for impr… Show more

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Cited by 31 publications
(7 citation statements)
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“…This penalty method is similar in spirit to the proximal term [29] that helps improve the conditioning of the KKT system. The benefit of adding the terminal cost to the algorithm performance will be demonstrated in the result section.…”
Section: Modified Backward Sweep Using a Penalty Methodsmentioning
confidence: 99%
“…This penalty method is similar in spirit to the proximal term [29] that helps improve the conditioning of the KKT system. The benefit of adding the terminal cost to the algorithm performance will be demonstrated in the result section.…”
Section: Modified Backward Sweep Using a Penalty Methodsmentioning
confidence: 99%
“…In Sec. IV-C, we benchmark GJK and our proposed accelerated gradients against the state-of-the-art quadratic programming solver ProxQP [50]. We show that GJK and our proposed accelerated variants vastly outperform generic quadratic programming (QP) solvers, making these QP solvers prohibitive for collision detection.…”
Section: B Acceleration Of Collision Detection and Distance Computationmentioning
confidence: 99%
“…As explained in Sec. II, in the case of two convex meshes, the collision problem can be formulated as a Quadratic Program (2) (QP), which can be solved using any generic QP solver [50], [53]- [56]. In Table II, we compare the performance of GJK and our proposed accelerations against the state-of-the-art ProxQP solver [50].…”
Section: Gjk-like Algorithms Vs Generic Quadratic Programming Solversmentioning
confidence: 99%
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“…By rolling out each iterative step of the optimization solver, the framework can backpropagate through the entire sequence, enabling direct training of these modules (Donti, Rolnick, and Kolter 2020). However, the rollingout solvers might not converge or take a very long time to converge, which can lead to suboptimal solutions and impact the overall performance of the system (Bambade et al 2023). Moreover, some methods based on alternating direction method of multipliers (ADMM) involve Hessian matrix computations, which can be computationally expensive, to recover gradients (Sun et al 2022).…”
Section: Introductionmentioning
confidence: 99%