GPU上でバッチ処理・微分可能なQPソルバーcuPIQP
CuPIQP: A Batched and Differentiable QP Solver on GPUs for Robot Learning and Control
近接内点法に基づき、密・疎・多段階のQPを統一的に扱うGPU向けバッチ型微分可能QPソルバーを提案し、大規模ロボット学習での高速化を実現した。
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著者: Fenglong Song, Roland Schwan, Yuwen Chen, Yuning Jiang, Colin N. Jones
分類: math.OC, cs.RO
原文アブストラクト
Quadratic programs (QPs) are fundamental building blocks of many robotic tasks such as inverse kinematics, whole-body control, and model predictive control. Extending these methods to large-scale robot learning and control requires solving many QPs concurrently and, for end-to-end learning, differentiating through their solutions. Efficient batched optimization is therefore essential to bringing established model-based methods into GPU-based robotics pipelines. We present \textsc{cuPIQP}, a batched and differentiable QP solver on GPUs based on a proximal interior-point method, with unified support for dense, sparse, and multistage problems. The solver exploits parallelism across independent QPs and their internal structure while preserving per-problem numerical updates and termination decisions. Benchmarks with up to 16384 QPs per batch demonstrate solve-time speedups of up to $18.8\times$ over \textsc{Moreau} and $4.26\times$ over eight-core \textsc{PIQP}. In an end-to-end learning task, \textsc{cuPIQP} accelerates training by $4.6\times$ over \textsc{QPAX} and $7.8\times$ over \textsc{Moreau}. By reducing the computational cost, \textsc{cuPIQP} provides efficient, reusable infrastructure for integrating model-based optimization into large-scale robot learning and control.