{"ID":2853977,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21773","arxiv_id":"2510.21773","title":"Real-Time QP Solvers: A Concise Review and Practical Guide Towards Legged Robots","abstract":"Quadratic programming (QP) underpins real-time robotics by enabling efficient, constrained optimization in state estimation, motion planning, and control. In legged locomotion and manipulation, essential modules like inverse dynamics, Model Predictive Control (MPC), and Whole-Body Control (WBC) are inherently QP-based, demanding reliable solutions amid tight timing, energy, and computational resources on embedded platforms. This paper presents a comprehensive analysis and benchmarking study of QP solvers for legged robotics. We begin by formulating the standard convex QP and classify solvers into principal algorithmic approaches: interior-point methods, active-set strategies, operator-splitting schemes, and augmented Lagrangian/proximal approaches, while also discussing solver code generation for fixed-structure QPs. Each solver is examined in terms of algorithmic structure, computational characteristics, and its ability to exploit problem structure and warm-starting. Performance is reviewed using publicly available benchmarks, with a focus on metrics such as computation time, constraint satisfaction, and robustness under perturbations. Unified comparison tables yield practical guidance for solver selection, underscoring trade-offs in speed, accuracy, and energy efficiency. Our findings emphasize the synergy between solvers, tasks, and hardware -- e.g., sparse structured IPMs for long-horizon MPC and dense active-set for high-frequency WBC to advance agile, autonomous legged systems, with emerging trends toward ill-conditioned, conic, and code-generated deployments.","short_abstract":"Quadratic programming (QP) underpins real-time robotics by enabling efficient, constrained optimization in state estimation, motion planning, and control. In legged locomotion and manipulation, essential modules like inverse dynamics, Model Predictive Control (MPC), and Whole-Body Control (WBC) are inherently QP-based,...","url_abs":"https://arxiv.org/abs/2510.21773","url_pdf":"https://arxiv.org/pdf/2510.21773v2","authors":"[\"Van Nam Dinh\"]","published":"2025-10-17T08:30:11Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}