{"ID":22952782,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19080","arxiv_id":"2609.19080","title":"ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control","abstract":"As robot capabilities increase, quadratic programming (QP)-based controllers must account for a similarly increasing number of constraints to ensure safe, reliable operation. Yet, with each added constraint, this introduces more chances of momentary conflict: in which case, a QP solver that returns an \"infeasible\" status leaves the controller with nothing to execute. To address this, we introduce ElastiQP, a modified dual active-set QP solver that relaxes every inequality constraint with an exact, per-constraint l1 penalty while keeping equality constraints (dynamics) hard. Notably, ElastiQP does so by folding the slack variables into the solver analytically, maintaining a constant size of the condensed linear system. On a suite of robot control benchmarks, ElastiQP achieves microsecond-level performance, matching or outperforming leading modern solvers on feasible problems. On infeasible problems, ElastiQP handles these gracefully, confining violations to strictly the conflicting inequality terms, returning a usable solution up to 40x faster than the best alternative solvers. ElastiQP is available as an open-source C++ header-only library, with Python and JAX interfaces, at https://github.com/StanfordASL/elastiqp.","short_abstract":"As robot capabilities increase, quadratic programming (QP)-based controllers must account for a similarly increasing number of constraints to ensure safe, reliable operation. Yet, with each added constraint, this introduces more chances of momentary conflict: in which case, a QP solver that returns an \"infeasible\" stat...","url_abs":"https://arxiv.org/abs/2609.19080","url_pdf":"https://arxiv.org/pdf/2609.19080v1","authors":"[\"Daniel Morton\",\"Jon Arrizabalaga\",\"Zachary Manchester\",\"Marco Pavone\"]","published":"2026-09-16T17:22:09Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"math.OC\"]","methods":"[]","has_code":false,"code_links":[{"ID":639780,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-17T02:12:05.498442134Z","DeletedAt":null,"paper_id":22952782,"paper_url":"https://arxiv.org/abs/2609.19080","paper_title":"ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control","repo_url":"https://github.com/StanfordASL/elastiqp","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}