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 this https URL.

Robotics (cs.RO); Optimization and Control (math.OC)

arXiv:2609.19080 [cs.RO]

(or arXiv:2609.19080v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.19080 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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