ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control

2026-09-16

AI Summary

为解决机器人控制中QP求解器因约束冲突导致的不可行问题，提出ElastiQP算法，通过引入l1惩罚项并保持线性系统规模不变，确保快速获得可行解。

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.

Problem

• Quadratic Programming
• Robot Control
• Constraints
• Infeasibility
• Safety

Innovation

• QP Solver
• Constraint Relaxation
• l1 Penalty
• Dual Active-Set Method
• Feasibility Guarantee