# ElastiQP：一种用于约束机器人控制的始终可行 QP 求解器

> 原文链接：https://robotics.hellobike.com/papers/2026-09-16-2609-19080
> 频道：papers | 更新日期：2026-09-16 | 标签：arxiv, cs.RO
> 核心摘要：ElastiQP通过带精确逐约束l1惩罚的改进对偶主动集QP求解器，解决约束冲突下控制无解问题，并在机器人控制基准上验证。

# ElastiQP：一种用于约束机器人控制的始终可行 QP 求解器

::: v-pre
> 原文链接：[ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control](https://arxiv.org/abs/2609.19080)（arXiv 2609.19080 · 发布日期：2026-09-16）

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

ElastiQP通过带精确逐约束l1惩罚的改进对偶主动集QP求解器，解决约束冲突下控制无解问题，并在机器人控制基准上验证。

## 核心要点

- 约束增多会提高瞬时冲突概率，传统QP返回不可行会使控制器无可执行解。
- 方法对每个不等式约束施加精确l1惩罚松弛，同时保持等式动力学约束为硬约束。
- 通过解析折叠松弛变量，保持凝聚线性系统规模恒定，实现微秒级性能。
- 在可行问题上匹配或优于现代领先求解器；不可行问题上将违反限制在冲突不等式项并更快返回可用解。

**验证范围与局限**：验证限于一组机器人控制基准，摘要未说明是否包含真机实验。

## 英文摘要 (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.

作者：Daniel Morton, Jon Arrizabalaga, Zachary R. Manchester, Marco Pavone
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## 原始参考来源 (Sources)

- [arXiv 2609.19080：ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control](https://arxiv.org/abs/2609.19080)