# DAOCP：用于最优控制问题的对偶主动集求解器

> 原文链接：https://robotics.hellobike.com/papers/2026-09-27-2609-33451
> 频道：papers | 更新日期：2026-09-27 | 标签：arxiv, cs.RO
> 核心摘要：DAOCP面向带逐阶段等式与不等式约束的线性二次最优控制，结合对偶主动集与结构递归计算，并在机器人基准上验证加速。

# DAOCP：用于最优控制问题的对偶主动集求解器

::: v-pre
> 原文链接：[DAOCP: a dual active set solver for optimal control problems](https://arxiv.org/abs/2609.33451)（arXiv 2609.33451 · 发布日期：2026-09-27）

**DAOCP: a dual active set solver for optimal control problems**

DAOCP面向带逐阶段等式与不等式约束的线性二次最优控制，结合对偶主动集与结构递归计算，并在机器人基准上验证加速。

## 核心要点

- 动机是现有主动集MPC求解器多处理稠密QP，难以利用典型最优控制问题结构。
- 方法将主动集的热启动能力与结构利用求解器的计算扩展性结合，推广Riccati递归与Cholesky分解关系。
- 该关系使对偶主动集迭代可直接在原始最优控制问题上递归计算，无需显式形成凝聚QP。
- 机器人基准中DAOCP在五个场景的四个最快；在58状态Atlas模型上平均求解时间较DAQP和HPIPM缩短9倍。

**验证范围与局限**：验证范围为摘要所述机器人基准五个场景，包括58状态Atlas模型。

## 英文摘要 (Abstract)

We present DAOCP, a dual active set solver for linear quadratic optimal control problems with stage-wise equality and inequality constraints. Active set methods are leading Model Predictive Control benchmarks for full-body robotics, but existing solvers operate on dense QPs, while typical problem dimensions favor methods that exploit the optimal control structure. DAOCP combines the warm-starting capabilities of active set algorithms with the better computational scaling of structure exploiting solvers, by relying on a generalization of the relationship between the Riccati recursion and the Cholesky factorization of the condensed Hessian. This result enables dual active set iterations to operate directly on the original optimal control problem through recursive computations, without explicitly forming the condensed quadratic program. On robotics benchmarks, DAOCP is the fastest of four solvers in four of five scenarios, cutting average solve time on a 58-state Atlas model by 9$\times$ relative to state of the art solvers DAQP and HPIPM.

作者：Alberto Zaupa, Samuel Erickson, Mikael Johansson
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## 原始参考来源 (Sources)

- [arXiv 2609.33451：DAOCP: a dual active set solver for optimal control problems](https://arxiv.org/abs/2609.33451)