DAOCP：一种用于最优控制问题的对偶有效集求解器
DAOCP: a dual active set solver for optimal control problems
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中文总结 AI 辅助
DAOCP是一种对偶有效集求解器，通过推广Riccati递归与Cholesky分解的关系，直接处理线性二次最优控制问题，在机器人基准上较现有求解器提速9倍。
中文摘要 AI 辅助
我们提出了DAOCP，一种用于具有逐阶段等式和不等式约束的线性二次最优控制问题的对偶有效集求解器。有效集方法是全身机器人学中领先的模型预测控制基准，但现有求解器处理稠密二次规划（QP），而典型的问题维度更倾向于利用最优控制结构的求解器。DAOCP结合了有效集算法的热启动能力与利用结构的求解器更好的计算扩展性，其基础是Riccati递归与压缩Hessian的Cholesky分解之间关系的推广。这一结果使得对偶有效集迭代能够通过递归计算直接作用于原始最优控制问题，而无需显式构造压缩二次规划。在机器人学基准测试中，DAOCP在五个场景中的四个场景中成为四个求解器中速度最快的，相对于最先进的求解器DAQP和HPIPM，在58状态Atlas模型上将平均求解时间缩短了9倍。
英文摘要
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.
发表机构
- KTH Royal Institute of Technology（皇家理工学院）
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