ElastiQP：用于约束机器人控制的始终可行的QP求解器
ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control
浏览论文内容
中文总结 AI 辅助
针对约束机器人控制中QP求解器因约束冲突而不可行的问题，提出ElastiQP，一种通过逐约束l1松弛和解析折叠松弛变量保持系统规模恒定的对偶有效集求解器，实现微秒级性能，并在不可行时快速返回可用解。
中文摘要 AI 辅助
随着机器人能力的提升，基于二次规划（QP）的控制器必须考虑数量同样增加的约束，以确保安全、可靠的操作。然而，每增加一个约束，就会引入更多瞬时冲突的可能性：在这种情况下，返回“不可行”状态的QP求解器会让控制器无指令可执行。为解决此问题，我们提出了ElastiQP，一种改进的对偶有效集QP求解器，它通过精确的、逐约束的l1惩罚来松弛每个不等式约束，同时保持等式约束（动力学）为硬约束。值得注意的是，ElastiQP通过将松弛变量解析地折叠进求解器中，保持压缩线性系统的规模恒定。在一组机器人控制基准测试中，ElastiQP实现了微秒级性能，在可行问题上与领先的现代求解器相当或更优。在不可行问题上，ElastiQP能优雅地处理，将违反限制在严格冲突的不等式项上，返回可用解的速度比最佳替代求解器快达40倍。ElastiQP作为开源C++头文件库提供，并带有Python和JAX接口，可在https URL获取。
英文摘要
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.
发表机构
- Stanford University（斯坦福大学）
- Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。
