提出新算法解决非线性随机控制中的安全约束问题，提升求解可行性与效果。
Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control
- 采用算子分裂将复杂问题拆解为可并行求解的子问题
- 在严格安全约束下仍能获得比传统方法更优的解
- 已在多种机器人场景和硬件上验证有效性
本文提出一种新算法，用于解决具有非线性动态和机会约束的分布引导问题。协方差引导（Covariance Steering, CS）是随机最优控制中的一种新兴方法，通过约束状态分布的一阶和二阶矩来降低问题复杂度，相比全分布控制更具可处理性。然而，现有求解非线性CS问题的方法（如顺序凸规划，SCP）常因约束过多而产生不可行或劣解。为此，本文提出算子分裂协方差引导方法，暂时解耦完整问题为可并行求解的子问题。该松弛策略不要求中间迭代满足所有约束，增强了探索能力，在非凸环境下显著提升可行性。多种机器人应用场景的仿真结果表明，所提方法在更严格的安全部分约束下仍能获得更优解。最后，通过硬件实测验证了该框架在真实系统中的适用性。
原文摘要 · Abstract (English)
This paper presents a novel algorithm for solving distribution steering problems featuring nonlinear dynamics and chance constraints. Covariance steering (CS) is an emerging methodology in stochastic optimal control that poses constraints on the first two moments of the state distribution -- thereby being more tractable than full distributional control. Nevertheless, a significant limitation of current approaches for solving nonlinear CS problems, such as sequential convex programming (SCP), is that they often generate infeasible or poor results due to the large number of constraints. In this paper, we address these challenges, by proposing an operator splitting CS approach that temporarily decouples the full problem into subproblems that can be solved in parallel. This relaxation does not require intermediate iterates to satisfy all constraints simultaneously prior to convergence, which enhances exploration and improves feasibility in such non-convex settings. Simulation results across a variety of robotics applications verify the ability of the proposed method to find better solutions even under stricter safety constraints than standard SCP. Finally, the applicability of our framework on real systems is also confirmed through hardware demonstrations
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