提出几何优化方法，让逆最优控制更快更稳。
Gradient based Bilevel for Inverse Optimal Control, a Riemannian approach
- 将逆最优控制重构为流形上的优化问题，利用几何结构提升稳定性。
- 实验显示准确率相当或更好，计算速度提升约4倍。
- 适合机器人与人体运动分析中的高效建模需求。
逆最优控制（IOC）旨在恢复解释观测轨迹的代价函数，使其成为最优控制问题的解。经典方法依赖双层优化，需反复求解嵌套最优控制问题，对实际系统计算成本过高。近期基于投影的方法虽具潜力，但使用梯度法时因违反标准约束资格条件而产生数值不稳定性。本文揭示这些困难源于IOC可行集的几何结构：满足最优性条件的轨迹自然构成一个流形。据此，我们提出黎曼逆最优控制（RIOC）方法，将观测轨迹投影到最优解流形上，通过构造保证可行性。在真实人臂轨迹上的实验表明，该方法在重建精度上达到或优于经典双层方法，同时计算时间减少约四倍。结果表明，几何优化方法可显著提升逆最优控制在机器人学与人体运动分析中的可扩展性与可靠性。
原文摘要 · Abstract (English)
Inverse Optimal Control (IOC) aims to recover the cost function that explains observed trajectories as solutions of an optimal control problem. Classical IOC formulations rely on bilevel optimization, which repeatedly solves a nested optimal control problem and quickly becomes computationally prohibitive for realistic systems. Recent projection-based approaches offer a promising alternative but suffer from numerical instability when solved with gradient-based methods due to violations of standard constraint qualifications. In this paper, we show that these difficulties stem from the geometric structure of the IOC feasible set. We demonstrate that the set of trajectories satisfying the optimality conditions naturally forms a manifold and reformulate IOC as an optimization problem on this manifold. Based on this insight, we propose a Riemannian Inverse Optimal Control (RIOC) method that projects observed trajectories onto the manifold of optimal solutions while preserving feasibility by construction. Experiments on real human arm trajectories show that the proposed method achieves comparable or better reconstruction accuracy than classical bilevel IOC while reducing computation time by about a factor of four. These results highlight the potential of geometric optimization methods to improve the scalability and reliability of IOC for robotics and human motion analysis.
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