发表机构
School of Aerospace Engineering, Georgia Institute of Technology; College of Science and Engineering, University of Minnesota; School of Engineering and Applied Sciences, Harvard University（佐治亚理工学院航空航天工程学院; 明尼苏达大学科学与工程学院; 哈佛大学工程与应用科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过薛定谔桥采样重新审视轨迹优化，提出伴随薛定谔桥采样器（ASBS）处理硬约束下的吉布斯采样，实验验证了其在接触丰富任务中的有效性。
AI 中文摘要
我们重新审视了有限时域轨迹优化与薛定谔桥采样之间的关系。从推断的角度看，KL正则化的轨迹优化问题可以通过从吉布斯-玻尔兹曼分布中采样来求解，该分布的能量即轨迹代价，而伴随薛定谔桥采样器（ASBS）是一种无模拟的扩散采样器，专为这种非归一化目标设计。相比之下，硬性等式路径约束和终端约束将可行决策变量限制在一个零测度可行流形上，目标函数必须在该流形上内蕴地重新定义。具体而言：（a）我们分析了两种互补的参数化方法：滚动参数化，其中动力学被消除，仅剩余约束塑造流形；以及双射击参数化，其中状态和控制被联合采样，动力学本身成为流形的一部分；（b）我们建立了正则性条件，在这些条件下两个可行集都是光滑嵌入流形；（c）在紧致性和路径连通性假设下，我们通过黎曼ASBS从所得的内蕴吉布斯测度中采样，并通过指数松弛变量处理严格不等式。实验，包括接触丰富的运动和操作任务，证明了两种机制的有效性。
英文摘要
We take a new look at the relation between finite-horizon trajectory optimization and Schrödinger bridge sampling. Viewed as inference, KL-regularized trajectory optimization is solved by sampling from a Gibbs--Boltzmann distribution whose energy is the trajectory cost, and the adjoint Schrödinger bridge sampler (ASBS) is a simulation-free diffusion sampler designed for exactly such unnormalized targets. Hard equality path and terminal constraints, by contrast, confine the admissible decision variables to a measure-zero feasibility manifold, on which the target must be redefined intrinsically. In particular: $(a)$ we analyze two complementary parametrizations; a rollout parametrization, in which the dynamics are eliminated and only the remaining constraints shape the manifold, and a double-shooting parametrization, in which states and controls are sampled jointly and the dynamics themselves become part of the manifold; $(b)$ we establish regularity conditions under which both admissible sets are smooth embedded manifolds; $(c)$ under compactness and path-connectedness assumptions, we sample from the resulting intrinsic Gibbs measures via Riemannian ASBS, treating strict inequalities through exponential slack variables. Experiments, including contact-rich locomotion and manipulation, demonstrate the effectiveness of both regimes.
