Coordinated multi-arm manipulation requires satisfying multiple simultaneous geometric constraints across high-dimensional configuration spaces, which poses a significant challenge for traditional planning and control methods. In this work, we propose Adaptive Diffusion Constrained Sampling (ADCS), a generative framework that flexibly integrates both equality (e.g., relative and absolute pose constraints) and structured inequality constraints (e.g., proximity to object surfaces) into an energy-based diffusion model. Equality constraints are modeled using dedicated energy networks trained on pose differences in Lie algebra space, while inequality constraints are represented via Signed Distance Functions (SDFs) and encoded into learned constraint embeddings, allowing the model to reason about complex spatial regions. A key innovation of our method is a Transformer-based architecture that learns to weight constraint-specific energy functions at inference time, enabling flexible and context-aware constraint integration. Moreover, we adopt a two-phase sampling strategy that improves precision and sample diversity by combining Langevin dynamics with resampling and density-aware re-weighting. Experimental results on dual-arm manipulation tasks show that ADCS significantly improves sample diversity and generalization across settings demanding precise coordination and adaptive constraint handling.

翻译：协调的多臂操作需要满足高维构型空间中多个同时存在的几何约束，这对传统规划与控制方法构成了重大挑战。本研究提出自适应扩散约束采样（ADCS），一种生成式框架，能够灵活地将等式约束（如相对与绝对位姿约束）和结构化不等式约束（如接近物体表面）整合到基于能量的扩散模型中。等式约束通过训练于李代数空间位姿差的专用能量网络进行建模，而不等式约束则通过符号距离函数表示并编码到学习的约束嵌入中，使模型能够推理复杂的空间区域。我们方法的一个关键创新是采用基于Transformer的架构，该架构学习在推理时对特定约束的能量函数进行加权，从而实现灵活且上下文感知的约束集成。此外，我们采用两阶段采样策略，通过将朗之万动力学与重采样及密度感知重加权相结合，提高了采样精度与多样性。在双臂操作任务上的实验结果表明，ADCS在需要精确协调和自适应约束处理的各种场景中，显著提升了样本多样性和泛化能力。