Adaptive Diffusion Constrained Sampling for Bimanual Robot Manipulation

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.

Constrained Gaussian Process Motion Planning via Stein Variational Newton Inference

Gaussian Process Motion Planning (GPMP) is a widely used framework for generating smooth trajectories within a limited compute time--an essential requirement in many robotic applications. However, traditional GPMP approaches often struggle with enforcing hard nonlinear constraints and rely on Maximum a Posteriori (MAP) solutions that disregard the full Bayesian posterior. This limits planning diversity and ultimately hampers decision-making. Recent efforts to integrate Stein Variational Gradient Descent (SVGD) into motion planning have shown promise in handling complex constraints. Nonetheless, these methods still face persistent challenges, such as difficulties in strictly enforcing constraints and inefficiencies when the probabilistic inference problem is poorly conditioned. To address these issues, we propose a novel constrained Stein Variational Gaussian Process Motion Planning (cSGPMP) framework, incorporating a GPMP prior specifically designed for trajectory optimization under hard constraints. Our approach improves the efficiency of particle-based inference while explicitly handling nonlinear constraints. This advancement significantly broadens the applicability of GPMP to motion planning scenarios demanding robust Bayesian inference, strict constraint adherence, and computational efficiency within a limited time. We validate our method on standard benchmarks, achieving an average success rate of 98.57% across 350 planning tasks, significantly outperforming competitive baselines. This demonstrates the ability of our method to discover and use diverse trajectory modes, enhancing flexibility and adaptability in complex environments, and delivering significant improvements over standard baselines without incurring major computational costs.