Closing the Motion Execution Gap: From Semantic Motion Task Constraints to Kinematic Control

Bridging abstract semantics and precise physical control remains a fundamental challenge in open-world robotic manipulation. While recent data-driven policies show promise, their reliance on isolated contact points or latent affordance embeddings lacks the rigorous kinematic constraints necessary for complex articulated objects.To overcome the limitation, we introduce RelAfford6D, a novel training-free framework centered on a Relational 6D Affordance Graph. Given a free-form instruction, our system deduces a semantic topology linking a primary interacting part to its physical anchor. By elevating these topological nodes into precise metric $SE(3)$ poses via vision foundation models, we analytically formulate downstream execution as a kinematic constraint satisfaction problem. The robot synthesizes continuous trajectories by tracking strictly defined physical manifolds (e.g., revolute or prismatic orbits). Coupled with a closed-loop tracking mechanism for dynamic replanning against disturbances, our physically grounded approach achieves superior zero-shot success rates, cross-category generalization and execution robustness in both simulation and the real world environments, outperforming existing data-driven baselines.

Planning long-horizon manipulation motions using a set of predefined skills is a central challenge in robotics; solving it efficiently could enable general-purpose robots to tackle novel tasks by flexibly composing generic skills. Solutions to this problem lie in an infinitely vast space of parameterized skill sequences -- a space where common incremental methods struggle to find sequences that have non-obvious intermediate steps. Some approaches reason over lower-dimensional, symbolic spaces, which are more tractable to explore but may be brittle and are laborious to construct. In this work, we introduce MOSAIC, a skill-centric, multi-directional planning approach that targets these challenges by reasoning about which skills to employ and where they are most likely to succeed, by utilizing physics simulation to estimate skill execution outcomes. Specifically, MOSAIC employs two complementary skill families: Generators, which identify ``islands of competence'' where skills are demonstrably effective, and Connectors, which link these skill-trajectories by solving boundary value problems. By focusing planning efforts on regions of high competence, MOSAIC efficiently discovers physically-grounded solutions. We demonstrate its efficacy on complex long-horizon problems in both simulation and the real world, using a diverse set of skills including generative diffusion models, motion planning algorithms, and manipulation-specific models. Visit skill-mosaic.github.io for demonstrations and examples.

Generalizable robot manipulation requires not only task-level reasoning over unseen scenes, but also reliable grounding of visual plans into embodiment-specific execution. To bridge this gap, we propose VICX (Video generation and In-Context eXecution), a decoupled closed-loop manipulation framework. In VICX, a frozen video generation model produces vision-language-conditioned high-level visual plans, while a Video-to-Trajectory In-Context Operator Network (V2T-ICON) serves as the task-agnostic interface that grounds these plans into executable robot-state trajectories. To improve execution generalization, V2T-ICON operates on segmentation-extracted arm-only frame observations and uses retrieved image-state pairs as in-context prompts, allowing a robust and generalizable visual-to-state mapping at inference time without parameter updates. Experiments on Meta-World show that VICX supports cross-task generalization, closed-loop self-correction, and cross-embodiment transfer, demonstrating dual generalization across both task semantics and robot execution. The project webpage can be found here: https://scaling-group.github.io/vicx/.