Virtues of Ordered Chaos: Planning with Topple Actions in Tabletop Stack Rearrangement

Rearranging densely packed tabletop objects is challenging when parallel-gripper picks are infeasible without sufficient clearance around an object. This work studies the problem characteristics for practically motivated settings with uniformly sized blocks placed at planar tabletop grid locations. Since purely prehensile removal can become infeasible, a directional knock primitive is therefore introduced and the optimal knock-pick variant of the problem is formulated. The work proposes a series of abstractions wherein minimal constraining gadgets are covered to identify the necessary knocks. Utilizing a maximum-weight perfect matching on a graphical abstraction yields efficient polynomial-time computation of the optimal plan that minimizes the number of actions. Experiments are reported for increasing grid sizes in synthetic settings as well as in IsaacSim. The theoretical observations provide a promising stepping stone towards rigorously building efficient manipulation strategies that interleave prehensile and non-prehensile actions.

To perform complex manipulation planning, autonomous robots are required to abstract continuous, high-dimensional sensorimotor interactions into discrete object and action representations. Earlier work either categorized objects based on visual appearances, which fails to distinguish objects that appear similar but behave differently, or based on effects under interaction, but was limited to predefined actions. To address these limitations, we propose a model that jointly discovers high-level manipulation primitives and object categories through a binary bottleneck layer, trained to predict multi-modal outcomes, including object motion, contact, and force feedback, from random interaction data. Building on these discovered binary representations, we leverage a discrete planning method that uses intermediate steps in the predicted effect trajectory to enable partial action executions for precise low-level control. Additionally, we evaluate our framework's generalization capabilities on novel objects by assigning object categories through comparing a small number of interaction effects with the predicted effects of learned object symbols, enabling few-shot generalization based on behavior rather than visual similarity. We conduct experiments on tabletop repositioning and stacking tasks, and confirm that our effect-driven planning approach outperforms both a state-of-the-art method and a visual-based alternative in planning precision across seen and novel objects.

Open-ended tabletop manipulation requires agents to not only understand natural language but also adapt to dynamic environments and execution failures. We present ACE (Agentic Control for Embodied Manipulation), a zero-shot workflow reasoning framework for tabletop pick-and-place from natural language. Rather than relying on direct low-level action mapping, ACE combines agentic workflow reasoning with two robot-facing executable skills: a visual grounding interface and a reusable pick-and-place primitive. To bridge semantic reasoning and physical control, the active sub-goal is grounded into a mask-mediated vision-action interface. This unified mask specifies the target object and destination, is tracked over time, exposed for human verification, and ultimately passed to a task-agnostic downstream policy for execution. Crucially, ACE operates in a closed loop supported by a multi-timescale memory. After an action is executed, the system automatically verifies whether the intended sub-goal succeeded, using the outcome to advance, retry, repair, or replan. This enables online adaptation to user corrections, scene changes, and physical failures. We evaluate ACE on logically complex, long-horizon tasks, including zero-shot multi-step equation formation with number cubes and constraint-based object retrieval. ACE demonstrates task-level zero-shot generalization on novel semantic constraints and randomized tabletop scenes without task-specific retraining. Specifically, while standard end-to-end baselines struggle to complete these logically demanding tasks, ACE achieves a 50% success rate in equation formation and a 70% success rate in constraint retrieval. This contrast demonstrates that explicit workflow reasoning and mask-mediated control offer a robust, practical route toward adaptable robotic manipulation.