Monte-Carlo planning, as exemplified by Monte-Carlo Tree Search (MCTS), has demonstrated remarkable performance in applications with finite spaces. In this paper, we consider Monte-Carlo planning in an environment with continuous state-action spaces, a much less understood problem with important applications in control and robotics.

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In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial robot, this configuration space is $SE(3)=\mathbb{R}^3\times SO(3)$. The subdivision of $\mathbb{R}^3$ is standard but so far, there are no global subdivision schemes for $SO(3)$. We recently introduced a representation for $SO(3)$ suitable for subdivision. This paper investigates the distortion of the natural metric on $SO(3)$ caused by our representation. The proper framework for this study lies in the Riemannian geometry of $SO(3)$, enabling us to obtain sharp distortion bounds.

Multi-Agent Pathfinding is used in areas including multi-robot formations, warehouse logistics, and intelligent vehicles. However, many environments are incomplete or frequently change, making it difficult for standard centralized planning or pure reinforcement learning to maintain both global solution quality and local flexibility. This paper introduces a hybrid framework that integrates D* Lite global search with multi-agent reinforcement learning, using a switching mechanism and a freeze-prevention strategy to handle dynamic conditions and crowded settings. We evaluate the framework in the discrete POGEMA environment and compare it with baseline methods. Experimental outcomes indicate that the proposed framework substantially improves success rate, collision rate, and path efficiency. The model is further tested on the EyeSim platform, where it maintains feasible Pathfinding under frequent changes and large-scale robot deployments.

--Precisely grasping an object is a challenging task due to pose uncertainties. Conventional methods have used cameras and fixtures to reduce object uncertainty. They are effective but require intensive preparation, such as designing jigs based on the object geometry and calibrating cameras with high-precision tools fabricated using lasers. In this study, we propose a method to reduce the uncertainty of the position and orientation of a grasped object without using a fixture or a camera. Our method is based on the concepts that the flat finger pads of a parallel gripper can reduce uncertainty along its opening/closing direction through flat surface contact. Three orthogonal grasps by parallel grippers with flat finger pads collectively constrain an object's position and orientation to a unique state. Guided by the concepts, we develop a regrasp planning and admittance control approach that sequentially finds and leverages three orthogonal grasps of two robotic arms to eliminate uncertainties in the object pose. We evaluated the proposed method on different initial object uncertainties and verified that the method have satisfactory repeatability accuracy. It outperforms an AR marker detection method implemented using cameras and laser jet printers under standard laboratory conditions. Significant challenge in robotic manipulation lies in addressing the uncertainties associated with object grasping. The uncertainties often arise from errors in environmental registration, inaccuracies in object pose recognition, and unbalanced contact during grasping that leads to pose deviations. The uncertainties can result in discrepancies between the actual and expected pose of objects or tools, potentially causing task failures.

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Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained transformer models in generating equations as sequences, leveraging large-scale pre-training on synthetic datasets and offering notable advantages in terms of inference time over classical Genetic Programming (GP) methods. However, these models primarily rely on supervised pre-training objectives borrowed from text generation and overlook equation discovery goals like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search planning algorithm into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable equation verification feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise

Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward reasoning (e.g., straightforward arithmetic), it is less effective for constraint solving problems that require more sophisticated planning and search.