M^3P-R1: Reinforcement Learning for Large Language Model Guided Multi-Modal Motion Planning via MIP Code Generation

Large Language Models (LLMs) possess extensive foundational knowledge and moderate reasoning abilities, making them suitable for general task planning in open-world scenarios. However, it is challenging to ground a LLM-generated plan to be executable for the specified robot with certain restrictions. This paper introduces CLMASP, an approach that couples LLMs with Answer Set Programming (ASP) to overcome the limitations, where ASP is a non-monotonic logic programming formalism renowned for its capacity to represent and reason about a robot's action knowledge. CLMASP initiates with a LLM generating a basic skeleton plan, which is subsequently tailored to the specific scenario using a vector database. This plan is then refined by an ASP program with a robot's action knowledge, which integrates implementation details into the skeleton, grounding the LLM's abstract outputs in practical robot contexts. Our experiments conducted on the VirtualHome platform demonstrate CLMASP's efficacy. Compared to the baseline executable rate of under 2% with LLM approaches, CLMASP significantly improves this to over 90%.

Multi-constraint planning involves identifying, evaluating, and refining candidate plans while satisfying multiple, potentially conflicting constraints. Existing large language model (LLM) approaches face fundamental limitations in this domain. Pure reasoning paradigms, which rely on long natural language chains, are prone to inconsistency, error accumulation, and prohibitive cost as constraints compound. Conversely, LLMs combined with coding- or solver-based strategies lack flexibility: they often generate problem-specific code from scratch or depend on fixed solvers, failing to capture generalizable logic across diverse problems. To address these challenges, we introduce the Scalable COde Planning Engine (SCOPE), a framework that disentangles query-specific reasoning from generic code execution. By separating reasoning from execution, SCOPE produces solver functions that are consistent, deterministic, and reusable across queries while requiring only minimal changes to input parameters. SCOPE achieves state-of-the-art performance while lowering cost and latency. For example, with GPT-4o, it reaches 93.1% success on TravelPlanner, a 61.6% gain over the best baseline (CoT) while cutting inference cost by 1.4x and time by ~4.67x. Code is available at https://github.com/DerrickGXD/SCOPE.

Robotic manipulation requires the effective integration of heterogeneous inputs, including visual observations, language instructions, and trajectory representations, to generate accurate actions. Existing transformer-based policies typically process these heterogeneous modalities within a shared parameter space, which often leads to modality interference and inefficient representation learning, especially in data-scarce scenarios. While Mixture-of-Experts (MoE) offers a scalable solution through expert specialization, conventional routing mechanisms are often sensitive to such cross-modal representation discrepancies, resulting in unstable expert assignment and expert collapse. In this work, we propose MATE (Multi-ModAl TrajEctory Policies), a novel trajectory prediction framework built upon MoE. Specifically, we introduce a Multi-Modal MoE architecture to achieve fine-grained sub-token feature decoupling, and design a cross-modal cosine router for stable and scale-invariant expert assignment across heterogeneous modalities. We further employ temperature-controlled routing and stochastic noise injection to improve expert balance and prevent premature routing collapse under scarce demonstrations. Experiments on the LIBERO benchmark show that our MATE consistently outperforms prior work under data scarcity. It achieves a 4.75% improvement in average success rate over the trajectory-guided counterpart. Real-world experiments on robotic ping-pong also suggest that the predicted trajectories can provide useful guidance for downstream robotic execution, further indicating the practical feasibility of our algorithm.