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

arXiv · AI, language, vision and robotics · article · Sep 16, 2026 · UTC

Multi-Modal Motion Planning (M$^3$P) requires joint reasoning over continuous motions and discrete mode transitions, making it difficult to solve efficiently. For instance, a bipedal robot may walk to a target location and then use its arms to grasp an object. This scenario captures both mode transitions and continuous dynamics, yielding feasible paths that neither purely discrete nor continuous planners can handle. While Mixed-Integer Programming (MIP) offers a principled framework, constructing tractable formulations for non-convex problems is typically manual and domain-specific, especially

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