What Makes a Good Symbol for Hybrid Discrete-Continuous Planning?

Intelligent agents must reason over both continuous dynamics and discrete representations to generate effective plans in complex environments. Previous studies have shown that symbolic abstractions can emerge from neural effect predictors trained with a robot's unsupervised exploration. However, these methods rely on deterministic symbolic domains, lack mechanisms to verify the generated symbolic plans, and operate only at the abstract level, often failing to capture the continuous dynamics of the environment. To overcome these limitations, we propose a bilevel neuro-symbolic framework in which learned probabilistic symbolic rules generate candidate plans rapidly at the high level, and learned continuous effect models verify these plans and perform forward search when necessary at the low level. Our experiments on multi-object manipulation tasks demonstrate that the proposed bilevel method outperforms symbolic-only approaches, reliably identifying failing plans through verification, and achieves planning performance statistically comparable to continuous forward search while resolving most problems via efficient symbolic reasoning.

In dynamic open-world environments, autonomous agents often encounter novelties that hinder their ability to find plans to achieve their goals. Specifically, traditional symbolic planners fail to generate plans when the robot's planning domain lacks the operators that enable it to interact appropriately with novel objects in the environment. We propose a neuro-symbolic architecture that integrates symbolic planning, reinforcement learning, and a large language model (LLM) to learn how to handle novel objects. In particular, we leverage the common sense reasoning capability of the LLM to identify missing operators, generate plans with the symbolic AI planner, and write reward functions to guide the reinforcement learning agent in learning control policies for newly identified operators. Our method outperforms the state-of-the-art methods in operator discovery as well as operator learning in continuous robotic domains.Our webpage and code can be access here: https://helenlu66.github.io/hybridLLMguided/

Task planning often suffers from severe efficiency bottlenecks when robots must reason over long-horizon action sequences under complex logical constraints, including object affordances, spatial relationships, and sequential action dependencies. Recent neuro-symbolic methods improve planning efficiency by learning object-importance scores to prune task-irrelevant objects, but they typically rely on fixed offline supervision generated from full search spaces. This creates a train-test mismatch: at deployment, the planner operates in pruned search spaces induced by the model's own imperfect predictions, leading to exposure bias and degraded planning performance. To address this challenge, we formulate object-importance learning for task planning as an imperative learning-based bilevel optimization problem. The upper level optimizes a neural scorer, while the lower level solves a symbolic planning problem in the score-pruned search space. To stabilize this learning process, we introduce a 3R strategy into the lower-level planning, using parallel Repair, Restart, and Rollback recovery to provide reliable and adaptive feedback for upper-level learning. Experiments on three challenging benchmarks demonstrate state-of-the-art performance, including an 80.04% reduction in failure rate and a 57.14% reduction in planning time. We further validate the framework on a quadruped-based mobile manipulator in simulation and the real world, demonstrating its potential for efficient and deployable neuro-symbolic task planning.