Meta-Optimization and Program Search using Language Models for Task and Motion Planning (2505.03725v1)

Abstract: Intelligent interaction with the real world requires robotic agents to jointly reason over high-level plans and low-level controls. Task and motion planning (TAMP) addresses this by combining symbolic planning and continuous trajectory generation. Recently, foundation model approaches to TAMP have presented impressive results, including fast planning times and the execution of natural language instructions. Yet, the optimal interface between high-level planning and low-level motion generation remains an open question: prior approaches are limited by either too much abstraction (e.g., chaining simplified skill primitives) or a lack thereof (e.g., direct joint angle prediction). Our method introduces a novel technique employing a form of meta-optimization to address these issues by: (i) using program search over trajectory optimization problems as an interface between a foundation model and robot control, and (ii) leveraging a zero-order method to optimize numerical parameters in the foundation model output. Results on challenging object manipulation and drawing tasks confirm that our proposed method improves over prior TAMP approaches.

• The paper introduces Meta-Optimization and Program Search (MOPS), a novel framework using a three-tiered optimization hierarchy combining language models, black-box optimization, and gradient-based trajectory optimization for improved robotic task and motion planning.
• Empirical evaluations demonstrate MOPS outperforms existing approaches, including other foundation model methods, showing higher task success rates in varied robotic manipulation and drawing environments, particularly for complex spatial tasks.
• The proposed methodology integrates advanced AI by using LLMs as semantic optimizers and layered optimization, bridging the gap between symbolic task plans and concrete motion constraints to enhance the precision and practical deployment of robots.

Meta-Optimization and LLMs in Task and Motion Planning

The paper presents an innovative methodology for Task and Motion Planning (TAMP) that utilizes meta-optimization and LLMs, addressing the intricate problem of integrating high-level task planning with detailed motion trajectories in robotic manipulation. It introduces Meta-Optimization and Program Search (MOPS), a framework that combines the strengths of foundation models and a layered optimization strategy. This approach aims to overcome limitations of existing TAMP methods by bridging the gap between symbolic reasoning and geometric precision, ultimately enhancing robotic task execution.

Overview of Methodology

The essence of the paper lies in the treatment of TAMP as a meta-optimization problem. MOPS uniquely transforms the task planning challenge into a three-tiered optimization hierarchy:

1. LLM Program Search: LLMs initiate the optimization process by selecting relevant constraints that define the trajectory non-linear program (NLP). This step leverages LLMs to interpret high-level goals into actionable mathematical constraints, essentially guiding the trajectory generation process with semantic understanding.
2. Constraint Parameter Optimization: A black-box optimizer refines the continuous parameters of the trajectory constraints proposed by the LLM. This optimization aims at enhancing task performance metrics by fine-tuning the numerical aspects that are initially approximated by the LLM, such as precise joint positions and orientations.
3. Gradient-Based Trajectory Optimization: The final layer involves solving the parameterized NLP using gradient-based techniques to produce smooth and feasible trajectories. This ensures that the paths generated meet all task constraints efficiently, focusing on minimizing physical aspects such as joint accelerations while satisfying task-specific geometric constraints.

By iteratively refining each level based on feedback from previous executions, MOPS achieves convergence toward optimal task execution plans, balancing abstract goal interpretation with concrete trajectory realism.

Experimental Insights and Results

The empirical evaluation showcases MOPS's superior performance over classic TAMP approaches and recent FM-based models like Code-as-Policies (CaP) and PRoC3S. Across varied tasks in object manipulation and drawing environments, MOPS consistently demonstrates improved task success rates by leveraging its robust optimization strategy. Notably, in complex scenarios requiring intricate spatial reasoning—such as drawing accurately on tilted surfaces—MOPS's ability to refine constraint parameters yields markedly precise outputs compared to non-optimizing methods.

Further analysis highlights the critical contribution of meta-optimization, particularly the role of black-box optimization in enhancing the precision and success of task execution under constrained conditions. This underscores the shift from random sampling towards more systematic numerical optimization within the TAMP context.

Implications and Future Work

The proposed methodology holds significant potential for advancing the practical deployment of AI in robotics, moving beyond traditional symbolic and simplified model constraints to a dynamic, optimization-driven approach. The integration of LLMs as semantic optimizers opens avenues for handling diverse tasks with fine-grained precision, thereby addressing one of the core challenges in robotic manipulation—the gap between symbolic task plans and concrete motion constraints.

Future research could explore extending MOPS by adapting real-time learning mechanisms for optimizing task-specific cost functions or implementing state estimation techniques to cater to scenarios with partial observability. Additionally, bridging MOPS with visual LLMs (VLMs) could enable real-time decision-making in less structured environments, facilitating the application to broader domains and complex industrial tasks.

In conclusion, the paper's contribution to the field is marked by its innovative fusion of LLMs with layered optimization, offering a comprehensive framework for enhancing robotic task and motion planning efficacy. It paves the way for leveraging advanced AI methodologies to tackle the intricate intersections of reasoning, planning, and precise control in autonomous systems.