D-LGP: Dynamic Logic-Geometric Program for Reactive Task and Motion Planning

Abstract: Many real-world sequential manipulation tasks involve a combination of discrete symbolic search and continuous motion planning, collectively known as combined task and motion planning (TAMP). However, prevailing methods often struggle with the computational burden and intricate combinatorial challenges, limiting their applications for online replanning in the real world. To address this, we propose Dynamic Logic-Geometric Program (D-LGP), a novel approach integrating Dynamic Tree Search and global optimization for efficient hybrid planning. Through empirical evaluation on three benchmarks, we demonstrate the efficacy of our approach, showcasing superior performance in comparison to state-of-the-art techniques. We validate our approach through simulation and demonstrate its reactive capability to cope with online uncertainty and external disturbances in the real world. Project webpage: https://sites.google.com/view/dyn-lgp.

• The paper introduces a novel D-LGP algorithm combining dynamic tree search with quadratic optimization to derive feasible and globally optimal task and motion plans.
• It employs mixed-integer quadratic programming and receding-horizon strategies to address the combinatorial and continuous challenges of TAMP.
• Empirical and real-world experiments demonstrate that D-LGP outperforms existing methods, offering enhanced efficiency and adaptability in dynamic environments.

Introduction

Robots are becoming increasingly essential in various tasks that involve both planning and physical manipulation. The effectiveness of these robotic systems in such tasks depends heavily on their ability to handle complex planning that involves both high-level decision-making and low-level control to execute actions. This intertwines two areas in robotics known as Task and Motion Planning (TAMP). However, TAMP is challenging due to the need to consider both the symbolic, discrete decisions and the continuous, geometric motions, which can result in significant computational complexities.

Dynamic Logic-Geometric Program (D-LGP)

To enhance the efficiency of TAMP, a method called Dynamic Logic-Geometric Program (D-LGP) has been presented. It combines a novel approach of Dynamic Tree Search (DTS) with global optimization techniques. The DTS offers a backpropagation mechanism to identify action skeletons, while quadratic optimization globally solves the non-convex, continuous space of motion planning. This combined approach aims to address the difficulties associated with finding feasible task sequences out of a large number of combinatorial choices and also producing a globally optimal motion plan in a substantially reduced computational time.

Feasibility and Optimality

The D-LGP algorithm provides a hierarchical framework, which enables the effective communication of feasible task sequences from the symbolic level to the geometric level. By utilizing mixed-integer quadratic programming, it can confidently derive globally optimal solutions or determine infeasibility in complex TAMP problems. Additionally, the algorithm's capability to rapidly produce solutions allows for its use in a receding-horizon planning fashion, accommodating real-world uncertainties and disturbances during robot manipulation tasks.

Empirical Evaluation and Robot Experiments

Empirical evaluations of the D-LGP approach were conducted on several benchmark problems, where robots were tasked with manipulating objects in sequences with long planning horizons. The results confirmed that D-LGP outperformed state-of-the-art comparative techniques with superior efficiency and optimality. Furthermore, real-world experiments with a robot demonstrated D-LGP's adaptability to dynamic environments, successfully accounting for unexpected changes during task execution.

Conclusion

D-LGP offers an innovative solution to the intricacies of TAMP for real-world robotic manipulation. It successfully bridges the gap between task-level planning and motion-level planning, producing highly efficient and reliable outcomes. The D-LGP framework showcases the potential for advanced robotic systems to operate effectively in complex, dynamic environments by intelligently planning and executing tasks with an awareness of both their symbolic and geometric implications.