Optimization-based Task and Motion Planning under Signal Temporal Logic Specifications using Logic Network Flow

2024-09-27

arXiv.org

AI Summary

Efficient optimization of signal temporal logic (STL) constraints remains challenging in multi-robot motion planning. Method: This paper proposes a mixed-integer linear programming (MILP) framework grounded in logical network flows. Its core innovation is the first encoding of STL predicates as polyhedral constraints on directed graph edges—replacing conventional node-based constraints in logic trees—and the introduction of dynamic network flow modeling to achieve tighter convex relaxations. Contribution/Results: This design significantly improves branch-and-bound efficiency: on multi-robot benchmarks, it substantially reduces solution time compared to logic-tree-based approaches. As problem scale increases, it attains superior upper and lower bounds with fewer branching nodes, demonstrating enhanced scalability and convergence properties.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper proposes an optimization-based task and motion planning framework, named ``Logic Network Flow", to integrate signal temporal logic (STL) specifications into efficient mixed-binary linear programmings. In this framework, temporal predicates are encoded as polyhedron constraints on each edge of the network flow, instead of as constraints between the nodes as in the traditional Logic Tree formulation. Synthesized with Dynamic Network Flows, Logic Network Flows render a tighter convex relaxation compared to Logic Trees derived from these STL specifications. Our formulation is evaluated on several multi-robot motion planning case studies. Empirical results demonstrate that our formulation outperforms Logic Tree formulation in terms of computation time for several planning problems. As the problem size scales up, our method still discovers better lower and upper bounds by exploring fewer number of nodes during the branch-and-bound process, although this comes at the cost of increased computational load for each node when exploring branches.

Problem

• Integrates STL specifications into mixed-binary linear programming.
• Encodes temporal predicates as polyhedron constraints on network edges.
• Outperforms Logic Tree in computation time and node exploration.

Innovation

• Optimization-based task and motion planning framework
• Logic Network Flow with STL specifications
• Tighter convex relaxation using polyhedron constraints