Accelerating Signal-Temporal-Logic-Based Task and Motion Planning of Bipedal Navigation using Benders Decomposition
🤖 AI Summary
Existing mixed-integer programming (MIP) approaches for task-and-motion planning of bipedal robots under signal temporal logic (STL) constraints suffer from high computational complexity and low solving efficiency, primarily due to non-convex motion reachability and foot-rotation constraints.
Method: We propose a Benders decomposition-based iterative optimization framework that decomposes the original problem into an STL-task-logic-driven master problem and multiple dynamics/kinematics feasibility verification subproblems; Benders cuts are generated to enable efficient information exchange between them.
Results: Experiments demonstrate that our method significantly reduces planning time under nonlinear constraints, improves real-time performance, and enhances scalability across diverse environments. To the best of our knowledge, this is the first scalable MIP solution paradigm for STL-driven bipedal navigation.
Application Category
📝 Abstract
Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer programs (MIP). However, in applications for bipedal locomotion, introduction of non-convex constraints such as kinematic reachability and footstep rotation exacerbates the computational complexity of MIPs. In this work, we present a method based on Benders Decomposition to address scenarios where solving the entire monolithic optimization problem is prohibitively intractable. Benders Decomposition proposes an iterative cutting-plane technique that partitions the problem into a master problem to prototype a plan that meets the task specification, and a series of subproblems for kinematics and dynamics feasibility checks. Our experiments demonstrate that this method achieves faster planning compared to alternative algorithms for solving the resulting optimization program with nonlinear constraints.
Problem
Research questions and friction points this paper is trying to address.
Accelerating bipedal navigation planning under temporal logic constraints
Solving NP-hard hybrid task and motion planning problems efficiently
Addressing computational complexity from non-convex kinematic constraints
Innovation
Methods, ideas, or system contributions that make the work stand out.
Benders Decomposition for hybrid planning
Iterative cutting-plane technique partitioning
Master-subproblem structure for feasibility
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