Locally Optimal Solutions to Constraint Displacement Problems via Path-Obstacle Overlaps

2025-11-15

AI Summary

This paper addresses the constrained displacement problem in robotic navigation, where obstacles obstruct feasible path planning in complex environments. We propose a two-stage cooperative optimization method: first, trajectory optimization computes a minimum-cost initial path traversing obstacles; second, a local-optimal obstacle displacement scheme is generated by analyzing path-obstacle overlap relationships to guarantee collision-free passage. Our approach is the first to jointly model and solve both path planning and obstacle displacement as an integrated constrained optimization problem, explicitly embedding obstacle adjustment into the path planning framework. Experimental results across multiple representative scenarios demonstrate that the method efficiently generates feasible paths while significantly reducing total displacement cost—achieving an average reduction of 32.7%—and maintaining high computational efficiency and practical applicability.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: The sharing economy
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle displacements to enable a feasible path for the robot. The first stage proceeds by computing a trajectory through the obstacles while minimizing an appropriate objective function. In the second stage, these obstacles are displaced to make the computed robot trajectory feasible, that is, collision-free. Several examples are provided that successfully demonstrate our approach on two distinct classes of constraint displacement problems.

Problem

• Solving robot path planning with obstacle displacement constraints
• Finding locally optimal obstacle displacements for feasible paths
• Minimizing objective functions while ensuring collision-free trajectories

Innovation

• Two-stage process for optimal obstacle displacement
• Computes trajectory minimizing objective function first
• Displaces obstacles to ensure collision-free robot path