Fleet Trajectory Planning Across MUTEX Zones With Subproblem Decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The coordination of multiple vehicles in confined areas with mutually exclusive zones (MUTEX) is computationally complex and inefficient, particularly due to the NP-hard nature of combinatorial decisions, leading to significant computational effort in realistic scenarios.
Innovation Solution
A method that decomposes the vehicle trajectory planning problem into smaller, independent subproblems by identifying and removing irrelevant MUTEX zone constraints using dual variables, allowing for parallel computation of trajectory plans for vehicle subsets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If optimal control methods are used to compute coordinated vehicle trajectories, then safety constraints are satisfied, but computational complexity scales cubically with the number of vehicles
Solution Approach 1:
The patent divides the fleet of vehicles into multiple subsets based on spatial regions and MUTEX zone relationships. Each subset is optimized independently through separate NLP problems, transforming one large cubic-complexity problem into multiple smaller problems with reduced individual complexity.
Solution Approach 2:
The patent introduces a spatial dimension to the optimization problem by defining regions and using spatial relationships to determine subset assignments. This transforms the problem from a purely combinatorial vehicle-pair analysis to a spatially-structured optimization that reduces computational burden.
2Manufacturing precision
If the NLP is solved for all vehicles jointly over long horizons, then optimal coordinated trajectories are obtained, but the NLP becomes the predominant component in computational complexity
Solution Approach 1:
The patent segments the fleet into multiple subsets that are optimized independently. This segmentation maintains optimization quality within each subset while dramatically reducing the computational time required compared to solving one large joint NLP for all vehicles.
Solution Approach 2:
The patent performs preliminary classification of vehicles into subsets based on spatial regions and MUTEX relationships before solving the NLP problems. This preliminary action enables the decomposition of the optimization problem, reducing computational time while preserving trajectory quality.
3Productivity
If the coordination problem is decomposed into smaller subproblems, then computational efficiency is improved, but the solution space may be reduced
Solution Approach 1:
The patent segments the problem based on spatial regions and MUTEX zone relationships, ensuring that vehicles in different regions with no mutual exclusivity constraints are optimized independently. This segmentation maintains solution optimality while improving computational efficiency.
Solution Approach 2:
The patent uses feedback from the classification stage to guide the NLP optimization process. The subset assignments are determined based on MUTEX relationships and spatial positions, providing feedback that ensures optimal solutions are found within each subset while maintaining overall fleet coordination.
Data Source
AI summary
A method of planning trajectories for vehicles operating in a common environment, wherein movements of each vehicle are controllable by a control signal is provided the method includes for each vehicle, obtaining a predefined vehicle path to be traversed; performing a first computation to obtain a vehicle crossing order at each mutually exclusive—MUTEX—zone between two vehicle paths, wherein the first computation is subject to safety constraints; and performing trajectory planning subject to the obtained vehicle crossing order at the MUTEX zones, to obtain a control signal for each of the vehicles. The method further includes assigning a dependency metric to each pair of vehicles, and partitioning the vehicles into a number NSG of vehicle subsets such that the dependency metric exceeds a threshold within each, wherein the trajectory planning is performed as multiple independent subproblems, each relating to one of the vehicle subsets.