Trajectory Planning via Phase Space Cell Division
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Solution Overview
Problem
Current trajectory planning methods for robots fail to minimize motion costs and achieve quasi-minimum-cost motion with high accuracy, as they either rely on stochastic methods or require high linearity assumptions, limiting their applicability.
Innovation Solution
A trajectory planning method that divides the state space into cells to minimize approximation errors due to discretization, using a cell generating section to create a search tree where each cell contains no more than one node, allowing for the determination of a path from the current state to the goal state with minimized motion costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the phase space is divided uniformly along each axis with individually determined cell sizes, then the trajectory planning can be performed through continuous search, but the motion costs cannot be minimized effectively and the planning accuracy is limited
Solution Approach 1:
The phase space is divided into multiple cells along each axis, creating a grid structure that enables systematic search while managing complexity through organized segmentation of the continuous state space
Solution Approach 2:
Cell sizes are determined individually for each axis based on local characteristics of the phase space, allowing finer resolution in critical regions and coarser resolution in less critical regions, thereby minimizing approximation errors while controlling overall complexity
2Measurement precision
If a stochastic method like RRT is used for state transitions in phase space, then the method is simple to implement, but minimum-cost motion cannot necessarily be realized
Solution Approach 1:
The phase space is pre-divided into cells with optimized sizes before the search process begins, establishing a structured framework that guides the subsequent search to achieve minimum-cost motion while maintaining systematic complexity management
Solution Approach 2:
The search method dynamically explores the phase space by transitioning between cells, adapting the search strategy based on the cost function while operating within the pre-established cell structure, combining systematic organization with flexible exploration
3Adaptability or versatility
If quantization of the state space is utilized with the assumption of high linearity, then the method can provide structured search, but the application is limited to certain types of machines alone
Solution Approach 1:
Cell sizes are individually determined for each axis based on local phase space characteristics, allowing the method to adapt to different machine types and nonlinearities by adjusting resolution locally rather than requiring global linearity assumptions
Solution Approach 2:
The cell size parameters are optimized to minimize approximation errors for the specific application, allowing the method to be adapted to different machine types by changing the cell division parameters rather than requiring fundamental algorithmic changes
Data Source
AI summary
A trajectory planning method according to the present invention is one for obtaining a trajectory for controlling a state of an object toward a goal state by a trajectory planning system. The method includes the steps of dividing, by a cell generating section for dividing a state space of the object into cells, the state space into cells in such a way that approximation error due to discretization is minimized for a predetermined number of cells; generating, by a search tree generating section, a search tree which corresponds to state transition of the object in such a way that each cell does not contain more than one of nodes of branches of the search tree; and determining, by a trajectory generating section, a path from the current state to the goal state of the object using the search tree.