Path Signature Trajectory Tracking With Lower Computing Load
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Solution Overview
Problem
Determining a trajectory for controlling an object to follow a path requires significant memory, time, or computing resources, particularly in tasks like path prediction and optimization.
Innovation Solution
The use of path signatures to determine a trajectory, where path signatures represent geometric characteristics of a path, allowing for efficient identification of actions for an object to follow the path.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional path prediction and optimization methods are used to determine trajectory, then accurate path following is achieved, but significant memory, time, and computing resources are consumed
Solution Approach 1:
The patent extracts only the essential geometric characteristics of the path (curvature, torsion, and their derivatives) to form path signatures, rather than processing complete trajectory data. This extraction approach maintains path following accuracy while significantly reducing the computational burden by working with compact signature representations instead of full path histories
Solution Approach 2:
Instead of predicting the entire future trajectory and then optimizing it, the patent inverts the approach by using path signatures to directly compute optimal control actions at each step. The method works backwards from the desired path geometry to determine control inputs, rather than forwards from current state to future trajectory
2Measurement precision
If comprehensive path prediction is performed to ensure accurate trajectory tracking, then tracking precision is improved, but time consumption increases
Solution Approach 1:
The patent performs preliminary computation of path signatures and their geometric characteristics before actual trajectory execution. By pre-processing the path into signature form with pre-computed curvature and torsion values, the system eliminates the need for complex real-time predictions during execution, thus maintaining precision while reducing runtime computation time
Solution Approach 2:
The path is segmented into discrete signature points with computed geometric properties, allowing the system to process only relevant segments rather than the entire path continuously. This segmentation enables efficient lookup and comparison operations during trajectory tracking without requiring comprehensive real-time path prediction
3Measurement precision
If detailed path optimization is performed to minimize deviation from reference path, then path following accuracy is improved, but memory requirements increase
Solution Approach 1:
The patent extracts only the essential geometric features (curvature, torsion, and their derivatives) needed for path following, discarding redundant path information. This extraction creates compact path signature representations that maintain sufficient accuracy for trajectory tracking while occupying minimal memory space
Solution Approach 2:
Instead of storing and processing complete reference path trajectories, the patent creates simplified signature copies that capture the essential geometric characteristics. These signature copies serve as sufficient representations for computation, reducing memory requirements while preserving the necessary information for accurate path following
Data Source
AI summary
Apparatuses, systems, and techniques to determine a trajectory of an object along a path. In at least one embodiment, one or more path signatures are used to identify one or more actions to be performed by an object to track a reference path.