Reference Line Coordinate Transformation for Moving Object Localization
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Solution Overview
Problem
Raw path data from sensors on moving objects, such as vehicles, is insufficient for high-precision absolute localization along a trajectory, and existing conversion methods from Cartesian to reference line-based coordinates are incomplete or inaccurate, leading to errors in object tracking and orientation.
Innovation Solution
A system and method that preprocess raw data by generating a reference line, converting Cartesian coordinates to reference line-based coordinates, and extending image data with kinematic values and yaw angles, ensuring accurate and robust transformation without distortion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If Cartesian coordinates are used to track moving objects, then the object position can be described in a simple coordinate system, but errors in estimation cause the object to drift outside the reference line and computational complexity increases significantly
Solution Approach 1:
The patent introduces a reference line as an intermediary element between the Cartesian coordinate system and the object tracking system. The reference line serves as a mediator that transforms Cartesian coordinates into reference line-based coordinates (s, d), where s is the longitudinal distance along the reference line and d is the lateral distance from the reference line. This intermediary transformation resolves the contradiction by maintaining the simplicity of Cartesian coordinates for data collection while providing the reliability of reference line-based coordinates for accurate tracking.
Solution Approach 2:
The patent changes the parameter system from pure Cartesian coordinates (x, y) to reference line-based coordinates (s, d). This parameter transformation allows the system to maintain the ease of Cartesian coordinate collection while achieving superior tracking reliability. The transformation equations convert Cartesian positions into longitudinal and lateral displacements relative to the reference line, eliminating the drift problem while preserving computational simplicity.
2Measurement precision
If complex reference line geometry with sharp turns is used to define the trajectory, then the trajectory can accurately represent complex paths, but solving polynomials with large coefficients becomes computationally intensive
Solution Approach 1:
The patent segments the complex reference line geometry into discrete control points that define the trajectory. Instead of working with a single complex polynomial representing the entire reference line, the system divides the reference line into segments between control points. This segmentation allows the system to represent complex trajectories with high precision while reducing computational complexity by processing smaller, more manageable segments rather than solving large polynomial systems.
Solution Approach 2:
The patent transforms the problem from two-dimensional Cartesian coordinates to a one-dimensional longitudinal parameter s along the reference line, plus a small lateral offset d. This dimensional transformation simplifies the computational problem by reducing the complexity of polynomial solving while maintaining the ability to represent complex three-dimensional trajectories. The reference line parameterization converts complex geometric constraints into simpler algebraic relationships.
3Productivity
If direct transformation from slip angle and coordinates to absolute yaw angle is performed, then the yaw angle can be obtained, but discontinuity at 0 degrees and loss of precision due to error accumulation occur
Solution Approach 1:
The patent implements feedback mechanisms to correct yaw angle calculations. Instead of using direct transformation that accumulates errors, the system uses feedback from the reference line-based coordinate system to correct and refine yaw angle estimates. The reference line provides a stable reference frame that feedback-corrects the yaw angle calculations, eliminating discontinuities at 0 degrees and reducing error accumulation while maintaining calculation speed.
Data Source
AI summary
Techniques for preparing data for high-precision absolute localization of a moving object along a trajectory are provided. In one technique, a sequence of points is stored, where each point corresponds to a different set of Cartesian coordinates. A curve is generated that approximates a line that passes through the sequence of points. Based on the curve, a set of points is generated on the curve, where the set of points is different than the sequence of points. New Cartesian coordinates are generated for each point in the set of points. After generating the new Cartesian coordinates, Cartesian coordinates of a position of a moving object are determined.