R-function Lane Keeping Trajectory Optimization
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Solution Overview
Problem
Current lane keeping systems in vehicles face challenges due to complexity and computational intensity, leading to tradeoffs between accuracy and efficiency, resulting in less robust systems for determining trajectories that maintain the vehicle within a lane.
Innovation Solution
The implementation of R-functions to calculate an analytic penalty/cost associated with crossing geometric lane boundaries, using sensor data and map information to define a reference system and evaluate vehicle boundary points, integrated with trajectory optimization for efficient and accurate lane keeping.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional lane keeping methods are used, then lane keeping functionality is provided, but computational complexity increases and processing efficiency decreases
Solution Approach 1:
The patent replaces traditional geometric methods (piecewise linear approximations, polygon definitions, point-in-polygon tests) with an analytic field-based approach using R-functions. This substitution transforms discrete geometric computations into continuous field evaluations, significantly reducing computational complexity while maintaining lane keeping accuracy.
Solution Approach 2:
The patent changes the fundamental parameters of lane keeping representation from discrete geometric entities (lines, polygons, points) to continuous analytic fields defined by R-functions. This parameter transformation enables gradient-based optimization and reduces the computational burden of trajectory evaluation while preserving the ability to accurately represent curved lane boundaries.
2Measurement precision
If accurate lane keeping is achieved through complex geometric methods, then lane keeping accuracy improves, but computational load increases
Solution Approach 1:
The patent substitutes complex geometric computations with analytic field evaluations using R-functions. This allows accurate representation of curved lane boundaries through continuous mathematical functions rather than discrete geometric primitives, achieving high precision with reduced computational load suitable for real-time autonomous vehicle systems.
3Device complexity
If piecewise linear approximation is used to represent curved lane boundaries, then computational complexity is reduced, but manufacturing precision (boundary accuracy) deteriorates
Solution Approach 1:
The patent transforms the representation of curved lane boundaries from piecewise linear segments to continuous analytic R-functions. This parameter change enables exact representation of curved boundaries while maintaining computational efficiency, as the analytic functions can be evaluated directly without requiring multiple discrete segments to approximate the curve.
Data Source
AI summary
System, methods, and other embodiments described herein relate to lane keeping in a vehicle. In one embodiment, a method includes determining lane boundaries according to at least the sensor data and a map. The method includes defining a reference system over a lane defined by the lane boundaries. The method includes evaluating vehicle boundary points within the reference system as a cost in optimizing a trajectory of the vehicle and using an R-function that defines geometric relationships between the vehicle boundary points and the reference system. The method includes providing an indicator about the trajectory to control the vehicle.