Quintic Polynomial Reference Line Optimization for Autonomous Vehicles
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Solution Overview
Problem
Conventional trajectory planning for autonomous driving vehicles relies on high-quality reference lines, but map data from sensors often results in unstable and oscillating trajectories due to lack of smoothness, making it difficult to generate stable paths.
Innovation Solution
A constrained numerical optimization method is used to generate a smooth and piecewise concatenated reference line with minimal curvature changes by connecting 2D points with quintic polynomial spiral paths, optimizing their coefficients to ensure smooth connections and minimal curvature changes along the reference line.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If map data from sensors is directly used as reference line, then the reference line generation is simple and fast, but the trajectory becomes unstable and oscillating due to lack of smoothness
Solution Approach 1:
The reference line is segmented into multiple reference line segments, each represented by a quintic polynomial function. This segmentation allows independent optimization of each segment while maintaining overall continuity, resolving the contradiction by enabling both computational efficiency and trajectory smoothness through localized polynomial fitting rather than processing the entire path at once.
Solution Approach 2:
The patent changes the parameter representation from raw sensor coordinates to quintic polynomial coefficients. By optimizing these coefficients subject to continuity constraints (matching position, direction, curvature, and curvature derivative at segment boundaries), the system transforms unstable sensor data into smooth, reliable trajectories while maintaining generation speed through efficient numerical optimization.
2Device complexity
If conventional trajectory planning is used with sensor map data, then the system complexity is low, but the trajectory quality is poor with oscillations and instability
Solution Approach 1:
The patent applies curvature-based smoothing by representing each reference line segment with a quintic polynomial that explicitly models curvature properties. By optimizing curvature continuity across segments and minimizing curvature changes within segments, the system achieves smooth trajectories without requiring complex mechanical or geometric constructions, maintaining relatively simple system architecture.
Solution Approach 2:
The patent replaces traditional mechanical or geometric trajectory smoothing methods with numerical optimization of polynomial coefficients. This substitution uses computational mathematics (optimizing quintic polynomial parameters subject to continuity constraints) instead of complex mechanical smoothing devices or iterative geometric algorithms, achieving high trajectory quality with moderate system complexity.
3Manufacturing precision
If quintic polynomial spiral paths are used to connect 2D points, then the reference line smoothness is improved with minimal curvature changes, but the computational complexity increases
Solution Approach 1:
The patent performs preliminary segmentation of the reference line into manageable quintic polynomial segments before optimization. By pre-defining the polynomial order and segment boundaries, the system reduces the complexity of the subsequent optimization problem, allowing efficient computation of smooth trajectories with minimal curvature changes without requiring real-time complex calculations.
Solution Approach 2:
The quintic polynomial functions serve as intermediary representations between raw sensor data and the final trajectory. These polynomials act as mathematical mediators that smooth the transition between discrete sensor points while maintaining computational tractability through their well-defined properties (continuity, differentiability), reducing the overall computational complexity compared to direct point-to-point interpolation methods.
Data Source
AI summary
A first reference line representing a trajectory from a first location to a second location associated with an autonomous driving vehicle (ADV) is received. The first reference line is segmented into a number of reference line segments. For each of the reference line segments, a quintic polynomial function is defined to represent the reference line segment. An objective function is determined based on the quintic polynomial functions of the reference line segments. An optimization is performed on coefficients of the quintic polynomial functions in view of a set of constraints associated with the reference line segments, such that an output of the objective function reaches minimum while the constraints are satisfied. A second reference line is then generated based on the optimized parameters or coefficients of the quintic polynomial functions of the objective function. The second reference line is then utilized to plan and control the ADV.