Smooth Road Reference for Autonomous Driving via 2D Constrained Smoothing Spline
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Solution Overview
Problem
Autonomous driving vehicles face challenges in navigating smoothly and avoiding obstacles due to the lack of effective path and speed planning algorithms that ensure stable vehicle control, especially in dynamic environments with obstacles and traffic information.
Innovation Solution
The implementation of a system that uses quadratic programming optimization to generate smooth path and speed trajectories based on perceived obstacles and traffic information, by segmenting the path into polynomial functions and applying constraints to ensure smooth connections and optimal cost minimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If traditional path planning algorithms are used, then the vehicle can navigate to locations, but the reference line lacks smoothness leading to unstable vehicle control
Solution Approach 1:
The path planning algorithm segments the reference line into multiple polynomial curve segments, where each segment is defined by control points and coefficients. This segmentation allows independent optimization of each segment's smoothness while maintaining overall path continuity, directly resolving the contradiction between navigation capability and reference line smoothness for stable vehicle control.
Solution Approach 2:
The patent applies curved polynomial segments (specifically cubic and quadratic polynomials) instead of straight line segments to create a smooth reference line. The curvature continuity enforced through constraint equations ensures that adjacent segments connect smoothly, eliminating abrupt direction changes and improving vehicle control stability while maintaining navigation accuracy.
2Manufacturing precision
If path planning is performed without constraints, then computational speed is faster, but the generated trajectory lacks smoothness and optimality
Solution Approach 1:
The algorithm performs preliminary actions by pre-defining the polynomial structure and constraint equations before actual path optimization. The constraint equations for continuity and smoothness are established in advance, allowing the optimization process to directly solve for optimal coefficients rather than iteratively adjusting parameters, thus achieving high-precision smooth trajectories with reduced computational time.
3Stability of the object's composition
If speed planning is not optimized, then the vehicle can travel along the path, but the speed trajectory is not smooth leading to unstable control
Solution Approach 1:
The speed planning algorithm segments the speed trajectory into multiple polynomial segments corresponding to different path segments. Each speed segment is optimized independently with continuity constraints at segment boundaries, ensuring smooth transitions in speed while maintaining stable vehicle control throughout the journey.
Solution Approach 2:
The algorithm optimizes speed trajectory by changing speed parameters (velocity, acceleration) as polynomial functions of position or time along the path. This parameterization allows smooth variation of speed characteristics while satisfying dynamic constraints, directly improving vehicle control stability through smooth speed transitions.
4Device complexity
If simple polynomial functions are used, then computational complexity is reduced, but the ability to handle obstacles and traffic information is limited
Solution Approach 1:
The path planning algorithm applies local quality by using different polynomial orders and constraint types for different path segments based on local environmental conditions. In obstacle-free regions, simpler polynomials are used for computational efficiency, while in regions with obstacles or traffic information, higher-order polynomials with additional constraints are applied to achieve precise obstacle avoidance, thus balancing algorithm complexity with adaptability.
Solution Approach 2:
The algorithm dynamically adjusts the polynomial parameters and constraint equations based on real-time obstacle and traffic information. When obstacles are detected, the control points and constraint equations are updated to generate avoidance paths, while maintaining the underlying polynomial framework for computational efficiency. This dynamic adaptation enables versatile obstacle handling without requiring a completely complex algorithmic structure.
Data Source
AI summary
According to some embodiments, a system determines a number of boundary areas having predetermined dimensions centered around each of a number of control points of a first reference line. The system selects a number of two-dimensional polynomials each representing a segment of an optimal reference line between adjacent control points. The system defines a set of constraints to the two-dimensional polynomials to at least ensure the two-dimensional polynomials passes through each of the boundary areas. The system performs a quadratic programming (QP) optimization on a target function such that a total cost of the target function reaches minimum while the set of constraints are satisfied. The system generates a second reference line representing the optimal reference line based on the QP optimization to control the ADV autonomously according to the second reference line.