Vehicle Path Planning With Clothoid Curves for Continuous Steering
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Solution Overview
Problem
Current path planning systems for autonomous vehicles face challenges in constructing continuous curvature paths suitable for real-time control, as existing methods often require computationally expensive iterative processes and may not guarantee feasible solutions, leading to discontinuous curvature paths that cause unnecessary delays and tire wear.
Innovation Solution
The system employs a method to determine analytical functions for various patterns of elementary paths, using geometrical constraints to transform discontinuous Reeds-Shepp paths into continuous curvature paths by replacing circular arcs with clothoid turns, allowing for off-line determination of optimal geometrical constraints to avoid iterative optimization and ensure continuous curvature transitions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Reeds-Shepp paths with multiple line and circular arc segments are used, then the path length is minimized, but the curvature becomes discontinuous causing vehicle stops and stationary steering
Solution Approach 1:
The patent replaces circular arc segments with clothoid segments in the path composition. Clothoid segments have continuously varying curvature that can be smoothly connected to line segments, eliminating the discontinuous curvature transitions of Reeds-Shepp paths. This parameter change in the mathematical description of path segments resolves the contradiction by maintaining path efficiency while eliminating stationary steering requirements.
Solution Approach 2:
The patent introduces clothoid curves which have continuously varying curvature properties, replacing the fixed curvature of circular arcs. The clothoid's curvature changes continuously along the path length, enabling smooth transitions between path segments without abrupt changes. This curvature continuity eliminates the need for stationary steering operations while maintaining optimal path length characteristics.
2Reliability
If conventional iterative optimization methods are used to find continuous curvature paths, then feasible solutions may be found, but the computational process is prohibitively expensive for real-time control
Solution Approach 1:
The patent pre-establishes the mathematical framework for clothoid-based path segments and their continuous curvature properties before real-time path planning is needed. By deriving and storing the analytical solutions for clothoid segment parameters and their connection conditions, the system eliminates the need for iterative optimization during real-time operation. This preliminary mathematical preparation resolves the contradiction by ensuring feasible continuous curvature paths can be computed efficiently without expensive iterative processes.
3Reliability
If multiple elementary paths of different kinds are combined, then continuous curvature can be achieved, but the path construction becomes time-consuming
Solution Approach 1:
The patent establishes a universal path construction framework using clothoid segments that can serve multiple functions: they provide continuous curvature transitions, maintain optimal path length, and enable analytical computation. By making clothoid segments the universal building block for all path planning scenarios, the system achieves continuous curvature without time-consuming iterative processes, as the same mathematical framework applies to all path construction cases.
Data Source
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AI summary
A system for controlling a motion of a vehicle includes a memory to store a set of analytical functions corresponding to a set of patterns of elementary paths. Each pattern represents a continuous path and each analytical function is determined for a corresponding pattern to provide an analytical solution for input states of the vehicle defining a continuous path connecting the input states by a sequential compositions of the elementary paths following the corresponding pattern. The system includes a path planner to select from the memory, in response to receiving an initial state and a target state of the vehicle, an analytical function corresponding to a minimum cost of the continuous curvature path connecting the initial state with the target state and to analytically determine parameters of the continuous curvature path using the selected analytical function and a controller to control the motion of the vehicle according to the parameters of the continuous curvature path.