Vehicle Path Planning Using Discrete Point Constraints
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing path planning methodologies for vehicles, particularly those with minimum turning radius constraints, face difficulties in incorporating non-linear constraints and often fail when optimal solutions involve velocities close to zero, limiting their effectiveness in determining globally optimal trajectories.
Innovation Solution
A method and apparatus for determining a vehicle path by optimizing an ordered sequence of path points, constraining distance and angle between points, and incorporating constraints such as minimum turning radius, initial velocity, and gear switching, to generate a feasible and optimal trajectory that accounts for non-linear dynamics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If linear approximation of vehicle dynamics is used in path planning, then the path planning problem can be solved using MILP, but the minimum turning radius constraint cannot be properly incorporated due to its nonlinear nature
Solution Approach 1:
The patent changes the parameter representation from continuous vehicle dynamics to discrete path point sequences with constrained geometric relationships. By parameterizing the path as a sequence of points with fixed distances and angle constraints, the nonlinear turning radius constraint is transformed into linear constraints that can be handled by MILP.
Solution Approach 2:
The patent segments the continuous vehicle trajectory into discrete path points connected by straight line segments. This segmentation allows the application of linear constraints between consecutive path points, effectively approximating the vehicle's turning behavior while maintaining computational tractability for MILP solvers.
2Reliability
If additional constraints on vehicle dynamics are implemented in MILP processes, then valid trajectories can be produced, but the processes fail when optimal solutions contain velocities close to zero
Solution Approach 1:
The patent extracts the velocity-dependent dynamics constraints from the path planning problem and reformulates them as purely spatial constraints on path point positions and angles. This separation allows the path geometry to be determined independently of velocity considerations, enabling successful planning even when optimal velocities are close to zero.
Solution Approach 2:
Instead of constraining vehicle dynamics directly and deriving the path from dynamic feasibility, the patent inverts the approach by first defining the path geometry through spatial constraints and then determining velocities that satisfy the dynamics. This inversion resolves the conflict between dynamic constraints and low-velocity optimality.
3Loss of time
If conventional MILP path planning is used, then computation is efficient, but the method cannot handle nonlinear constraints such as minimum turning radius
Solution Approach 1:
The patent transforms the nonlinear turning radius constraint into linear constraints by changing the parameters from continuous vehicle states to discrete path point coordinates with fixed inter-point distances and angle constraints. This parameter transformation maintains computational efficiency while enabling the handling of minimum turning radius requirements.
Data Source
AI summary
Disclosed are methods and apparatus for determining a path (4) for a vehicle (2). The method comprises providing starting and final positions for the vehicle (2), and using the provided positions, determining an ordered sequence of points, thereby providing the path (4) for the vehicle (2). Performing the optimisation process comprises: minimising a distance between the final position and a last point in the sequence; for each point other than a last point in the sequence, constraining a distance between that point and the next point to be equal to a predefined distance; and, for each path point other than the first and last points, constraining an angle between a line that connects that point to the point that precedes it and a line that connects that point to the next point to be greater than or equal to a predefined angle.