Aircraft Path Planning Using Linear Waypoint Approximation
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Solution Overview
Problem
Current path planning methodologies for airborne vehicles are inadequate due to their failure to account for non-linear constraints related to height and climb performance, making them complex and computationally intensive, unlike those for ground vehicles which use linear approximations.
Innovation Solution
A method that decomposes the non-linear path planning problem for airborne vehicles into two sequential linear problems, allowing for the determination of optimal waypoint heights and velocity profiles using linear programming techniques, thereby simplifying the process and reducing computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If linear approximation is used in path planning for ground vehicles, then processing speed is improved and computational power required is minimized, but the methodology cannot adequately handle airborne vehicle constraints such as height and climb performance
Solution Approach 1:
The patent segments the path planning problem into discrete waypoints with associated height and time bounds. By dividing the continuous flight path into discrete segments between waypoints, the non-linear airborne vehicle constraints can be handled through a series of linear optimizations at each segment, maintaining computational efficiency while improving accuracy for aircraft-specific constraints.
Solution Approach 2:
The patent transforms the non-linear climb performance constraints into linear parameter relationships by expressing climb rate as a function of speed and height bounds at waypoints. This parameter transformation allows the use of linear programming techniques while still capturing the essential non-linear behavior of aircraft climb performance, resolving the contradiction between computational simplicity and physical accuracy.
2Reliability
If non-linear optimization is used to account for climb performance and speed profiles in airborne vehicles, then accuracy is improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent applies segmentation by dividing the flight path into discrete waypoints and processing each segment independently through linear optimization. This breaks down the complex non-linear problem into manageable linear sub-problems, reducing overall computational complexity while maintaining accuracy through the cumulative effect of optimized segments.
Solution Approach 2:
The patent changes the mathematical parameters from continuous non-linear variables to discrete linear bounds at waypoints. By expressing climb performance and speed constraints as linear inequalities involving height and time bounds at discrete points, the patent enables the use of efficient linear programming algorithms instead of computationally intensive non-linear optimization methods.
3Productivity
If linear programming is used to decompose the path planning problem into two linear sub-problems, then computational effort is reduced and processing speed is improved, but the ability to directly model non-linear climb performance is lost
Solution Approach 1:
The patent applies parameter changes by transforming non-linear climb performance relationships into linear parameter bounds. Instead of directly modeling non-linear climb rate equations, the patent expresses constraints in terms of linear relationships between height, speed, and time at discrete waypoints, allowing linear programming to achieve both computational efficiency and adequate modeling accuracy.
Solution Approach 2:
The patent segments the continuous non-linear climb performance into discrete linear approximations at each waypoint segment. By processing each segment independently with linear constraints and combining the results, the patent achieves computational efficiency through linear programming while maintaining sufficient accuracy through the cumulative optimization of all segments.
Data Source
Figure 1(a)~1(b)
Figure 2~3
Figure 4~4(a)
AI summary
A profiling approach for determining a path for an aircraft, using a method comprising the steps of determining at least two waypoints between a starting position and a desired terminal position for the aircraft, determining a path for the aircraft between the starting position and the terminal position, by performing a linear approximation of the heights of the waypoints such that the average height change between waypoints is minimised, and constrained by a maximum climb angle of said aircraft, and performing a linear approximation of arrival times for each of the waypoints and aircraft speeds between the waypoints, constrained by permissible velocity of said aircraft on the slope between the waypoints. In this way, the non-linear relationship between climb rate and speed is approximated with linear equations, because determination of the path between each set of two waypoints is broken into two linear problems.