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Simple Trajectory Smoothing for UAV Reference Path Planning Based on Decoupling, Spatial Modeling and Linear Programming

Mogens Plessen

Abstract

A method for trajectory smoothing for UAV reference path planning is presented. It is derived based on the dynamics of a Dubins airplane model, and involves a decoupling step, spatial modeling and linear programming. The decoupling step enables algebraic control laws for flight-path angle and speed control. Only for roll angle control an optimization step is applied, involving the solution of a small linear program. Two variations are discussed. They differ by reference centerline tracking and the introduction of a path shaping constraint. The benefit of natural dimensionality reduction for spatial modeling is discussed. The simplicity of the overall method is highlighted. An extension to acrobative flight is outlined, which comes at the cost of a model approximation, however at the gain of maintaining the general model structure. An extension of the method to tractor path planning along 3D terrain is discussed. The method is validated in simulations.

Simple Trajectory Smoothing for UAV Reference Path Planning Based on Decoupling, Spatial Modeling and Linear Programming

Abstract

A method for trajectory smoothing for UAV reference path planning is presented. It is derived based on the dynamics of a Dubins airplane model, and involves a decoupling step, spatial modeling and linear programming. The decoupling step enables algebraic control laws for flight-path angle and speed control. Only for roll angle control an optimization step is applied, involving the solution of a small linear program. Two variations are discussed. They differ by reference centerline tracking and the introduction of a path shaping constraint. The benefit of natural dimensionality reduction for spatial modeling is discussed. The simplicity of the overall method is highlighted. An extension to acrobative flight is outlined, which comes at the cost of a model approximation, however at the gain of maintaining the general model structure. An extension of the method to tractor path planning along 3D terrain is discussed. The method is validated in simulations.
Paper Structure (12 sections, 16 equations, 6 figures)

This paper contains 12 sections, 16 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Problem Solution
  4. Decoupling of dynamics
  5. Step 1: Control of flight-path angle $\gamma$
  6. Step 2: Control of roll angle $\phi$
  7. Step 3: Speed control $v$
  8. Extension for acrobatic flight
  9. Extension for tractor path planning along 3D terrain
  10. Numerical Experiments
  11. Discussion, Limitations and Outlook
  12. Conclusion

Figures (6)

  • Figure 1: Illustration of the Dubins airplane model. For simplicity it is depicted as a triangle. States and control variables are annotated. Different colors are used to differentiate positions, angles and velocity. See \ref{['eq_dubins']} for interpretation.
  • Figure 2: Illustration of the effects of LP1 and LP2 for an edgy reference smoothing example.
  • Figure 3: Illustration of 10 numerical experiments. For Ex. 1 a path generated by the method from mclain2014implementing served as reference. For the other examples waypoints were defined, then connected by uniform interpolation, before the method from Sect. \ref{['subsec_gamma']}-\ref{['subsec_acrobatic']} was applied. For example, for Ex. 3 there were 9 waypoints.
  • Figure 4: Illustration of a detail discussed in Sect. \ref{['subsec_gamma']}.
  • Figure 5: A very unfavorable reference can still be tracked. See Sect. \ref{['sec_discussion']}.
  • ...and 1 more figures