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3D Trajectory Planning for Underactuated Vehicles

Learn about PRM-based trajectory planning in 3D space for underactuated vehicles, including aircraft dynamics modeling and stability adjustment techniques. Explore PRM-based path planning and homing guidance strategies for efficient motion planning.

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3D Trajectory Planning for Underactuated Vehicles

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  1. CS326a Motion Planning Professor J-C. Latombe PRM-based Trajectory Planningfor Underactuated Vehiclesin 3-D Space Dongkyu Choi Jinwhan Kim

  2. Aircraft Dynamics Model • 6 DOF (3 positions & 3 orientations) • 12 states (x, u, z, u, v, w, , , , p, q, r) • 2 inputs (E, R)

  3. Equations of Motion in 3-D Space

  4. -4.4110  4.3150 j -0.0100  0.0401 j -4.4110  4.3150 j -0.0310  0.0273 j -0.1792  2.0316 j -2.5724 0.0017 -1.7120  1.1595 j 0.0000 0.0000 Stability Adjustment • Twin-piston engined general aviation aircraft Vcruise = 250 km Length ≈ 10 m • Poles of the longitudinal modes • Poles of the lateral modes

  5. PRM based Path-Planning • Pseudo-code (D. Hsu, R. Kindel, J.C. Latombe, and S. Rock , 2002 ) Insert an initial milestone into T(Milestone set) Repeat Pick a milestone m from T with a probability Pick a control function u from U with a probability Pick a time duration td for propagation m’ = Propagate(m,u,td) if a path from m to m’ is collision-free Add m’ into T If m’Endgame region exit with success if I=N exit with failure

  6. Milestone Scatter Plot R=50° , E=50° , w/o Speed Constr. R=30° , E=20° , w/o Speed Constr. R=30° , E=10° , w/ Speed Constr.

  7. Homing Guidance and Control Bearing Angle • Assume (t) = 0 • This can be accomplished by controlling ailerons. • This makes it possible to decouple 6-DOF dynamics into vertical and horizontal dynamics. • Vertical-mode PD controller • Horizontal-mode PD controller

  8. Modified PRM based Path-Planning • Pseudo-code Insert an initial milestone into T(Milestone set) Repeat Pick a milestone m from T with a probability Pick a control function u from U with a probability Pick a time duration td for propagation m’ = Propagate(m,u,td) if a path from m to m’ is collision-free Add m’ into T If m’  Endgame region exit with success // Apply homing control uh(t) from m’ to the goal If (m’ = Propagate(m, uh(t),td<tlim))  Endgame region exit with success if i=N exit with failure

  9. Example: Planned Path

  10. Example: Planned Path(cont’d)

  11. Performance Statistics

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