1 / 26

Automated Guided Vehicle Optimal Control Problem

Automated Guided Vehicle Optimal Control Problem. Preliminary Research. Reijer Idema. Automated Guided Vehicle Optimal Control Problem. Supervisors: prof.dr.ir. P. Wesseling dr.ir. Kees Vuik ir. Patrick H.F. Segeren dr.ir. Ren é Jager. FROG Navigation Systems. FROG Navigation Systems

jill
Download Presentation

Automated Guided Vehicle Optimal Control Problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Automated Guided VehicleOptimal Control Problem Preliminary Research Reijer Idema

  2. Automated Guided Vehicle Optimal Control Problem Supervisors: prof.dr.ir.P.Wesseling dr.ir.KeesVuik ir.Patrick H.F. Segeren dr.ir.René Jager

  3. FROG Navigation Systems FROG Navigation Systems www.frog.nl • AGV : Automated Guided Vehicle • industrial transport • public transport • entertainment • FROG : Free Ranging On Grid • grid of magnets

  4. FROG Navigation Systems

  5. Problem Formulation (Textual) Suppose an AGV has to perform an action in the world. Find the best control input for the AGV to achieve the action.

  6. Example Problem 1/3 Vehicle model: • point mass • throttle on/off • instant steering • orientation = path direction Vehicle task: • hallway (2D) • collect at A • deliver at B

  7. Example Problem 2/3 Internal state space: • throttle: • steering wheel: • collect/deliver:N/A External state space: • position: • orientation: • velocity: • collect/deliver: N/A

  8. Example Problem 3/3 Task: • begin position/orientation • end position/orientation Internal Constraints: • [no jumping] • [no sharp corners] External Constraints: • keep clear of obstacles

  9. Constraint Projection

  10. Problem Formulation (Mathematical)

  11. Tools Path description: • NURBS curves Solver Algorithm: • Local search methods

  12. NURBS Curves NURBS: Non-Uniform Rational B-Spline: • parametric curve: C(u) = (x(u),y(u)) • piecewise rational function

  13. B-Spline Definition

  14. Knot Vector Properties Knot vector: U = {u0,…,um} • knot multiplicity k • non-periodic: u0 = … = up = a um-p = … = um = b consequence: C(u0)=P0, C(um)=Pn

  15. Basis Function Properties Basis function: Ni,p(u;U) • depends only on degree p and knot vector U • local support property: • partition of unity • non-negativity • polynomial on each knot span • C on the interior of a knot span • Cp-k at a knot with multiplicity k

  16. Cubic Basis Functions

  17. B-Spline Properties B-Spline: C(u;P,U) • piecewise polynomial • C on the interior of a knot span • Cp-k at a knot with multiplicity k • local modification scheme moving Pi modifies C(u) only on [ui,ui+p+1) • strong convex hull property

  18. NURBS Definition

  19. NURBS Properties NURBS: C(u;P,U,W) • piecewise rational • C on the interior of a knot span • Cp-k at a knot with multiplicity k • local modification scheme moving Pi or changing wi modifies C(u) only on [ui,ui+p+1) • strong convex hull property

  20. Homogeneous Representation A rational curves of dimension d can be represented by a non-rational curve of dimension d+1 using homogeneous coordinates.

  21. B-Spline Operations 1/2 • knot insertion and knot refinement • knot removal • degree elevation • degree reduction • point inversion and point projection • reparameterization • conversion to and from piecewise power basis form

  22. B-Spline Operations 2/2 • control point and weight modification relatively easy calculations • high level shaping tools warping, flattening, bending and constraint based curve shaping • curve fitting interpolation and approximation

  23. Research Planning 1/3 Task: • path from A to B Vehicle model: • point mass • 2D work area • orientation = path direction • disconnect velocity Extensions: • vehicle body • higher dimensions (crabbing, etc.)

  24. Research Planning 2/3 Internal constraints: • general description • constraint preserving operations External constraints: • hull curve • collision free path

  25. Research Planning 3/3 Cost and heuristics: • cost function time, energy consumption • heuristics straight, circular corner Solver algorithm: • highly constructive • local search

  26. Q & A ?

More Related