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2.5 KiB
ReStructuredText
77 lines
2.5 KiB
ReStructuredText
Dubins path planning
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A sample code for Dubins path planning.
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.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DubinsPath/animation.gif?raw=True
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Dubins path
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~~~~~~~~~~~~
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Dubins path is a analytical path planning algorithm for a simple car model.
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It can generates a shortest path between two 2D poses (x, y, yaw) with maximum curvature constraint and tangent(yaw angle) constraint.
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Generated paths consist of 3 segments of maximum curvature curves or a straight line segment.
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Each segment type can is categorized by 3 type: 'Right turn (R)' , 'Left turn (L)', and 'Straight (S).'
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Possible path will be at least one of these six types: RSR, RSL, LSR, LSL, RLR, LRL.
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Dubins path planner can output each segment type and distance of each course segment.
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For example, a RSR Dubins path is:
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.. image:: RSR.jpg
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:width: 400px
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Each segment distance can be calculated by:
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:math:`\alpha = mod(-\theta)`
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:math:`\beta = mod(x_{e, yaw} - \theta)`
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:math:`p^2 = 2 + d ^ 2 - 2\cos(\alpha-\beta) + 2d(\sin\alpha - \sin\beta)`
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:math:`t = atan2(\cos\beta - \cos\alpha, d + \sin\alpha - \sin\beta)`
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:math:`d_1 = mod(-\alpha + t)`
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:math:`d_2 = p`
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:math:`d_3 = mod(\beta - t)`
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where :math:`\theta` is tangent and d is distance from :math:`x_s` to :math:`x_e`
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A RLR Dubins path is:
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.. image:: RLR.jpg
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:width: 200px
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Each segment distance can be calculated by:
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:math:`t = (6.0 - d^2 + 2\cos(\alpha-\beta) + 2d(\sin\alpha - \sin\beta)) / 8.0`
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:math:`d_2 = mod(2\pi - acos(t))`
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:math:`d_1 = mod(\alpha - atan2(\cos\beta - \cos\alpha, d + \sin\alpha - \sin\beta) + d_2 / 2.0)`
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:math:`d_3 = mod(\alpha - \beta - d_1 + d_2)`
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You can generate a path from these information and the maximum curvature information.
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A path type which has minimum course length among 6 types is selected,
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and then a path is constructed based on the selected type and its distances.
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API
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~~~~~~~~~~~~~~~~~~~~
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.. autofunction:: PathPlanning.DubinsPath.dubins_path_planner.plan_dubins_path
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Reference
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~~~~~~~~~~~~~~~~~~~~
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- `On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents <https://www.jstor.org/stable/2372560?origin=crossref>`__
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- `Dubins path - Wikipedia <https://en.wikipedia.org/wiki/Dubins_path>`__
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- `15.3.1 Dubins Curves <http://planning.cs.uiuc.edu/node821.html>`__
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- `A Comprehensive, Step-by-Step Tutorial to Computing Dubin’s Paths <https://gieseanw.wordpress.com/2012/10/21/a-comprehensive-step-by-step-tutorial-to-computing-dubins-paths/>`__
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