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clean up doc dir (#563)
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Atsushi Sakai
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docs/modules/path_planning/path_planning.rst
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docs/modules/path_planning/path_planning.rst
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.. _path_planning:
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Path Planning
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=============
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Dynamic Window Approach
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-----------------------
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This is a 2D navigation sample code with Dynamic Window Approach.
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- `The Dynamic Window Approach to Collision
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Avoidance <https://www.ri.cmu.edu/pub_files/pub1/fox_dieter_1997_1/fox_dieter_1997_1.pdf>`__
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|DWA|
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Grid based search
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-----------------
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Dijkstra algorithm
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~~~~~~~~~~~~~~~~~~
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This is a 2D grid based shortest path planning with Dijkstra's
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algorithm.
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|Dijkstra|
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In the animation, cyan points are searched nodes.
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.. _a*-algorithm:
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A\* algorithm
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~~~~~~~~~~~~~
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This is a 2D grid based shortest path planning with A star algorithm.
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|astar|
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In the animation, cyan points are searched nodes.
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Its heuristic is 2D Euclid distance.
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.. _a*-algorithm:
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D\* algorithm
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~~~~~~~~~~~~~
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This is a 2D grid based shortest path planning with D star algorithm.
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|dstar|
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The animation shows a robot finding its path avoiding an obstacle using the D* search algorithm.
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Ref:
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- `D* search Wikipedia <https://en.wikipedia.org/wiki/D*>`__
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Potential Field algorithm
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~~~~~~~~~~~~~~~~~~~~~~~~~
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This is a 2D grid based path planning with Potential Field algorithm.
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|PotentialField|
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In the animation, the blue heat map shows potential value on each grid.
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Ref:
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- `Robotic Motion Planning:Potential
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Functions <https://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf>`__
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Model Predictive Trajectory Generator
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-------------------------------------
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This is a path optimization sample on model predictive trajectory
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generator.
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This algorithm is used for state lattice planner.
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Path optimization sample
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~~~~~~~~~~~~~~~~~~~~~~~~
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|4|
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Lookup table generation sample
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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|5|
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Ref:
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- `Optimal rough terrain trajectory generation for wheeled mobile
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robots <http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328>`__
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State Lattice Planning
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----------------------
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This script is a path planning code with state lattice planning.
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This code uses the model predictive trajectory generator to solve
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boundary problem.
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Ref:
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- `Optimal rough terrain trajectory generation for wheeled mobile
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robots <http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328>`__
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- `State Space Sampling of Feasible Motions for High-Performance Mobile
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Robot Navigation in Complex
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Environments <http://www.frc.ri.cmu.edu/~alonzo/pubs/papers/JFR_08_SS_Sampling.pdf>`__
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Uniform polar sampling
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~~~~~~~~~~~~~~~~~~~~~~
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|6|
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Biased polar sampling
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~~~~~~~~~~~~~~~~~~~~~
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|7|
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Lane sampling
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~~~~~~~~~~~~~
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|8|
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.. _probabilistic-road-map-(prm)-planning:
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Probabilistic Road-Map (PRM) planning
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-------------------------------------
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|PRM|
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This PRM planner uses Dijkstra method for graph search.
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In the animation, blue points are sampled points,
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Cyan crosses means searched points with Dijkstra method,
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The red line is the final path of PRM.
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Ref:
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- `Probabilistic roadmap -
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Wikipedia <https://en.wikipedia.org/wiki/Probabilistic_roadmap>`__
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Voronoi Road-Map planning
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-------------------------
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|VRM|
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This Voronoi road-map planner uses Dijkstra method for graph search.
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In the animation, blue points are Voronoi points,
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Cyan crosses mean searched points with Dijkstra method,
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The red line is the final path of Vornoi Road-Map.
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Ref:
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- `Robotic Motion
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Planning <https://www.cs.cmu.edu/~motionplanning/lecture/Chap5-RoadMap-Methods_howie.pdf>`__
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.. _rapidly-exploring-random-trees-(rrt):
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Rapidly-Exploring Random Trees (RRT)
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------------------------------------
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Basic RRT
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~~~~~~~~~
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|9|
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This is a simple path planning code with Rapidly-Exploring Random Trees
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(RRT)
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Black circles are obstacles, green line is a searched tree, red crosses
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are start and goal positions.
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.. _rrt*:
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RRT\*
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~~~~~
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|10|
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This is a path planning code with RRT\*
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Black circles are obstacles, green line is a searched tree, red crosses
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are start and goal positions.
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.. include:: rrt_star.rst
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Ref:
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- `Incremental Sampling-based Algorithms for Optimal Motion
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Planning <https://arxiv.org/abs/1005.0416>`__
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- `Sampling-based Algorithms for Optimal Motion
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Planning <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.419.5503&rep=rep1&type=pdf>`__
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RRT with dubins path
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~~~~~~~~~~~~~~~~~~~~
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|PythonRobotics|
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Path planning for a car robot with RRT and dubins path planner.
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.. _rrt*-with-dubins-path:
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RRT\* with dubins path
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~~~~~~~~~~~~~~~~~~~~~~
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|AtsushiSakai/PythonRobotics|
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Path planning for a car robot with RRT\* and dubins path planner.
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.. _rrt*-with-reeds-sheep-path:
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RRT\* with reeds-sheep path
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~~~~~~~~~~~~~~~~~~~~~~~~~~~
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|11|
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Path planning for a car robot with RRT\* and reeds sheep path planner.
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.. _informed-rrt*:
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Informed RRT\*
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~~~~~~~~~~~~~~
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|irrt|
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This is a path planning code with Informed RRT*.
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The cyan ellipse is the heuristic sampling domain of Informed RRT*.
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Ref:
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- `Informed RRT\*: Optimal Sampling-based Path Planning Focused via
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Direct Sampling of an Admissible Ellipsoidal
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Heuristic <https://arxiv.org/pdf/1404.2334.pdf>`__
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.. _batch-informed-rrt*:
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Batch Informed RRT\*
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~~~~~~~~~~~~~~~~~~~~
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|irrt2|
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This is a path planning code with Batch Informed RRT*.
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Ref:
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- `Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the
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Heuristically Guided Search of Implicit Random Geometric
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Graphs <https://arxiv.org/abs/1405.5848>`__
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.. _closed-loop-rrt*:
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Closed Loop RRT\*
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~~~~~~~~~~~~~~~~~
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A vehicle model based path planning with closed loop RRT*.
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|CLRRT|
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In this code, pure-pursuit algorithm is used for steering control,
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PID is used for speed control.
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Ref:
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- `Motion Planning in Complex Environments using Closed-loop
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Prediction <http://acl.mit.edu/papers/KuwataGNC08.pdf>`__
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- `Real-time Motion Planning with Applications to Autonomous Urban
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Driving <http://acl.mit.edu/papers/KuwataTCST09.pdf>`__
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- `[1601.06326] Sampling-based Algorithms for Optimal Motion Planning
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Using Closed-loop Prediction <https://arxiv.org/abs/1601.06326>`__
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.. _lqr-rrt*:
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LQR-RRT\*
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~~~~~~~~~
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This is a path planning simulation with LQR-RRT*.
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A double integrator motion model is used for LQR local planner.
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|LQRRRT|
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Ref:
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- `LQR-RRT\*: Optimal Sampling-Based Motion Planning with Automatically
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Derived Extension
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Heuristics <http://lis.csail.mit.edu/pubs/perez-icra12.pdf>`__
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- `MahanFathi/LQR-RRTstar: LQR-RRT\* method is used for random motion
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planning of a simple pendulum in its phase
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plot <https://github.com/MahanFathi/LQR-RRTstar>`__
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Cubic spline planning
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---------------------
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A sample code for cubic path planning.
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This code generates a curvature continuous path based on x-y waypoints
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with cubic spline.
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Heading angle of each point can be also calculated analytically.
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|12|
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|14|
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B-Spline planning
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-----------------
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|B-Spline|
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This is a path planning with B-Spline curse.
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If you input waypoints, it generates a smooth path with B-Spline curve.
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The final course should be on the first and last waypoints.
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Ref:
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- `B-spline - Wikipedia <https://en.wikipedia.org/wiki/B-spline>`__
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.. _eta^3-spline-path-planning:
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Eta^3 Spline path planning
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--------------------------
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|eta3|
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This is a path planning with Eta^3 spline.
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Ref:
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- `\\eta^3-Splines for the Smooth Path Generation of Wheeled Mobile
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Robots <https://ieeexplore.ieee.org/document/4339545/>`__
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Bezier path planning
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--------------------
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A sample code of Bezier path planning.
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It is based on 4 control points Beier path.
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|Bezier1|
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If you change the offset distance from start and end point,
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You can get different Beizer course:
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|Bezier2|
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Ref:
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- `Continuous Curvature Path Generation Based on Bezier Curves for
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Autonomous
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Vehicles <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.294.6438&rep=rep1&type=pdf>`__
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Quintic polynomials planning
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----------------------------
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Motion planning with quintic polynomials.
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|2|
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It can calculate 2D path, velocity, and acceleration profile based on
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quintic polynomials.
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Ref:
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- `Local Path Planning And Motion Control For Agv In
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Positioning <http://ieeexplore.ieee.org/document/637936/>`__
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Dubins path planning
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--------------------
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A sample code for Dubins path planning.
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|dubins|
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Ref:
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- `Dubins path -
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Wikipedia <https://en.wikipedia.org/wiki/Dubins_path>`__
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Reeds Shepp planning
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--------------------
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A sample code with Reeds Shepp path planning.
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|RSPlanning|
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Ref:
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- `15.3.2 Reeds-Shepp
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Curves <http://planning.cs.uiuc.edu/node822.html>`__
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- `optimal paths for a car that goes both forwards and
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backwards <https://pdfs.semanticscholar.org/932e/c495b1d0018fd59dee12a0bf74434fac7af4.pdf>`__
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- `ghliu/pyReedsShepp: Implementation of Reeds Shepp
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curve. <https://github.com/ghliu/pyReedsShepp>`__
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LQR based path planning
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-----------------------
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A sample code using LQR based path planning for double integrator model.
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|RSPlanning2|
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Optimal Trajectory in a Frenet Frame
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------------------------------------
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|15|
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This is optimal trajectory generation in a Frenet Frame.
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The cyan line is the target course and black crosses are obstacles.
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The red line is predicted path.
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Ref:
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- `Optimal Trajectory Generation for Dynamic Street Scenarios in a
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Frenet
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Frame <https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf>`__
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- `Optimal trajectory generation for dynamic street scenarios in a
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Frenet Frame <https://www.youtube.com/watch?v=Cj6tAQe7UCY>`__
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.. |DWA| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DynamicWindowApproach/animation.gif
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.. |Dijkstra| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Dijkstra/animation.gif
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.. |astar| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/AStar/animation.gif
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.. |dstar| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStar/animation.gif
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.. |PotentialField| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/PotentialFieldPlanning/animation.gif
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.. |4| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ModelPredictiveTrajectoryGenerator/kn05animation.gif
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.. |5| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/ModelPredictiveTrajectoryGenerator/lookuptable.png?raw=True
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.. |6| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/UniformPolarSampling.gif
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.. |7| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/BiasedPolarSampling.gif
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.. |8| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/LaneSampling.gif
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.. |PRM| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ProbabilisticRoadMap/animation.gif
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.. |VRM| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/VoronoiRoadMap/animation.gif
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.. |9| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRT/animation.gif
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.. |10| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTstar/animation.gif
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.. |PythonRobotics| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTDubins/animation.gif
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.. |AtsushiSakai/PythonRobotics| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarDubins/animation.gif
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.. |11| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarReedsShepp/animation.gif
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.. |irrt| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/InformedRRTStar/animation.gif
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.. |irrt2| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BatchInformedRRTStar/animation.gif
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.. |CLRRT| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClosedLoopRRTStar/animation.gif
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.. |LQRRRT| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRRRTStar/animation.gif
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.. |12| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/CubicSpline/Figure_1.png?raw=True
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.. |13| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/CubicSpline/Figure_2.png?raw=True
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.. |14| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/CubicSpline/Figure_3.png?raw=True
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.. |B-Spline| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BSplinePath/Figure_1.png?raw=True
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.. |eta3| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Eta3SplinePath/animation.gif
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.. |Bezier1| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BezierPath/Figure_1.png?raw=True
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.. |Bezier2| image:: https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BezierPath/Figure_2.png?raw=True
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.. |2| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/QuinticPolynomialsPlanner/animation.gif
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.. |dubins| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DubinsPath/animation.gif?raw=True
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.. |RSPlanning| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ReedsSheppPath/animation.gif?raw=true
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.. |RSPlanning2| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRPlanner/animation.gif?raw=true
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.. |15| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/animation.gif
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