mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
synced 2026-01-12 23:58:04 -05:00
fix batch_informed_rrtstar.py
This commit is contained in:
Atsushi Sakai
@@ -14,10 +14,11 @@ author: Karan Chawla(@karanchawla)
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Reference: https://arxiv.org/abs/1405.5848
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"""
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import random
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import numpy as np
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import math
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import random
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import matplotlib.pyplot as plt
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import numpy as np
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show_animation = True
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@@ -26,8 +27,14 @@ class RTree(object):
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# Class to represent the explicit tree created
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# while sampling through the state space
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def __init__(self, start=[0, 0], lowerLimit=[0, 0], upperLimit=[10, 10], resolution=1):
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def __init__(self, start=None, lowerLimit=None, upperLimit=None, resolution=1.0):
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if upperLimit is None:
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upperLimit = [10, 10]
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if lowerLimit is None:
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lowerLimit = [0, 0]
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if start is None:
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start = [0, 0]
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self.vertices = dict()
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self.edges = []
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self.start = start
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@@ -42,20 +49,21 @@ class RTree(object):
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self.num_cells[idx] = np.ceil(
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(upperLimit[idx] - lowerLimit[idx]) / resolution)
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vertex_id = self.realWorldToNodeId(start)
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vertex_id = self.real_world_to_node_id(start)
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self.vertices[vertex_id] = []
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def getRootId(self):
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@staticmethod
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def get_root_id():
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# return the id of the root of the tree
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return 0
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def addVertex(self, vertex):
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def add_vertex(self, vertex):
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# add a vertex to the tree
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vertex_id = self.realWorldToNodeId(vertex)
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vertex_id = self.real_world_to_node_id(vertex)
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self.vertices[vertex_id] = []
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return vertex_id
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def addEdge(self, v, x):
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def add_edge(self, v, x):
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# create an edge between v and x vertices
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if (v, x) not in self.edges:
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self.edges.append((v, x))
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@@ -63,7 +71,7 @@ class RTree(object):
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self.vertices[v].append(x)
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self.vertices[x].append(v)
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def realCoordsToGridCoord(self, real_coord):
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def real_coords_to_grid_coord(self, real_coord):
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# convert real world coordinates to grid space
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# depends on the resolution of the grid
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# the output is the same as real world coords if the resolution
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@@ -71,10 +79,10 @@ class RTree(object):
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coord = [0] * self.dimension
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for i in range(len(coord)):
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start = self.lowerLimit[i] # start of the grid space
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coord[i] = np.around((real_coord[i] - start) / self.resolution)
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coord[i] = int(np.around((real_coord[i] - start) / self.resolution))
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return coord
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def gridCoordinateToNodeId(self, coord):
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def grid_coordinate_to_node_id(self, coord):
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# This function maps a grid coordinate to a unique
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# node id
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nodeId = 0
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@@ -85,12 +93,12 @@ class RTree(object):
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nodeId = nodeId + coord[i] * product
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return nodeId
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def realWorldToNodeId(self, real_coord):
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def real_world_to_node_id(self, real_coord):
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# first convert the given coordinates to grid space and then
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# convert the grid space coordinates to a unique node id
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return self.gridCoordinateToNodeId(self.realCoordsToGridCoord(real_coord))
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return self.grid_coordinate_to_node_id(self.real_coords_to_grid_coord(real_coord))
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def gridCoordToRealWorldCoord(self, coord):
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def grid_coord_to_real_world_coord(self, coord):
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# This function smaps a grid coordinate in discrete space
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# to a configuration in the full configuration space
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config = [0] * self.dimension
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@@ -102,7 +110,7 @@ class RTree(object):
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config[i] = start + grid_step
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return config
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def nodeIdToGridCoord(self, node_id):
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def node_id_to_grid_coord(self, node_id):
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# This function maps a node id to the associated
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# grid coordinate
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coord = [0] * len(self.lowerLimit)
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@@ -115,12 +123,10 @@ class RTree(object):
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node_id = node_id - (coord[i] * prod)
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return coord
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def nodeIdToRealWorldCoord(self, nid):
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# This function maps a node in discrete space to a configuraiton
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def node_id_to_real_world_coord(self, nid):
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# This function maps a node in discrete space to a configuration
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# in the full configuration space
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return self.gridCoordToRealWorldCoord(self.nodeIdToGridCoord(nid))
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# Uses Batch Informed Trees to find a path from start to goal
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return self.grid_coord_to_real_world_coord(self.node_id_to_grid_coord(nid))
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class BITStar(object):
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@@ -135,6 +141,8 @@ class BITStar(object):
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self.maxrand = randArea[1]
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self.maxIter = maxIter
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self.obstacleList = obstacleList
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self.startId = None
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self.goalId = None
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self.vertex_queue = []
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self.edge_queue = []
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@@ -154,8 +162,8 @@ class BITStar(object):
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upperLimit=upperLimit, resolution=0.01)
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def setup_planning(self):
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self.startId = self.tree.realWorldToNodeId(self.start)
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self.goalId = self.tree.realWorldToNodeId(self.goal)
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self.startId = self.tree.real_world_to_node_id(self.start)
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self.goalId = self.tree.real_world_to_node_id(self.goal)
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# add goal to the samples
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self.samples[self.goalId] = self.goal
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@@ -163,9 +171,9 @@ class BITStar(object):
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self.f_scores[self.goalId] = 0
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# add the start id to the tree
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self.tree.addVertex(self.start)
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self.tree.add_vertex(self.start)
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self.g_scores[self.startId] = 0
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self.f_scores[self.startId] = self.computeHeuristicCost(
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self.f_scores[self.startId] = self.compute_heuristic_cost(
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self.startId, self.goalId)
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# max length we expect to find in our 'informed' sample space, starts as infinite
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@@ -182,11 +190,11 @@ class BITStar(object):
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# first column of idenity matrix transposed
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id1_t = np.array([1.0, 0.0, 0.0]).reshape(1, 3)
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M = np.dot(a1, id1_t)
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U, S, Vh = np.linalg.svd(M, 1, 1)
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U, S, Vh = np.linalg.svd(M, True, True)
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C = np.dot(np.dot(U, np.diag(
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[1.0, 1.0, np.linalg.det(U) * np.linalg.det(np.transpose(Vh))])), Vh)
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self.samples.update(self.informedSample(
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self.samples.update(self.informed_sample(
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200, cBest, cMin, xCenter, C))
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return etheta, cMin, xCenter, C, cBest
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@@ -207,7 +215,7 @@ class BITStar(object):
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else:
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m = 100
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cBest = self.g_scores[self.goalId]
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self.samples.update(self.informedSample(
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self.samples.update(self.informed_sample(
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m, cBest, cMin, xCenter, C))
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# make the old vertices the new vertices
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@@ -225,26 +233,25 @@ class BITStar(object):
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foundGoal = False
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# run until done
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while (iterations < self.maxIter):
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while iterations < self.maxIter:
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cBest = self.setup_sample(iterations,
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foundGoal, cMin, xCenter, C, cBest)
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# expand the best vertices until an edge is better than the vertex
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# this is done because the vertex cost represents the lower bound
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# on the edge cost
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while(self.bestVertexQueueValue() <= self.bestEdgeQueueValue()):
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self.expandVertex(self.bestInVertexQueue())
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while self.best_vertex_queue_value() <= self.best_edge_queue_value():
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self.expand_vertex(self.best_in_vertex_queue())
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# add the best edge to the tree
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bestEdge = self.bestInEdgeQueue()
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bestEdge = self.best_in_edge_queue()
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self.edge_queue.remove(bestEdge)
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# Check if this can improve the current solution
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estimatedCostOfVertex = self.g_scores[bestEdge[0]] + self.computeDistanceCost(
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bestEdge[0], bestEdge[1]) + self.computeHeuristicCost(bestEdge[1], self.goalId)
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estimatedCostOfEdge = self.computeDistanceCost(self.startId, bestEdge[0]) + self.computeHeuristicCost(
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bestEdge[0], bestEdge[1]) + self.computeHeuristicCost(bestEdge[1], self.goalId)
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actualCostOfEdge = self.g_scores[bestEdge[0]] + \
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self.computeDistanceCost(bestEdge[0], bestEdge[1])
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estimatedCostOfVertex = self.g_scores[bestEdge[0]] + self.compute_distance_cost(
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bestEdge[0], bestEdge[1]) + self.compute_heuristic_cost(bestEdge[1], self.goalId)
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estimatedCostOfEdge = self.compute_distance_cost(self.startId, bestEdge[0]) + self.compute_heuristic_cost(
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bestEdge[0], bestEdge[1]) + self.compute_heuristic_cost(bestEdge[1], self.goalId)
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actualCostOfEdge = self.g_scores[bestEdge[0]] + self.compute_distance_cost(bestEdge[0], bestEdge[1])
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f1 = estimatedCostOfVertex < self.g_scores[self.goalId]
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f2 = estimatedCostOfEdge < self.g_scores[self.goalId]
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@@ -252,46 +259,44 @@ class BITStar(object):
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if f1 and f2 and f3:
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# connect this edge
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firstCoord = self.tree.nodeIdToRealWorldCoord(
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firstCoord = self.tree.node_id_to_real_world_coord(
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bestEdge[0])
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secondCoord = self.tree.nodeIdToRealWorldCoord(
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secondCoord = self.tree.node_id_to_real_world_coord(
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bestEdge[1])
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path = self.connect(firstCoord, secondCoord)
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lastEdge = self.tree.realWorldToNodeId(secondCoord)
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lastEdge = self.tree.real_world_to_node_id(secondCoord)
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if path is None or len(path) == 0:
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continue
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nextCoord = path[len(path) - 1, :]
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nextCoordPathId = self.tree.realWorldToNodeId(
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nextCoordPathId = self.tree.real_world_to_node_id(
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nextCoord)
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bestEdge = (bestEdge[0], nextCoordPathId)
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if(bestEdge[1] in self.tree.vertices.keys()):
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if bestEdge[1] in self.tree.vertices.keys():
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continue
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else:
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try:
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del self.samples[bestEdge[1]]
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except(KeyError):
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except KeyError:
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pass
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eid = self.tree.addVertex(nextCoord)
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eid = self.tree.add_vertex(nextCoord)
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self.vertex_queue.append(eid)
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if eid == self.goalId or bestEdge[0] == self.goalId or bestEdge[1] == self.goalId:
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print("Goal found")
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foundGoal = True
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self.tree.addEdge(bestEdge[0], bestEdge[1])
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self.tree.add_edge(bestEdge[0], bestEdge[1])
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g_score = self.computeDistanceCost(
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g_score = self.compute_distance_cost(
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bestEdge[0], bestEdge[1])
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self.g_scores[bestEdge[1]] = g_score + \
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self.g_scores[bestEdge[0]]
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self.f_scores[bestEdge[1]] = g_score + \
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self.computeHeuristicCost(bestEdge[1], self.goalId)
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self.updateGraph()
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self.g_scores[bestEdge[1]] = g_score + self.g_scores[bestEdge[0]]
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self.f_scores[bestEdge[1]] = g_score + self.compute_heuristic_cost(bestEdge[1], self.goalId)
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self.update_graph()
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# visualize new edge
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if animation:
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self.drawGraph(xCenter=xCenter, cBest=cBest,
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cMin=cMin, etheta=etheta, samples=self.samples.values(),
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start=firstCoord, end=secondCoord, tree=self.tree.edges)
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self.draw_graph(xCenter=xCenter, cBest=cBest,
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cMin=cMin, etheta=etheta, samples=self.samples.values(),
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start=firstCoord, end=secondCoord)
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self.remove_queue(lastEdge, bestEdge)
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@@ -306,14 +311,13 @@ class BITStar(object):
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return self.find_final_path()
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def find_final_path(self):
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plan = []
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plan.append(self.goal)
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plan = [self.goal]
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currId = self.goalId
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while (currId != self.startId):
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plan.append(self.tree.nodeIdToRealWorldCoord(currId))
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while currId != self.startId:
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plan.append(self.tree.node_id_to_real_world_coord(currId))
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try:
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currId = self.nodes[currId]
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except(KeyError):
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except KeyError:
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print("cannot find Path")
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return []
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@@ -324,29 +328,30 @@ class BITStar(object):
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def remove_queue(self, lastEdge, bestEdge):
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for edge in self.edge_queue:
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if(edge[1] == bestEdge[1]):
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if self.g_scores[edge[1]] + self.computeDistanceCost(edge[1], bestEdge[1]) >= self.g_scores[self.goalId]:
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if(lastEdge, bestEdge[1]) in self.edge_queue:
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if edge[1] == bestEdge[1]:
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dist_cost = self.compute_distance_cost(edge[1], bestEdge[1])
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if self.g_scores[edge[1]] + dist_cost >= self.g_scores[self.goalId]:
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if (lastEdge, bestEdge[1]) in self.edge_queue:
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self.edge_queue.remove(
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(lastEdge, bestEdge[1]))
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def connect(self, start, end):
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# A function which attempts to extend from a start coordinates
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# to goal coordinates
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steps = int(self.computeDistanceCost(self.tree.realWorldToNodeId(
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start), self.tree.realWorldToNodeId(end)) * 10)
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steps = int(self.compute_distance_cost(self.tree.real_world_to_node_id(
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start), self.tree.real_world_to_node_id(end)) * 10)
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x = np.linspace(start[0], end[0], num=steps)
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y = np.linspace(start[1], end[1], num=steps)
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for i in range(len(x)):
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if(self._collisionCheck(x[i], y[i])):
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if(i == 0):
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if self._collision_check(x[i], y[i]):
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if i == 0:
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return None
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# if collision, send path until collision
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return np.vstack((x[0:i], y[0:i])).transpose()
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return np.vstack((x, y)).transpose()
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def _collisionCheck(self, x, y):
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def _collision_check(self, x, y):
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for (ox, oy, size) in self.obstacleList:
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dx = ox - x
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dy = oy - y
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@@ -355,45 +360,44 @@ class BITStar(object):
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return True # collision
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return False
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# def prune(self, c):
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def computeHeuristicCost(self, start_id, goal_id):
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def compute_heuristic_cost(self, start_id, goal_id):
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# Using Manhattan distance as heuristic
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start = np.array(self.tree.nodeIdToRealWorldCoord(start_id))
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goal = np.array(self.tree.nodeIdToRealWorldCoord(goal_id))
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start = np.array(self.tree.node_id_to_real_world_coord(start_id))
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goal = np.array(self.tree.node_id_to_real_world_coord(goal_id))
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return np.linalg.norm(start - goal, 2)
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def computeDistanceCost(self, vid, xid):
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def compute_distance_cost(self, vid, xid):
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# L2 norm distance
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start = np.array(self.tree.nodeIdToRealWorldCoord(vid))
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stop = np.array(self.tree.nodeIdToRealWorldCoord(xid))
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start = np.array(self.tree.node_id_to_real_world_coord(vid))
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stop = np.array(self.tree.node_id_to_real_world_coord(xid))
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return np.linalg.norm(stop - start, 2)
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# Sample free space confined in the radius of ball R
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def informedSample(self, m, cMax, cMin, xCenter, C):
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def informed_sample(self, m, cMax, cMin, xCenter, C):
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samples = dict()
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print("g_Score goal id: ", self.g_scores[self.goalId])
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for i in range(m + 1):
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if cMax < float('inf'):
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r = [cMax / 2.0,
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math.sqrt(cMax**2 - cMin**2) / 2.0,
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math.sqrt(cMax**2 - cMin**2) / 2.0]
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math.sqrt(cMax ** 2 - cMin ** 2) / 2.0,
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math.sqrt(cMax ** 2 - cMin ** 2) / 2.0]
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L = np.diag(r)
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xBall = self.sampleUnitBall()
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xBall = self.sample_unit_ball()
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rnd = np.dot(np.dot(C, L), xBall) + xCenter
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rnd = [rnd[(0, 0)], rnd[(1, 0)]]
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random_id = self.tree.realWorldToNodeId(rnd)
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random_id = self.tree.real_world_to_node_id(rnd)
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samples[random_id] = rnd
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else:
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rnd = self.sampleFreeSpace()
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random_id = self.tree.realWorldToNodeId(rnd)
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rnd = self.sample_free_space()
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random_id = self.tree.real_world_to_node_id(rnd)
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samples[random_id] = rnd
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return samples
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# Sample point in a unit ball
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def sampleUnitBall(self):
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@staticmethod
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def sample_unit_ball():
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a = random.random()
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b = random.random()
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@@ -404,63 +408,64 @@ class BITStar(object):
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b * math.sin(2 * math.pi * a / b))
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return np.array([[sample[0]], [sample[1]], [0]])
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def sampleFreeSpace(self):
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def sample_free_space(self):
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rnd = [random.uniform(self.minrand, self.maxrand),
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random.uniform(self.minrand, self.maxrand)]
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return rnd
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def bestVertexQueueValue(self):
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if(len(self.vertex_queue) == 0):
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def best_vertex_queue_value(self):
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if len(self.vertex_queue) == 0:
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return float('inf')
|
||||
values = [self.g_scores[v]
|
||||
+ self.computeHeuristicCost(v, self.goalId) for v in self.vertex_queue]
|
||||
+ self.compute_heuristic_cost(v, self.goalId) for v in self.vertex_queue]
|
||||
values.sort()
|
||||
return values[0]
|
||||
|
||||
def bestEdgeQueueValue(self):
|
||||
if(len(self.edge_queue) == 0):
|
||||
def best_edge_queue_value(self):
|
||||
if len(self.edge_queue) == 0:
|
||||
return float('inf')
|
||||
# return the best value in the queue by score g_tau[v] + c(v,x) + h(x)
|
||||
values = [self.g_scores[e[0]] + self.computeDistanceCost(e[0], e[1])
|
||||
+ self.computeHeuristicCost(e[1], self.goalId) for e in self.edge_queue]
|
||||
values = [self.g_scores[e[0]] + self.compute_distance_cost(e[0], e[1])
|
||||
+ self.compute_heuristic_cost(e[1], self.goalId) for e in self.edge_queue]
|
||||
values.sort(reverse=True)
|
||||
return values[0]
|
||||
|
||||
def bestInVertexQueue(self):
|
||||
def best_in_vertex_queue(self):
|
||||
# return the best value in the vertex queue
|
||||
v_plus_vals = [(v, self.g_scores[v] + self.computeHeuristicCost(v, self.goalId))
|
||||
v_plus_vals = [(v, self.g_scores[v] + self.compute_heuristic_cost(v, self.goalId))
|
||||
for v in self.vertex_queue]
|
||||
v_plus_vals = sorted(v_plus_vals, key=lambda x: x[1])
|
||||
# print(v_plus_vals)
|
||||
return v_plus_vals[0][0]
|
||||
|
||||
def bestInEdgeQueue(self):
|
||||
e_and_values = [(e[0], e[1], self.g_scores[e[0]] + self.computeDistanceCost(
|
||||
e[0], e[1]) + self.computeHeuristicCost(e[1], self.goalId)) for e in self.edge_queue]
|
||||
def best_in_edge_queue(self):
|
||||
e_and_values = [(e[0], e[1], self.g_scores[e[0]] + self.compute_distance_cost(
|
||||
e[0], e[1]) + self.compute_heuristic_cost(e[1], self.goalId)) for e in self.edge_queue]
|
||||
e_and_values = sorted(e_and_values, key=lambda x: x[2])
|
||||
|
||||
return (e_and_values[0][0], e_and_values[0][1])
|
||||
return e_and_values[0][0], e_and_values[0][1]
|
||||
|
||||
def expandVertex(self, vid):
|
||||
def expand_vertex(self, vid):
|
||||
self.vertex_queue.remove(vid)
|
||||
|
||||
# get the coordinates for given vid
|
||||
currCoord = np.array(self.tree.nodeIdToRealWorldCoord(vid))
|
||||
currCoord = np.array(self.tree.node_id_to_real_world_coord(vid))
|
||||
|
||||
# get the nearest value in vertex for every one in samples where difference is
|
||||
# less than the radius
|
||||
neigbors = []
|
||||
for sid, scoord in self.samples.items():
|
||||
scoord = np.array(scoord)
|
||||
if(np.linalg.norm(scoord - currCoord, 2) <= self.r and sid != vid):
|
||||
if np.linalg.norm(scoord - currCoord, 2) <= self.r and sid != vid:
|
||||
neigbors.append((sid, scoord))
|
||||
|
||||
# add an edge to the edge queue is the path might improve the solution
|
||||
for neighbor in neigbors:
|
||||
sid = neighbor[0]
|
||||
estimated_f_score = self.computeDistanceCost(
|
||||
self.startId, vid) + self.computeHeuristicCost(sid, self.goalId) + self.computeDistanceCost(vid, sid)
|
||||
h_cost = self.compute_heuristic_cost(sid, self.goalId)
|
||||
estimated_f_score = self.compute_distance_cost(
|
||||
self.startId, vid) + h_cost + self.compute_distance_cost(vid, sid)
|
||||
if estimated_f_score < self.g_scores[self.goalId]:
|
||||
self.edge_queue.append((vid, sid))
|
||||
|
||||
@@ -469,22 +474,22 @@ class BITStar(object):
|
||||
|
||||
def add_vertex_to_edge_queue(self, vid, currCoord):
|
||||
if vid not in self.old_vertices:
|
||||
neigbors = []
|
||||
neighbors = []
|
||||
for v, edges in self.tree.vertices.items():
|
||||
if v != vid and (v, vid) not in self.edge_queue and (vid, v) not in self.edge_queue:
|
||||
vcoord = self.tree.nodeIdToRealWorldCoord(v)
|
||||
if(np.linalg.norm(vcoord - currCoord, 2) <= self.r):
|
||||
neigbors.append((vid, vcoord))
|
||||
v_coord = self.tree.node_id_to_real_world_coord(v)
|
||||
if np.linalg.norm(currCoord - v_coord, 2) <= self.r:
|
||||
neighbors.append((vid, v_coord))
|
||||
|
||||
for neighbor in neigbors:
|
||||
for neighbor in neighbors:
|
||||
sid = neighbor[0]
|
||||
estimated_f_score = self.computeDistanceCost(self.startId, vid) + \
|
||||
self.computeDistanceCost(
|
||||
vid, sid) + self.computeHeuristicCost(sid, self.goalId)
|
||||
if estimated_f_score < self.g_scores[self.goalId] and (self.g_scores[vid] + self.computeDistanceCost(vid, sid)) < self.g_scores[sid]:
|
||||
estimated_f_score = self.compute_distance_cost(self.startId, vid) + self.compute_distance_cost(
|
||||
vid, sid) + self.compute_heuristic_cost(sid, self.goalId)
|
||||
if estimated_f_score < self.g_scores[self.goalId] and (
|
||||
self.g_scores[vid] + self.compute_distance_cost(vid, sid)) < self.g_scores[sid]:
|
||||
self.edge_queue.append((vid, sid))
|
||||
|
||||
def updateGraph(self):
|
||||
def update_graph(self):
|
||||
closedSet = []
|
||||
openSet = []
|
||||
currId = self.startId
|
||||
@@ -498,22 +503,21 @@ class BITStar(object):
|
||||
openSet.remove(currId)
|
||||
|
||||
# Check if we're at the goal
|
||||
if(currId == self.goalId):
|
||||
self.nodes[self.goalId]
|
||||
if currId == self.goalId:
|
||||
break
|
||||
|
||||
if(currId not in closedSet):
|
||||
if currId not in closedSet:
|
||||
closedSet.append(currId)
|
||||
|
||||
# find a non visited successor to the current node
|
||||
successors = self.tree.vertices[currId]
|
||||
for succesor in successors:
|
||||
if(succesor in closedSet):
|
||||
if succesor in closedSet:
|
||||
continue
|
||||
else:
|
||||
# claculate tentative g score
|
||||
g_score = self.g_scores[currId] + \
|
||||
self.computeDistanceCost(currId, succesor)
|
||||
self.compute_distance_cost(currId, succesor)
|
||||
if succesor not in openSet:
|
||||
# add the successor to open set
|
||||
openSet.append(succesor)
|
||||
@@ -522,14 +526,13 @@ class BITStar(object):
|
||||
|
||||
# update g and f scores
|
||||
self.g_scores[succesor] = g_score
|
||||
self.f_scores[succesor] = g_score + \
|
||||
self.computeHeuristicCost(succesor, self.goalId)
|
||||
self.f_scores[succesor] = g_score + self.compute_heuristic_cost(succesor, self.goalId)
|
||||
|
||||
# store the parent and child
|
||||
self.nodes[succesor] = currId
|
||||
|
||||
def drawGraph(self, xCenter=None, cBest=None, cMin=None, etheta=None,
|
||||
samples=None, start=None, end=None, tree=None):
|
||||
def draw_graph(self, xCenter=None, cBest=None, cMin=None, etheta=None,
|
||||
samples=None, start=None, end=None):
|
||||
plt.clf()
|
||||
for rnd in samples:
|
||||
if rnd is not None:
|
||||
@@ -549,9 +552,10 @@ class BITStar(object):
|
||||
plt.grid(True)
|
||||
plt.pause(0.01)
|
||||
|
||||
def plot_ellipse(self, xCenter, cBest, cMin, etheta): # pragma: no cover
|
||||
@staticmethod
|
||||
def plot_ellipse(xCenter, cBest, cMin, etheta): # pragma: no cover
|
||||
|
||||
a = math.sqrt(cBest**2 - cMin**2) / 2.0
|
||||
a = math.sqrt(cBest ** 2 - cMin ** 2) / 2.0
|
||||
b = cBest / 2.0
|
||||
angle = math.pi / 2.0 - etheta
|
||||
cx = xCenter[0]
|
||||
|
||||
Reference in New Issue
Block a user