mapf_gym.py

import gym
from gym import spaces
import numpy as np
from collections import OrderedDict
from threading import Lock
import sys
from matplotlib.colors import hsv_to_rgb
import random
import math
import copy
import cpp_mstar
from od_mstar3.col_set_addition import NoSolutionError, OutOfTimeError
from gym.envs.classic_control import rendering        

'''
    Observation: (position maps of current agent, current goal, other agents, other goals, obstacles)
        
    Action space: (Tuple)
        agent_id: positive integer
        action: {0:STILL, 1:MOVE_NORTH, 2:MOVE_EAST, 3:MOVE_SOUTH, 4:MOVE_WEST,
        5:NE, 6:SE, 7:SW, 8:NW}
    Reward: ACTION_COST for each action, GOAL_REWARD when robot arrives at target
'''
ACTION_COST, IDLE_COST, GOAL_REWARD, COLLISION_REWARD,FINISH_REWARD,BLOCKING_COST = -0.3, -.5, 0.0, -2.,20.,-1.
opposite_actions = {0: -1, 1: 3, 2: 4, 3: 1, 4: 2, 5: 7, 6: 8, 7: 5, 8: 6}
JOINT = False # True for joint estimation of rewards for closeby agents
dirDict = {0:(0,0),1:(0,1),2:(1,0),3:(0,-1),4:(-1,0),5:(1,1),6:(1,-1),7:(-1,-1),8:(-1,1)}
actionDict={v:k for k,v in dirDict.items()}
class State(object):
    '''
    State.
    Implemented as 2 2d numpy arrays.
    first one "state":
        static obstacle: -1
        empty: 0
        agent = positive integer (agent_id)
    second one "goals":
        agent goal = positive int(agent_id)
    '''
    def __init__(self, world0, goals, diagonal, num_agents=1):
        assert(len(world0.shape) == 2 and world0.shape==goals.shape)
        self.state                    = world0.copy()
        self.goals                    = goals.copy()
        self.num_agents               = num_agents
        self.agents, self.agents_past, self.agent_goals = self.scanForAgents()
        self.diagonal=diagonal
        assert(len(self.agents) == num_agents)

    def scanForAgents(self):
        agents = [(-1,-1) for i in range(self.num_agents)]
        agents_last = [(-1,-1) for i in range(self.num_agents)]        
        agent_goals = [(-1,-1) for i in range(self.num_agents)]        
        for i in range(self.state.shape[0]):
            for j in range(self.state.shape[1]):
                if(self.state[i,j]>0):
                    agents[self.state[i,j]-1] = (i,j)
                    agents_last[self.state[i,j]-1] = (i,j)
                if(self.goals[i,j]>0):
                    agent_goals[self.goals[i,j]-1] = (i,j)
        assert((-1,-1) not in agents and (-1,-1) not in agent_goals)
        assert(agents==agents_last)
        return agents, agents_last, agent_goals

    def getPos(self, agent_id):
        return self.agents[agent_id-1]

    def getPastPos(self, agent_id):
        return self.agents_past[agent_id-1]

    def getGoal(self, agent_id):
        return self.agent_goals[agent_id-1]
    
    def diagonalCollision(self, agent_id, newPos):
        '''diagonalCollision(id,(x,y)) returns true if agent with id "id" collided diagonally with 
        any other agent in the state after moving to coordinates (x,y)
        agent_id: id of the desired agent to check for
        newPos: coord the agent is trying to move to (and checking for collisions)
        '''
#        def eq(f1,f2):return abs(f1-f2)<0.001
        def collide(a1,a2,b1,b2):
            '''
            a1,a2 are coords for agent 1, b1,b2 coords for agent 2, returns true if these collide diagonally
            '''
            return np.isclose( (a1[0]+a2[0]) /2. , (b1[0]+b2[0])/2. ) and np.isclose( (a1[1]+a2[1])/2. , (b1[1]+b2[1])/2. )
        assert(len(newPos) == 2);
        #up until now we haven't moved the agent, so getPos returns the "old" location
        lastPos = self.getPos(agent_id)
        for agent in range(1,self.num_agents+1):
            if agent == agent_id: continue
            aPast = self.getPastPos(agent)
            aPres = self.getPos(agent)
            if collide(aPast,aPres,lastPos,newPos): return True
        return False

    #try to move agent and return the status
    def moveAgent(self, direction, agent_id):
        ax=self.agents[agent_id-1][0]
        ay=self.agents[agent_id-1][1]

        # Not moving is always allowed
        if(direction==(0,0)):
            self.agents_past[agent_id-1]=self.agents[agent_id-1]
            return 1 if self.goals[ax,ay]==agent_id else 0

        # Otherwise, let's look at the validity of the move
        dx,dy =direction[0], direction[1]
        if(ax+dx>=self.state.shape[0] or ax+dx<0 or ay+dy>=self.state.shape[1] or ay+dy<0):#out of bounds
            return -1
        if(self.state[ax+dx,ay+dy]<0):#collide with static obstacle
            return -2
        if(self.state[ax+dx,ay+dy]>0):#collide with robot
            return -3
        # check for diagonal collisions
        if(self.diagonal):
            if self.diagonalCollision(agent_id,(ax+dx,ay+dy)):
                return -3
        # No collision: we can carry out the action
        self.state[ax,ay] = 0
        self.state[ax+dx,ay+dy] = agent_id
        self.agents_past[agent_id-1]=self.agents[agent_id-1]
        self.agents[agent_id-1] = (ax+dx,ay+dy)
        if self.goals[ax+dx,ay+dy]==agent_id:
            return 1
        elif self.goals[ax+dx,ay+dy]!=agent_id and self.goals[ax,ay]==agent_id:
            return 2
        else:
            return 0

    # try to execture action and return whether action was executed or not and why
    #returns:
    #     2: action executed and left goal
    #     1: action executed and reached goal (or stayed on)
    #     0: action executed
    #    -1: out of bounds
    #    -2: collision with wall
    #    -3: collision with robot
    def act(self, action, agent_id):
        # 0     1  2  3  4 
        # still N  E  S  W
        direction = self.getDir(action)
        moved = self.moveAgent(direction,agent_id)
        return moved

    def getDir(self,action):
        return dirDict[action]
    def getAction(self,direction):
        return actionDict[direction]

    # Compare with a plan to determine job completion
    def done(self):
        numComplete = 0
        for i in range(1,len(self.agents)+1):
            agent_pos = self.agents[i-1]
            if self.goals[agent_pos[0],agent_pos[1]] == i:
                numComplete += 1
        return numComplete==len(self.agents) #, numComplete/float(len(self.agents))


class MAPFEnv(gym.Env):
    def getFinishReward(self):
        return FINISH_REWARD
    metadata = {"render.modes": ["human", "ansi"]}

    # Initialize env
    def __init__(self, num_agents=1, observation_size=10,world0=None, goals0=None, DIAGONAL_MOVEMENT=False, SIZE=(10,40), PROB=(0,.5), FULL_HELP=False,blank_world=False):
        """
        Args:
            DIAGONAL_MOVEMENT: if the agents are allowed to move diagonally
            SIZE: size of a side of the square grid
            PROB: range of probabilities that a given block is an obstacle
            FULL_HELP
        """
        # Initialize member variables
        self.num_agents        = num_agents 
        #a way of doing joint rewards
        self.individual_rewards           = [0 for i in range(num_agents)]
        self.observation_size  = observation_size
        self.SIZE              = SIZE
        self.PROB              = PROB
        self.fresh             = True
        self.FULL_HELP         = FULL_HELP
        self.finished          = False
        self.mutex             = Lock()
        self.DIAGONAL_MOVEMENT = DIAGONAL_MOVEMENT

        # Initialize data structures
        self._setWorld(world0,goals0,blank_world=blank_world)
        if DIAGONAL_MOVEMENT:
            self.action_space = spaces.Tuple([spaces.Discrete(self.num_agents), spaces.Discrete(9)])
        else:
            self.action_space = spaces.Tuple([spaces.Discrete(self.num_agents), spaces.Discrete(5)])
        self.viewer           = None

    def isConnected(self,world0):
        sys.setrecursionlimit(10000)
        world0 = world0.copy()

        def firstFree(world0):
            for x in range(world0.shape[0]):
                for y in range(world0.shape[1]):
                    if world0[x,y]==0:
                        return x,y
        def floodfill(world,i,j):
            sx,sy=world.shape[0],world.shape[1]
            if(i<0 or i>=sx or j<0 or j>=sy):#out of bounds, return
                return
            if(world[i,j]==-1):return
            world[i,j] = -1
            floodfill(world,i+1,j)
            floodfill(world,i,j+1)
            floodfill(world,i-1,j)
            floodfill(world,i,j-1)

        i,j = firstFree(world0)
        floodfill(world0,i,j)
        if np.any(world0==0):
            return False
        else:
            return True

    def getObstacleMap(self):
        return (self.world.state==-1).astype(int)
    
    def getGoals(self):
        result=[]
        for i in range(1,self.num_agents+1):
            result.append(self.world.getGoal(i))
        return result
    
    def getPositions(self):
        result=[]
        for i in range(1,self.num_agents+1):
            result.append(self.world.getPos(i))
        return result
    
    def _setWorld(self, world0=None, goals0=None,blank_world=False):
        #blank_world is a flag indicating that the world given has no agent or goal positions 
        def getConnectedRegion(world,regions_dict,x,y):
            sys.setrecursionlimit(1000000)
            '''returns a list of tuples of connected squares to the given tile
            this is memoized with a dict'''
            if (x,y) in regions_dict:
                return regions_dict[(x,y)]
            visited=set()
            sx,sy=world.shape[0],world.shape[1]
            work_list=[(x,y)]
            while len(work_list)>0:
                (i,j)=work_list.pop()
                if(i<0 or i>=sx or j<0 or j>=sy):#out of bounds, return
                    continue
                if(world[i,j]==-1):
                    continue#crashes
                if world[i,j]>0:
                    regions_dict[(i,j)]=visited
                if (i,j) in visited:continue
                visited.add((i,j))
                work_list.append((i+1,j))
                work_list.append((i,j+1))
                work_list.append((i-1,j))
                work_list.append((i,j-1))
            regions_dict[(x,y)]=visited
            return visited
        #defines the State object, which includes initializing goals and agents
        #sets the world to world0 and goals, or if they are None randomizes world
        if not (world0 is None):
            if goals0 is None and not blank_world:
                raise Exception("you gave a world with no goals!")
            if blank_world:
                #RANDOMIZE THE POSITIONS OF AGENTS
                agent_counter = 1
                agent_locations=[]
                while agent_counter<=self.num_agents:
                    x,y       = np.random.randint(0,world0.shape[0]),np.random.randint(0,world0.shape[1])
                    if(world0[x,y] == 0):
                        world0[x,y]=agent_counter
                        agent_locations.append((x,y))
                        agent_counter += 1   
                #RANDOMIZE THE GOALS OF AGENTS
                goals0 = np.zeros(world0.shape).astype(int)
                goal_counter = 1
                agent_regions=dict()  
                while goal_counter<=self.num_agents:
                    agent_pos=agent_locations[goal_counter-1]
                    valid_tiles=getConnectedRegion(world0,agent_regions,agent_pos[0],agent_pos[1])#crashes
                    x,y  = random.choice(list(valid_tiles))
                    if(goals0[x,y]==0 and world0[x,y]!=-1):
                        goals0[x,y]    = goal_counter
                        goal_counter += 1
                self.initial_world = world0.copy()
                self.initial_goals = goals0.copy()
                self.world = State(self.initial_world,self.initial_goals,self.DIAGONAL_MOVEMENT,self.num_agents)
                return
            self.initial_world = world0
            self.initial_goals = goals0
            self.world = State(world0,goals0,self.DIAGONAL_MOVEMENT,self.num_agents)
            return

        #otherwise we have to randomize the world
        #RANDOMIZE THE STATIC OBSTACLES
        prob=np.random.triangular(self.PROB[0],.33*self.PROB[0]+.66*self.PROB[1],self.PROB[1])
        size=np.random.choice([self.SIZE[0],self.SIZE[0]*.5+self.SIZE[1]*.5,self.SIZE[1]],p=[.5,.25,.25])
        world     = -(np.random.rand(int(size),int(size))<prob).astype(int)

        #RANDOMIZE THE POSITIONS OF AGENTS
        agent_counter = 1
        agent_locations=[]
        while agent_counter<=self.num_agents:
            x,y       = np.random.randint(0,world.shape[0]),np.random.randint(0,world.shape[1])
            if(world[x,y] == 0):
                world[x,y]=agent_counter
                agent_locations.append((x,y))
                agent_counter += 1        
        
        #RANDOMIZE THE GOALS OF AGENTS
        goals = np.zeros(world.shape).astype(int)
        goal_counter = 1
        agent_regions=dict()     
        while goal_counter<=self.num_agents:
            agent_pos=agent_locations[goal_counter-1]
            valid_tiles=getConnectedRegion(world,agent_regions,agent_pos[0],agent_pos[1])
            x,y  = random.choice(list(valid_tiles))
            if(goals[x,y]==0 and world[x,y]!=-1):
                goals[x,y]    = goal_counter
                goal_counter += 1
        self.initial_world = world
        self.initial_goals = goals
        self.world = State(world,goals,self.DIAGONAL_MOVEMENT,num_agents=self.num_agents)

    # Returns an observation of an agent
    def _observe(self,agent_id):
        assert(agent_id>0)
        top_left=(self.world.getPos(agent_id)[0]-self.observation_size//2,self.world.getPos(agent_id)[1]-self.observation_size//2)
        bottom_right=(top_left[0]+self.observation_size,top_left[1]+self.observation_size)        
        obs_shape=(self.observation_size,self.observation_size)
        goal_map             = np.zeros(obs_shape)
        poss_map             = np.zeros(obs_shape)
        goals_map            = np.zeros(obs_shape)
        obs_map              = np.zeros(obs_shape)
        visible_agents=[]
        for i in range(top_left[0],top_left[0]+self.observation_size):
            for j in range(top_left[1],top_left[1]+self.observation_size):
                if i>=self.world.state.shape[0] or i<0 or j>=self.world.state.shape[1] or j<0:
                    #out of bounds, just treat as an obstacle
                    obs_map[i-top_left[0],j-top_left[1]]=1
                    continue
                if self.world.state[i,j]==-1:
                    #obstacles
                    obs_map[i-top_left[0],j-top_left[1]]=1
                if self.world.state[i,j]==agent_id:
                    #agent's position
                    poss_map[i-top_left[0],j-top_left[1]]=1
                elif self.world.goals[i,j]==agent_id:
                    #agent's goal
                    goal_map[i-top_left[0],j-top_left[1]]=1
                if self.world.state[i,j]>0 and self.world.state[i,j]!=agent_id:
                    #other agents' positions
                    visible_agents.append(self.world.state[i,j])
                    poss_map[i-top_left[0],j-top_left[1]]=1

        distance=lambda x1,y1,x2,y2:((x2-x1)**2+(y2-y1)**2)**.5
        for agent in visible_agents:
            x,y=self.world.getGoal(agent)
            if x<top_left[0] or x>=bottom_right[0] or y>=bottom_right[1] or y<top_left[1]:
                #out of observation
                min_node=(-1,-1)
                min_dist=1000
                for i in range(top_left[0],top_left[0]+self.observation_size):
                    for j in range(top_left[1],top_left[1]+self.observation_size):
                        d=distance(i,j,x,y)
                        if d<min_dist:
                            min_node=(i,j)
                            min_dist=d
                goals_map[min_node[0]-top_left[0],min_node[1]-top_left[1]]=1
            else:
                goals_map[x-top_left[0],y-top_left[1]]=1
        dx=self.world.getGoal(agent_id)[0]-self.world.getPos(agent_id)[0]
        dy=self.world.getGoal(agent_id)[1]-self.world.getPos(agent_id)[1]
        mag=(dx**2+dy**2)**.5
        if mag!=0:
            dx=dx/mag
            dy=dy/mag
        return ([poss_map,goal_map,goals_map,obs_map],[dx,dy,mag])




    # Resets environment
    def _reset(self, agent_id,world0=None,goals0=None):
        self.finished = False
        self.mutex.acquire()

        # Initialize data structures
        self._setWorld(world0,goals0)
        self.fresh = True
        
        self.mutex.release()
        if self.viewer is not None:
            self.viewer = None
        on_goal = self.world.getPos(agent_id) == self.world.getGoal(agent_id)
        #we assume you don't start blocking anyone (the probability of this happening is insanely low)
        return self._listNextValidActions(agent_id), on_goal,False

    def _complete(self):
        return self.world.done()
    
    def getAstarCosts(self,start, goal):
        #returns a numpy array of same dims as self.world.state with the distance to the goal from each coord
        def lowestF(fScore,openSet):
            #find entry in openSet with lowest fScore
            assert(len(openSet)>0)
            minF=2**31-1
            minNode=None
            for (i,j) in openSet:
                if (i,j) not in fScore:continue
                if fScore[(i,j)]<minF:
                    minF=fScore[(i,j)]
                    minNode=(i,j)
            return minNode      
        def getNeighbors(node):
            #return set of neighbors to the given node
            n_moves=9 if self.DIAGONAL_MOVEMENT else 5
            neighbors=set()
            for move in range(1,n_moves):#we dont want to include 0 or it will include itself
                direction=self.world.getDir(move)
                dx=direction[0]
                dy=direction[1]
                ax=node[0]
                ay=node[1]
                if(ax+dx>=self.world.state.shape[0] or ax+dx<0 or ay+dy>=self.world.state.shape[1] or ay+dy<0):#out of bounds
                    continue
                if(self.world.state[ax+dx,ay+dy]==-1):#collide with static obstacle
                    continue
                neighbors.add((ax+dx,ay+dy))
            return neighbors
        
        #NOTE THAT WE REVERSE THE DIRECTION OF SEARCH SO THAT THE GSCORE WILL BE DISTANCE TO GOAL
        start,goal=goal,start
        
        # The set of nodes already evaluated
        closedSet = set()
    
        # The set of currently discovered nodes that are not evaluated yet.
        # Initially, only the start node is known.
        openSet =set()
        openSet.add(start)
    
        # For each node, which node it can most efficiently be reached from.
        # If a node can be reached from many nodes, cameFrom will eventually contain the
        # most efficient previous step.
        cameFrom = dict()
    
        # For each node, the cost of getting from the start node to that node.
        gScore =dict()#default value infinity
    
        # The cost of going from start to start is zero.
        gScore[start] = 0
    
        # For each node, the total cost of getting from the start node to the goal
        # by passing by that node. That value is partly known, partly heuristic.
        fScore = dict()#default infinity
    
        #our heuristic is euclidean distance to goal
        heuristic_cost_estimate = lambda x,y:math.hypot(x[0]-y[0],x[1]-y[1])
        
        # For the first node, that value is completely heuristic.        
        fScore[start] = heuristic_cost_estimate(start, goal)
    
        while len(openSet) != 0:
            #current = the node in openSet having the lowest fScore value
            current = lowestF(fScore,openSet)
    
            openSet.remove(current)
            closedSet.add(current)
            for neighbor in getNeighbors(current):
                if neighbor in closedSet:
                    continue		# Ignore the neighbor which is already evaluated.
            
                if neighbor not in openSet:	# Discover a new node
                    openSet.add(neighbor)
                
                # The distance from start to a neighbor
                #in our case the distance between is always 1
                tentative_gScore = gScore[current] + 1
                if tentative_gScore >= gScore.get(neighbor,2**31-1):
                    continue		# This is not a better path.
            
                # This path is the best until now. Record it!
                cameFrom[neighbor] = current
                gScore[neighbor] = tentative_gScore
                fScore[neighbor] = gScore[neighbor] + heuristic_cost_estimate(neighbor, goal) 
    
        #parse through the gScores
        costs=self.world.state.copy()
        for (i,j) in gScore:
            costs[i,j]=gScore[i,j]
        return costs
    
    def astar(self,world,start,goal,robots=[]):
        '''robots is a list of robots to add to the world'''
        for (i,j) in robots:
            world[i,j]=1
        try:
            path=cpp_mstar.find_path(world,[start],[goal],1,5)
        except NoSolutionError:
            path=None
        for (i,j) in robots:
            world[i,j]=0
        return path
    
    def get_blocking_reward(self,agent_id):
        '''calculates how many robots the agent is preventing from reaching goal
        and returns the necessary penalty'''
        #accumulate visible robots
        other_robots=[]
        other_locations=[]
        inflation=10
        top_left=(self.world.getPos(agent_id)[0]-self.observation_size//2,self.world.getPos(agent_id)[1]-self.observation_size//2)
        bottom_right=(top_left[0]+self.observation_size,top_left[1]+self.observation_size)        
        for agent in range(1,self.num_agents):
            if agent==agent_id: continue
            x,y=self.world.getPos(agent)
            if x<top_left[0] or x>=bottom_right[0] or y>=bottom_right[1] or y<top_left[1]:
                continue
            other_robots.append(agent)
            other_locations.append((x,y))
        num_blocking=0
        world=self.getObstacleMap()
        for agent in other_robots:
            other_locations.remove(self.world.getPos(agent))
            #before removing
            path_before=self.astar(world,self.world.getPos(agent),self.world.getGoal(agent),
                                   robots=other_locations+[self.world.getPos(agent_id)])
            #after removing
            path_after=self.astar(world,self.world.getPos(agent),self.world.getGoal(agent),
                                   robots=other_locations)
            other_locations.append(self.world.getPos(agent))
            if (path_before is None and path_after is None):continue
            if (path_before is not None and path_after is None):continue
            if (path_before is None and path_after is not None)\
                or len(path_before)>len(path_after)+inflation:
                num_blocking+=1
        return num_blocking*BLOCKING_COST
            
        
    # Executes an action by an agent
    def _step(self, action_input,episode=0):
        #episode is an optional variable which will be used on the reward discounting
        self.fresh = False
        n_actions = 9 if self.DIAGONAL_MOVEMENT else 5

        # Check action input
        assert len(action_input) == 2, 'Action input should be a tuple with the form (agent_id, action)'
        assert action_input[1] in range(n_actions), 'Invalid action'
        assert action_input[0] in range(1, self.num_agents+1)

        # Parse action input
        agent_id = action_input[0]
        action   = action_input[1]

        # Lock mutex (race conditions start here)
        self.mutex.acquire()

        #get start location of agent
        agentStartLocation = self.world.getPos(agent_id)
        
        # Execute action & determine reward
        action_status = self.world.act(action,agent_id)
        valid_action=action_status >=0
        #     2: action executed and left goal
        #     1: action executed and reached/stayed on goal
        #     0: action executed
        #    -1: out of bounds
        #    -2: collision with wall
        #    -3: collision with robot
        blocking=False
        if action==0:#staying still
            if action_status == 1:#stayed on goal
                reward=GOAL_REWARD
                x=self.get_blocking_reward(agent_id)
                reward+=x
                if x<0:
                    blocking=True
            elif action_status == 0:#stayed off goal
                reward=IDLE_COST
        else:#moving
            if (action_status == 1): # reached goal
                reward = GOAL_REWARD
            elif (action_status == -3 or action_status==-2 or action_status==-1): # collision
                reward = COLLISION_REWARD
            elif (action_status == 2): #left goal
                reward=ACTION_COST
            else:
                reward=ACTION_COST
        self.individual_rewards[agent_id-1]=reward

        if JOINT:
            visible=[False for i in range(self.num_agents)]
            v=0
            #joint rewards based on proximity
            for agent in range(1,self.num_agents+1):
                #tally up the visible agents
                if agent==agent_id:
                    continue
                top_left=(self.world.getPos(agent_id)[0]-self.observation_size//2, \
                          self.world.getPos(agent_id)[1]-self.observation_size//2)
                pos=self.world.getPos(agent)
                if pos[0]>=top_left[0] and pos[0]<top_left[0]+self.observation_size\
                    and pos[1]>=top_left[1] and pos[1]<top_left[1]+self.observation_size:
                        #if the agent is within the bounds for observation
                        v+=1
                        visible[agent-1]=True
            if v>0:
                reward=self.individual_rewards[agent_id-1]/2
                #set the reward to the joint reward if we are 
                for i in range(self.num_agents):
                    if visible[i]:
                        reward+=self.individual_rewards[i]/(v*2)

        # Perform observation
        state = self._observe(agent_id) 

        # Done?
        done = self.world.done()
        self.finished |= done

        # next valid actions
        nextActions = self._listNextValidActions(agent_id, action,episode=episode)

        # on_goal estimation
        on_goal = self.world.getPos(agent_id) == self.world.getGoal(agent_id)
        
        # Unlock mutex
        self.mutex.release()
        return state, reward, done, nextActions, on_goal, blocking, valid_action

    def _listNextValidActions(self, agent_id, prev_action=0,episode=0):
        available_actions = [0] # staying still always allowed

        # Get current agent position
        agent_pos = self.world.getPos(agent_id)
        ax,ay     = agent_pos[0],agent_pos[1]
        n_moves   = 9 if self.DIAGONAL_MOVEMENT else 5

        for action in range(1,n_moves):
            direction = self.world.getDir(action)
            dx,dy     = direction[0],direction[1]
            if(ax+dx>=self.world.state.shape[0] or ax+dx<0 or ay+dy>=self.world.state.shape[1] or ay+dy<0):#out of bounds
                continue
            if(self.world.state[ax+dx,ay+dy]<0):#collide with static obstacle
                continue
            if(self.world.state[ax+dx,ay+dy]>0):#collide with robot
                continue
            # check for diagonal collisions
            if(self.DIAGONAL_MOVEMENT):
                if self.world.diagonalCollision(agent_id,(ax+dx,ay+dy)):
                    continue          
            #otherwise we are ok to carry out the action
            available_actions.append(action)

        if opposite_actions[prev_action] in available_actions:
            available_actions.remove(opposite_actions[prev_action])
                
        return available_actions

    def drawStar(self, centerX, centerY, diameter, numPoints, color):
        outerRad=diameter//2
        innerRad=int(outerRad*3/8)
        #fill the center of the star
        angleBetween=2*math.pi/numPoints#angle between star points in radians
        for i in range(numPoints):
            #p1 and p3 are on the inner radius, and p2 is the point
            pointAngle=math.pi/2+i*angleBetween
            p1X=centerX+innerRad*math.cos(pointAngle-angleBetween/2)
            p1Y=centerY-innerRad*math.sin(pointAngle-angleBetween/2)
            p2X=centerX+outerRad*math.cos(pointAngle)
            p2Y=centerY-outerRad*math.sin(pointAngle)
            p3X=centerX+innerRad*math.cos(pointAngle+angleBetween/2)
            p3Y=centerY-innerRad*math.sin(pointAngle+angleBetween/2)
            #draw the triangle for each tip.
            poly=rendering.FilledPolygon([(p1X,p1Y),(p2X,p2Y),(p3X,p3Y)])
            poly.set_color(color[0],color[1],color[2])
            poly.add_attr(rendering.Transform())
            self.viewer.add_onetime(poly)

    def create_rectangle(self,x,y,width,height,fill,permanent=False):
        ps=[(x,y),((x+width),y),((x+width),(y+height)),(x,(y+height))]
        rect=rendering.FilledPolygon(ps)
        rect.set_color(fill[0],fill[1],fill[2])
        rect.add_attr(rendering.Transform())
        if permanent:
            self.viewer.add_geom(rect)
        else:
            self.viewer.add_onetime(rect)
    def create_circle(self,x,y,diameter,size,fill,resolution=20):
        c=(x+size/2,y+size/2)
        dr=math.pi*2/resolution
        ps=[]
        for i in range(resolution):
            x=c[0]+math.cos(i*dr)*diameter/2
            y=c[1]+math.sin(i*dr)*diameter/2
            ps.append((x,y))
        circ=rendering.FilledPolygon(ps)
        circ.set_color(fill[0],fill[1],fill[2])
        circ.add_attr(rendering.Transform())
        self.viewer.add_onetime(circ)
    def initColors(self):
        c={a+1:hsv_to_rgb(np.array([a/float(self.num_agents),1,1])) for a in range(self.num_agents)}
        return c

    def _render(self, mode='human',close=False,screen_width=800,screen_height=800,action_probs=None):
        if close == True:
            return
        #values is an optional parameter which provides a visualization for the value of each agent per step
        size=screen_width/max(self.world.state.shape[0],self.world.state.shape[1])
        colors=self.initColors()
        if self.viewer==None:
            self.viewer=rendering.Viewer(screen_width,screen_height)
            self.reset_renderer=True
        if self.reset_renderer:
            self.create_rectangle(0,0,screen_width,screen_height,(.6,.6,.6),permanent=True)
            for i in range(self.world.state.shape[0]):
                start=0
                end=1
                scanning=False
                write=False
                for j in range(self.world.state.shape[1]):
                    if(self.world.state[i,j]!=-1 and not scanning):#free
                        start=j
                        scanning=True
                    if((j==self.world.state.shape[1]-1 or self.world.state[i,j]==-1) and scanning):
                        end=j+1 if j==self.world.state.shape[1]-1 else j
                        scanning=False
                        write=True
                    if write:
                        x=i*size
                        y=start*size
                        self.create_rectangle(x,y,size,size*(end-start),(1,1,1),permanent=True)
                        write=False
        for agent in range(1,self.num_agents+1):
            i,j=self.world.getPos(agent)
            x=i*size
            y=j*size
            color=colors[self.world.state[i,j]]
            self.create_rectangle(x,y,size,size,color)
            i,j=self.world.getGoal(agent)
            x=i*size
            y=j*size
            color=colors[self.world.goals[i,j]]
            self.create_circle(x,y,size,size,color)
            if self.world.getGoal(agent)==self.world.getPos(agent):
                color=(0,0,0)
                self.create_circle(x,y,size,size,color)
        if action_probs is not None:
            n_moves=9 if self.DIAGONAL_MOVEMENT else 5
            for agent in range(1,self.num_agents+1):
                #take the a_dist from the given data and draw it on the frame
                a_dist=action_probs[agent-1]
                if a_dist is not None:
                    for m in range(n_moves):
                        dx,dy=self.world.getDir(m)
                        x=(self.world.getPos(agent)[0]+dx)*size
                        y=(self.world.getPos(agent)[1]+dy)*size
                        s=a_dist[m]*size
                        self.create_circle(x,y,s,size,(0,0,0))
        self.reset_renderer=False
        result=self.viewer.render(return_rgb_array = mode=='rgb_array')
        return result

if __name__=='__main__':
    n_agents=8
    env=MAPFEnv(n_agents,PROB=(.3,.5),SIZE=(10,11),DIAGONAL_MOVEMENT=False)
    print(coordinationRatio(env))