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MultiRobotMotionPlanner.py
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# * --------------------------------------------------------------------------
# * File: MultiRobotMotionPlanner.py
# * ---------------------------------------------------------------------------
# * Copyright (c) 2016 The Regents of the University of California.
# * All rights reserved.
# *
# * Redistribution and use in source and binary forms, with or without
# * modification, are permitted provided that the following conditions
# * are met:
# * 1. Redistributions of source code must retain the above copyright
# * notice, this list of conditions and the following disclaimer.
# * 2. Redistributions in binary form must reproduce the above
# * copyright notice, this list of conditions and the following
# * disclaimer in the documentation and/or other materials provided
# * with the distribution.
# * 3. All advertising materials mentioning features or use of this
# * software must display the following acknowledgement:
# * This product includes software developed by Cyber-Physical
# * Systems Lab at UCLA and UC Berkeley.
# * 4. Neither the name of the University nor that of the Laboratory
# * may be used to endorse or promote products derived from this
# * software without specific prior written permission.
# *
# * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS''
# * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
# * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS
# * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
# * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
# * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
# * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
# * SUCH DAMAGE.
# *
# * Developed by: Yasser Shoukry
# */
import os
from solver import SMConvexSolver
import timeit
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
import matplotlib.patches as patches
import numpy as np
# TODO: Fix the PREFIX based counterexample
# TODO: add state constraints
#***************************************************************************************************
#***************************************************************************************************
#
# CLASS SMConvexSolver
#
#***************************************************************************************************
#***************************************************************************************************
class MultiRobotMotionPlanner:
# ========================================================
# Constructor
# ========================================================
def __init__(self, horizon, numberOfRobots, workspace, numberOfIntegrators):
print ('')
self.horizon = horizon
self.numberOfLTLBoolVars = 0
self.LTL = []
self.numberOfRobots = numberOfRobots
self.workspace = workspace
regions = workspace['regions']
self.numberOfRegions = len(regions)
self.topLevelFormula = []
self.numberOfIntegrators = numberOfIntegrators
# ***************************************************************************************************
# ***************************************************************************************************
#
# Solve For A Particular Horizon
#
# ***************************************************************************************************
# ***************************************************************************************************
def solve(self, robotsInitialState, robotsGoalState, inputConstraints, Ts,
safetyLimit, dwell):
numberOfSafetyConstraints = 0
for robotIndex in range(0, self.numberOfRobots):
for robotIndex2 in range(robotIndex+1, self.numberOfRobots):
numberOfSafetyConstraints += 4
numberOfStates = 2 * self.numberOfIntegrators
numberOfInputs = 2
numberOfBoolVars = self.numberOfLTLBoolVars
numOfRealVars = (numberOfStates + 2 * numberOfInputs) * self.horizon * dwell * self.numberOfRobots
robots, numOfConvIFClauses = self.__createsRobotDataStructure(self.numberOfRobots, dwell, self.horizon, numberOfStates, numberOfInputs, self.workspace)
solver = SMConvexSolver.SMConvexSolver(numberOfBoolVars, numOfRealVars, numOfConvIFClauses,
maxNumberOfIterations=10000,
verbose='OFF',
profiling='false',
numberOfCores=8,
counterExampleStrategy='IIS',
slackTolerance=1E-3)
# Add initial state constraints
start = timeit.default_timer()
self.__addInitialStateConstraints(solver, self.numberOfRobots, robots, robotsInitialState)
# Add Goal Constraints
start2 = timeit.default_timer()
if not self.LTL:
self.__addGoalStateConstraints(solver, self.numberOfRobots, robots, robotsGoalState)
else:
self.__LTLParser(solver, robots)
# Add Workspace constraints
start3 = timeit.default_timer()
self.__addWorkspaceConstraints(solver, self.numberOfRobots, robots, dwell, self.horizon, self.workspace)
# Add dynamics Constraints
start4 = timeit.default_timer()
self.__addDynamicsConstraints(solver, self.numberOfRobots, robots, dwell, self.horizon, Ts)
# Add input constraints
self.__addInputConstraints(solver, self.numberOfRobots, robots, dwell, self.horizon, inputConstraints)
# Add Safety Constraints
start5 = timeit.default_timer()
self.__addSafetyConstraints(solver, self.numberOfRobots, robots, dwell, self.horizon, safetyLimit, self.workspace)
end = timeit.default_timer()
print ('Feeding constraints time = ', end - start, start2 - start, start3 - start2, start4 - start3, start5 - start4, end - start5)
'''
# Add previous Counter Examples
for counterExample in previousCounterExamples:
if not counterExample:
continue
constraint = [ SMConvexSolver.NOT(solver.convIFClauses[counter]) for counter in counterExample ]
solver.addBoolConstraint(SMConvexSolver.OR(*constraint))
'''
stateTraj, booleanTraj, convIFModel = solver.solve()
counter_examples = solver.counterExamples
'''
for counterExample in counter_examples:
ceStr = 'CE: '
for ceElement in counterExample:
for horizonIndex in range(0, self.horizon):
convIFList = robots[0][horizonIndex]['regionsConstriantIndex']
if ceElement in convIFList:
ceStr = ceStr + str(convIFList.index(ceElement)) + ', '
break
print ceStr
print ('counterExamples', counter_examples)
'''
activeIFClauses = [i for i, x in enumerate(convIFModel) if x == True]
if not stateTraj:
return [], 0, counter_examples
robotsTraj = []
for robotIndex in range(0, self.numberOfRobots):
xTraj = []
yTraj = []
uxTraj = []
uyTraj = []
regionTraj = []
for horizonIndex in range(0, self.horizon):
regionTraj.append(activeIFClauses[horizonIndex] - horizonIndex * self.numberOfRegions)
for dwellIndex in range(0, dwell):
xTraj.append(stateTraj[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']])
yTraj.append(stateTraj[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']])
uxTraj.append(stateTraj[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['ux']])
uyTraj.append(stateTraj[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uy']])
trajectory = {'x': xTraj, 'y': yTraj, 'ux': uxTraj, 'uy': uyTraj}
robotsTraj.append(trajectory)
print( '\n======== Trajectory for Robot #', robotIndex, ' ==================')
print (xTraj)
print (yTraj)
print (uxTraj)
print (uyTraj)
print ('RegionTraj', regionTraj)
if self.LTL:
#if self.topLevelFormula['loopExists']:
startLoopPointers = [booleanTraj[i] for i in self.topLevelFormula['loopStart']]
loopIndexTrue = [i for i, x in enumerate(startLoopPointers) if x == True]
loopIndex = loopIndexTrue[0] * dwell
else:
loopIndex = -1
return robotsTraj, loopIndex, counter_examples
# ***************************************************************************************************
# ***************************************************************************************************
#
# Create "Robots" Data structure
#
# ***************************************************************************************************
# ***************************************************************************************************
def __createsRobotDataStructure(self, numberOfRobots, dwell, horizon, numberOfStates, numberOfInputs, workspace):
robots = []
robotStateShiftIndex = 0
convexIFShiftIndex = 0 # safety and region constraints
regions = workspace['regions']
numberOfRegions = len(regions)
# ---------- STATE VAR INDEX ----------------------------------------------------------------
for robotIndex in range(0, numberOfRobots):
robots.append([])
for horizonIndex in range(0, horizon):
robots[robotIndex].append([])
statesVarIndex = []
safetyConstraints = []
regionsConstraints = []
for dwellIndex in range(0, dwell):
indexInputX = 0 + robotStateShiftIndex
indexInputY = 1 + robotStateShiftIndex
indexInputNormX = 2 + robotStateShiftIndex
indexInputNormY = 3 + robotStateShiftIndex
U = [indexInputX, indexInputY]
indexX = 4 + robotStateShiftIndex
indexY = 5 + robotStateShiftIndex
derivativeShift = 6 + robotStateShiftIndex
derivativesX = range(derivativeShift, derivativeShift + self.numberOfIntegrators -1)
derivativeShift = derivativesX[-1] + 1
#print 'derivativeShift', derivativeShift
derivativesY = range(derivativeShift, derivativeShift + self.numberOfIntegrators - 1)
#indexXDot = 6 + robotStateShiftIndex
#indexYDot = 7 + robotStateShiftIndex
states = [indexX, indexY] + list(derivativesX) + list(derivativesY)
#print states
indecies = { 'ux': indexInputX,
'uy': indexInputY,
'inputs': U,
'uxNorm': indexInputNormX,
'uyNorm': indexInputNormY,
'x': indexX,
#'vx': indexXDot,
'y': indexY,
#'vy': indexYDot,
'states': states,
'derivatives': list(derivativesX) + list(derivativesY),
'integratorChainX': [indexX] + list(derivativesX),
'integratorChainY': [indexY] + list(derivativesY)
}
robotStateShiftIndex = robotStateShiftIndex + (numberOfStates + 2 * numberOfInputs)
statesVarIndex.append(indecies)
#robots[robotIndex][horizonIndex].append(statesVarIndex)
# Add indices for safety constraints (only for robots with index greater than current index)
for robotIndex2 in range(0, numberOfRobots):
if robotIndex2 <= robotIndex:
safetyConstraints.append([])
else:
safetyConstraints.append(range(convexIFShiftIndex, convexIFShiftIndex+4))
convexIFShiftIndex += 4
# Add indices for region constraints
regionsConstraints = range(convexIFShiftIndex, convexIFShiftIndex + numberOfRegions)
convexIFShiftIndex += numberOfRegions
if self.LTL and horizonIndex > 0:
consistencyConstraints = convexIFShiftIndex
convexIFShiftIndex = convexIFShiftIndex + 1
else:
consistencyConstraints = []
robots[robotIndex][horizonIndex] = {'stateIndex': statesVarIndex,
'safetyConstraintsIndex': safetyConstraints,
'regionsConstriantIndex': regionsConstraints,
'consistencyConstraintIndex': consistencyConstraints
}
#robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]
return robots, convexIFShiftIndex
# ***************************************************************************************************
# ***************************************************************************************************
#
# Add Initial Constraints
#
# ***************************************************************************************************
# ***************************************************************************************************
def __addInitialStateConstraints(self, solver, numberOfRobots, robots, robotsInitialState):
for robotIndex in range(0, numberOfRobots):
initialStateConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [robotsInitialState[robotIndex]['x0']],
[solver.rVars[robots[robotIndex][0]['stateIndex'][0]['x']]],
sense="E")
solver.addConvConstraint(initialStateConstraint)
initialStateConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [robotsInitialState[robotIndex]['y0']],
[solver.rVars[robots[robotIndex][0]['stateIndex'][0]['y']]],
sense="E")
solver.addConvConstraint(initialStateConstraint)
# all higher derivatives are set to zero
derivatives = robots[robotIndex][0]['stateIndex'][0]['derivatives']
for derivative in derivatives:
initialStateConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [0.0],[solver.rVars[derivative]],sense="E")
solver.addConvConstraint(initialStateConstraint)
# region constraint
initialRegion = robotsInitialState[robotIndex]['region']
solver.addBoolConstraint(
solver.convIFClauses[robots[robotIndex][0]['regionsConstriantIndex'][initialRegion]])
# ***************************************************************************************************
# ***************************************************************************************************
#
# Add Goal Constraints
#
# ***************************************************************************************************
# ***************************************************************************************************
def __addGoalStateConstraints(self, solver, numberOfRobots, robots, robotsGoalState):
for robotIndex in range(0, numberOfRobots):
goalStateConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [robotsGoalState[robotIndex]['xf']],
[solver.rVars[robots[robotIndex][-1]['stateIndex'][-1]['x']]],
sense="E")
solver.addConvConstraint(goalStateConstraint)
goalStateConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [robotsGoalState[robotIndex]['yf']],
[solver.rVars[robots[robotIndex][-1]['stateIndex'][-1]['y']]],
sense="E")
solver.addConvConstraint(goalStateConstraint)
# all higher derivatives are set to zero
derivatives = robots[robotIndex][-1]['stateIndex'][-1]['derivatives']
for derivative in derivatives:
goalStateConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [0.0], [solver.rVars[derivative]],
sense="E")
solver.addConvConstraint(goalStateConstraint)
# region constraint
goalRegion = robotsGoalState[robotIndex]['region']
solver.addBoolConstraint(
solver.convIFClauses[robots[robotIndex][-1]['regionsConstriantIndex'][goalRegion]]
)
# ***************************************************************************************************
# ***************************************************************************************************
#
# Add Workspace Constraints
#
# ***************************************************************************************************
# ***************************************************************************************************
def __addWorkspaceConstraints(self, solver, numberOfRobots, robots, dwell, horizon, workspace):
# if no regions are specified, then put only workspace constraints
if not workspace['regions']:
for robotIndex in range(0, numberOfRobots):
for horizonIndex in range(0, horizon):
for dwellIndex in range(0, dwell):
workspaceConstraint = SMConvexSolver.LPClause(np.array([[1]]), [workspace['xmin']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']]],
sense="G")
solver.addConvConstraint(workspaceConstraint)
workspaceConstraint = SMConvexSolver.LPClause(np.array([[1]]), [workspace['xmax']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']]],
sense="L")
solver.addConvConstraint(workspaceConstraint)
workspaceConstraint = SMConvexSolver.LPClause(np.array([[1]]), [workspace['ymin']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']]],
sense="G")
solver.addConvConstraint(workspaceConstraint)
workspaceConstraint = SMConvexSolver.LPClause(np.array([[1]]), [workspace['ymax']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']]],
sense="L")
solver.addConvConstraint(workspaceConstraint)
else:
regions = workspace['regions']
numberOfRegions = len(regions)
for robotIndex in range(0, numberOfRobots):
for horizonIndex in range(0, horizon):
for regionIndex in range(0, numberOfRegions):
rVars = []
# create the A matrix by rolling forward the regions[regionIndex]['A']
A_region = regions[regionIndex]['A']
A = np.zeros([dwell * np.shape(A_region)[0], dwell * np.shape(A_region)[1]])
b = []
rowIndex = 0
columnIndex = 0
for dwellIndex in range(0, dwell):
rVars.append(solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']])
rVars.append(solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']])
rows = range(rowIndex, rowIndex + np.shape(A_region)[0])
columns = range(columnIndex, columnIndex + np.shape(A_region)[1])
for rowCounter in range(0, len(rows)):
A[rows[rowCounter],:][columns] = A_region[rowCounter,:]
b.append(regions[regionIndex]['b'][rowCounter])
rowIndex += np.shape(A_region)[0]
columnIndex += np.shape(A_region)[1]
regionConstraint = SMConvexSolver.LPClause(
A,
b,
rVars,
sense="L")
regionsCosntraintsIndex = robots[robotIndex][horizonIndex]['regionsConstriantIndex'][regionIndex]
solver.setConvIFClause(regionConstraint, regionsCosntraintsIndex)
# Rule #1: You can not visit an obstacle region
if regions[regionIndex]['isObstacle']:
solver.addBoolConstraint(SMConvexSolver.NOT(solver.convIFClauses[regionsCosntraintsIndex]))
"""
Rule #2: You can move only through adjcaent regions:
unroll the state machine representing the workspace adjacency.
For the $i$ th partition, generate the follwoing clause
P_{i,k} => P_{adj1,k+1} OR P_{adj2,k+1} OR ... P_{adjn,k+1}
"""
if horizonIndex < horizon - 1:
adjacents = regions[regionIndex]['adjacents']
nextRegionsCosntraintsIndex = [robots[robotIndex][horizonIndex + 1]['regionsConstriantIndex'][i] for i in adjacents]
antecedent = solver.convIFClauses[regionsCosntraintsIndex]
consequent = [solver.convIFClauses[i] for i in nextRegionsCosntraintsIndex]
solver.addBoolConstraint(
SMConvexSolver.IMPLIES(antecedent, SMConvexSolver.OR(*consequent)))
"""
# ONLY ONE REGION AT A TIME #
for the $k$th time step , generate clause ensuring that only one partition is active
P_{1,k} + P_{2,k} + P_{p,k} = 1
where $p$ = number of partitions
"""
solver.addBoolConstraint(
sum([SMConvexSolver.BoolVar2Int(solver.convIFClauses[i]) for i in robots[robotIndex][horizonIndex]['regionsConstriantIndex']]) == 1)
# ***************************************************************************************************
# ***************************************************************************************************
#
# Add Input Constraints
#
# ***************************************************************************************************
# ***************************************************************************************************
def __addInputConstraints(self, solver, numberOfRobots, robots, dwell, horizon, inputConstraints):
# To minimize over L1 norm of inputs, we minimize over the auxiliary variables and bound the input from above
# and below with the auxiliary variables
for robotIndex in range(0, numberOfRobots):
for horizonIndex in range(0, horizon):
for dwellIndex in range(0, dwell):
solver.ConvSolver.objective.set_linear(
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uxNorm']], 1.0)
solver.ConvSolver.objective.set_linear(
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uyNorm']], 1.0)
rVars = [solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['ux']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uxNorm']]]
# ux \le uxNorm <==> ux - uxNorm \le 0
L1NormConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0]]), [0.0], rVars, sense="L")
solver.addConvConstraint(L1NormConstraint)
# ux >= -1 * uxNorm <==> -uxNorm - ux \le 0
L1NormConstraint = SMConvexSolver.LPClause(np.array([[-1.0, -1.0]]), [0.0], rVars, sense="L")
solver.addConvConstraint(L1NormConstraint)
rVars = [solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uy']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uyNorm']]]
# uy \le uyNorm <==> uy - uyNorm \le 0
L1NormConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0]]), [0.0], rVars, sense="L")
solver.addConvConstraint(L1NormConstraint)
# uy >= -1 * uyNorm <==> -uyNorm - uy \le 0
L1NormConstraint = SMConvexSolver.LPClause(np.array([[-1.0, -1.0]]), [0.0], rVars, sense="L")
solver.addConvConstraint(L1NormConstraint)
for robotIndex in range(0, numberOfRobots):
for horizonIndex in range(0, horizon):
for dwellIndex in range(0, dwell):
# max limit on ux
inputConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [inputConstraints[robotIndex]['uxMax']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['ux']]],
sense="L")
solver.addConvConstraint(inputConstraint)
# min limit on ux
inputConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [inputConstraints[robotIndex]['uxMin']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['ux']]],
sense="G")
solver.addConvConstraint(inputConstraint)
# max limit on uy
inputConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [inputConstraints[robotIndex]['uyMax']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uy']]],
sense="L")
solver.addConvConstraint(inputConstraint)
# min limit on uy
inputConstraint = SMConvexSolver.LPClause(np.array([[1.0]]), [inputConstraints[robotIndex]['uyMin']],
[solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uy']]],
sense="G")
solver.addConvConstraint(inputConstraint)
# ***************************************************************************************************
# ***************************************************************************************************
#
# Add Dynamics Constraints
#
# ***************************************************************************************************
# ***************************************************************************************************
def __addDynamicsConstraints(self, solver, numberOfRobots, robots, dwell, horizon, Ts):
for robotIndex in range(0, numberOfRobots):
for horizonIndex in range(0, horizon):
for dwellIndex in range(0, dwell):
if dwellIndex < dwell -1:
dwellIndexNext = dwellIndex + 1
horizonIndexNext = horizonIndex
else:
dwellIndexNext = 0
horizonIndexNext = horizonIndex + 1
if horizonIndex == horizon -1 and dwellIndex == dwell -1:
break
integratorChainX = robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['integratorChainX']
integratorChainY = robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['integratorChainY']
integratorChainXNext = robots[robotIndex][horizonIndexNext]['stateIndex'][dwellIndexNext][
'integratorChainX']
integratorChainYNext = robots[robotIndex][horizonIndexNext]['stateIndex'][dwellIndexNext][
'integratorChainY']
for integratorIndex in range(0, self.numberOfIntegrators - 1):
# state_i(t+1) = state_i(t) + Ts * state_{i + 1}(t)
vars = [
solver.rVars[integratorChainXNext[integratorIndex]],
solver.rVars[integratorChainX[integratorIndex]],
solver.rVars[integratorChainX[integratorIndex + 1]]
]
#print 'chainX', vars
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars,
sense="E")
solver.addConvConstraint(dynamicsConstraint)
vars = [
solver.rVars[integratorChainYNext[integratorIndex]],
solver.rVars[integratorChainY[integratorIndex]],
solver.rVars[integratorChainY[integratorIndex + 1]]
]
#print 'chainY', vars
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars,
sense="E")
solver.addConvConstraint(dynamicsConstraint)
vars = [solver.rVars[integratorChainXNext[-1]],
solver.rVars[integratorChainX[-1]],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['ux']]
]
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars,
sense="E")
solver.addConvConstraint(dynamicsConstraint)
vars = [solver.rVars[integratorChainYNext[-1]],
solver.rVars[integratorChainY[-1]],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uy']]
]
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars,
sense="E")
solver.addConvConstraint(dynamicsConstraint)
'''
# x(t+1) = x(t) + Ts * vx(t)
vars = [solver.rVars[robots[robotIndex][horizonIndexNext]['stateIndex'][dwellIndexNext]['x']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['vx']]
]
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars, sense="E")
solver.addConvConstraint(dynamicsConstraint)
# y(t+1) = y(t) + Ts * vy(t)
vars = [solver.rVars[robots[robotIndex][horizonIndexNext]['stateIndex'][dwellIndexNext]['y']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['vy']]
]
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars, sense="E")
solver.addConvConstraint(dynamicsConstraint)
# vx(t+1) = vx(t) + Ts * ux(t)
vars = [solver.rVars[robots[robotIndex][horizonIndexNext]['stateIndex'][dwellIndexNext]['vx']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['vx']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['ux']]
]
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars, sense="E")
solver.addConvConstraint(dynamicsConstraint)
# vy(t+1) = v(y) + Ts * uy(t)
vars = [solver.rVars[robots[robotIndex][horizonIndexNext]['stateIndex'][dwellIndexNext]['vy']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['vy']],
solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['uy']]
]
dynamicsConstraint = SMConvexSolver.LPClause(np.array([[1.0, -1.0, -1 * Ts]]), [0.0], vars, sense="E")
solver.addConvConstraint(dynamicsConstraint)
'''
# ***************************************************************************************************
# ***************************************************************************************************
#
# Add Safety Constraints
#
# ***************************************************************************************************
# ***************************************************************************************************
def __addSafetyConstraints(self, solver, numberOfRobots, robots, dwell, horizon, safetyLimit, workspace):
for horizonIndex in range(0, horizon):
for robotIndex in range(0, numberOfRobots):
for robotIndex2 in range(robotIndex+1, numberOfRobots):
safetyConstraintsIndex = robots[robotIndex][horizonIndex]['safetyConstraintsIndex'][robotIndex2]
# x0 - x1 > epsilon
rVars = []
A = np.zeros([dwell, 2*dwell])
b = []
sense = "G"
for dwellIndex in range(0, dwell):
rVars.append(solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']])
rVars.append(solver.rVars[robots[robotIndex2][horizonIndex]['stateIndex'][dwellIndex]['x']])
A[dwellIndex,:][2*dwellIndex: 2*dwellIndex + 2] = [1.0, -1.0]
b.append(safetyLimit)
safetyConstraint = SMConvexSolver.LPClause(A, b, rVars, sense)
solver.setConvIFClause(safetyConstraint, safetyConstraintsIndex[0])
# x1 - x0 > epsilon
rVars = []
A = np.zeros([dwell, 2 * dwell])
b = []
sense = "G"
for dwellIndex in range(0, dwell):
rVars.append(solver.rVars[robots[robotIndex2][horizonIndex]['stateIndex'][dwellIndex]['x']])
rVars.append(solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['x']])
A[dwellIndex, :][2 * dwellIndex: 2 * dwellIndex + 2] = [1.0, -1.0]
b.append(safetyLimit)
safetyConstraint = SMConvexSolver.LPClause(A, b, rVars, sense)
solver.setConvIFClause(safetyConstraint, safetyConstraintsIndex[1])
# y0 - y1 > epsilon
rVars = []
A = np.zeros([dwell, 2 * dwell])
b = []
sense = "G"
for dwellIndex in range(0, dwell):
rVars.append(solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']])
rVars.append(solver.rVars[robots[robotIndex2][horizonIndex]['stateIndex'][dwellIndex]['y']])
A[dwellIndex, :][2 * dwellIndex: 2 * dwellIndex + 2] = [1.0, -1.0]
b.append(safetyLimit)
safetyConstraint = SMConvexSolver.LPClause(A, b, rVars, sense)
solver.setConvIFClause(safetyConstraint, safetyConstraintsIndex[2])
# y1 - y0 > epsilon
rVars = []
A = np.zeros([dwell, 2 * dwell])
b = []
sense = "G"
for dwellIndex in range(0, dwell):
rVars.append(solver.rVars[robots[robotIndex2][horizonIndex]['stateIndex'][dwellIndex]['y']])
rVars.append(solver.rVars[robots[robotIndex][horizonIndex]['stateIndex'][dwellIndex]['y']])
A[dwellIndex, :][2 * dwellIndex: 2 * dwellIndex + 2] = [1.0, -1.0]
b.append(safetyLimit)
safetyConstraint = SMConvexSolver.LPClause(A, b, rVars, sense)
solver.setConvIFClause(safetyConstraint, safetyConstraintsIndex[3])
'''
# If robot1 is on the right, it can not be on the left at the same time
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.convIFClauses[safetyConstraintsIndex[0]],
SMConvexSolver.NOT(
solver.convIFClauses[safetyConstraintsIndex[1]]
)
)
)
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.convIFClauses[safetyConstraintsIndex[2]],
SMConvexSolver.NOT(
solver.convIFClauses[safetyConstraintsIndex[3]]
)
)
)
'''
# if robots are in two adjacent regions THEN:
# at least one of the safety conditions must be enforced (encoded using disjunction)
# The antecedent is encoded as (robot_1_at_region_1 AND robot_1_at_adj(region)_1) OR ( ) OR ( ) ...
regionConstraintsFirstRobot = robots[robotIndex][horizonIndex]['regionsConstriantIndex']
regionConstraintsSecondRobot = robots[robotIndex2][horizonIndex]['regionsConstriantIndex']
regionConstraints = []
for regioncounter in range(0, len(regionConstraintsFirstRobot)):
adjacents = workspace['regions'][regioncounter]['adjacents']
for adjacentCounter in range(0, len(adjacents)):
regionConstraints.append(SMConvexSolver.AND(solver.convIFClauses[regionConstraintsFirstRobot[regioncounter]],
solver.convIFClauses[regionConstraintsSecondRobot[adjacents[adjacentCounter]]]))
antecedent = SMConvexSolver.OR(*regionConstraints)
# if no regions are specified, then all robots are in the same region
if not workspace['regions']:
antecedent = True
constraint = [solver.convIFClauses[i] for i in safetyConstraintsIndex]
consequent = SMConvexSolver.OR(*constraint)
solver.addBoolConstraint(SMConvexSolver.IMPLIES(antecedent, consequent))
# ***************************************************************************************************
# ***************************************************************************************************
#
# LTL Parser
#
# ***************************************************************************************************
# ***************************************************************************************************
def __LTLParser(self, solver, robots):
# get the top level formula
for formula in self.LTL:
if formula['type'] == 'LTL':
topLevelFormula = formula
self.topLevelFormula = formula
self.__generateLTLBooleanConstraints(solver, formula, robots)
for formula in self.LTL:
if formula['type'] == 'atomic':
self.__generateAtomicBooleanConstraints(solver, formula, topLevelFormula, robots)
elif formula['type'] == 'compound1':
if formula['operator'] == 'G':
self.__generateCompoundGLOBALLYBooleanConstraints(solver, formula, topLevelFormula)
elif formula['operator'] == 'E':
self.__generateCompoundEVENTUALLYBooleanConstraints(solver, formula, topLevelFormula)
elif formula['operator'] == 'NOT':
self.__generateCompoundNOTBooleanConstraints(solver, formula, topLevelFormula)
elif formula['type'] == 'compound2':
if formula['operator'] == 'AND':
self.__generateCompoundANDBooleanConstraints(solver, formula, topLevelFormula)
elif formula['operator'] == 'OR':
self.__generateCompoundORBooleanConstraints(solver, formula, topLevelFormula)
elif formula['operator'] == 'RELEASE':
self.__generateCompoundRELEASEBooleanConstraints(solver, formula, topLevelFormula)
# ***************************************************************************************************
# ***************************************************************************************************
#
# TOP LEVEL LTL CONSTRAINTS
#
# ***************************************************************************************************
# ***************************************************************************************************
def __generateLTLBooleanConstraints(self, solver, formula, robots):
prop1 = self.LTL[formula['argument1']]
# LTLbVar <=> formulabVar(t)
# for all time t \in {0, L}
for horizonCounter in range(0, self.horizon):
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['formulaSatisfied']],
solver.bVars[prop1['boolVarsIndex'][horizonCounter]]
)
)
# the LTL boolean variables must be satisfied
solver.addBoolConstraint(solver.bVars[formula['formulaSatisfied']])
# ------------ Loop Constraints ---------------------
# loopStart_0 <=> false
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['loopStart'][0]],
False
)
)
# inLoop_0 <=> false
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['inLoop'][0]],
False
)
)
# 1 \le i \le k
for horizonCounter in range(1, self.horizon):
# inLoop_i <=> inLoop_{i -1 } OR loopStart_i
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['inLoop'][horizonCounter]],
SMConvexSolver.OR(
*[
solver.bVars[formula['loopStart'][horizonCounter]],
solver.bVars[formula['inLoop'][horizonCounter-1]],
]
)
)
)
# inLoop_{i-1} => NOT loopStart_{i}
solver.addBoolConstraint(
SMConvexSolver.IMPLIES(
solver.bVars[formula['inLoop'][horizonCounter-1]],
SMConvexSolver.NOT(
solver.bVars[formula['loopStart'][horizonCounter]]
)
)
)
# loopStart_i => (s_{i-1} = s_{horizon}) region consistency
for robotIndex in range(0, self.numberOfRobots):
for regionIndex in range(0, self.numberOfRegions):
solver.addBoolConstraint(
SMConvexSolver.IMPLIES(
solver.bVars[formula['loopStart'][horizonCounter]],
SMConvexSolver.EQUIV(
solver.convIFClauses[robots[robotIndex][horizonCounter - 1]['regionsConstriantIndex'][regionIndex]],
solver.convIFClauses[robots[robotIndex][-1]['regionsConstriantIndex'][regionIndex]],
)
)
)
# robot state constraints
stateStartLoop = robots[robotIndex][horizonCounter]['stateIndex'][0]['states']
stateEndLoop = robots[robotIndex][-1]['stateIndex'][-1]['states']
numberOFstates = len(stateStartLoop)
A = np.concatenate( (np.identity(numberOFstates), -1 *np.identity(numberOFstates)), axis = 1)
b = [0.0]*numberOFstates
#print 'consistency', robots[robotIndex][horizonCounter]['consistencyConstraintIndex'], stateStartLoop + stateEndLoop
consistencyConstraint = SMConvexSolver.LPClause(A, b, stateStartLoop + stateEndLoop, 'E')
solver.setConvIFClause(
consistencyConstraint,
robots[robotIndex][horizonCounter]['consistencyConstraintIndex']
)
solver.addBoolConstraint(
SMConvexSolver.IMPLIES(
solver.bVars[formula['loopStart'][horizonCounter]],
solver.convIFClauses[robots[robotIndex][horizonCounter]['consistencyConstraintIndex']]
)
)
# loopexists <=> inloop_{horizon}
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['loopExists']],
solver.bVars[formula['inLoop'][-1]]
)
)
# ***************************************************************************************************
# ***************************************************************************************************
#
# Encode Constraints for ATOMIC Propositions
#
# ***************************************************************************************************
# ***************************************************************************************************
def __generateAtomicBooleanConstraints(self, solver, formula, topLevelFormula, robots):
robotsIndex = formula['robots']
sense = formula['sense']
rhs = formula['rhs']
regionIndex = formula['region']
for horizonCounter in range(0, self.horizon):
ifVars = [robots[j][horizonCounter]['regionsConstriantIndex'][regionIndex] for j in robotsIndex]
if sense == 'GE':
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['boolVarsIndex'][horizonCounter]],
sum([SMConvexSolver.BoolVar2Int(solver.convIFClauses[j]) for j in ifVars]) >= rhs
)
)
elif sense == 'LE':
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['boolVarsIndex'][horizonCounter]],
sum([SMConvexSolver.BoolVar2Int(solver.convIFClauses[j]) for j in ifVars]) <= rhs
)
)
elif sense == 'E':
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['boolVarsIndex'][horizonCounter]],
sum([SMConvexSolver.BoolVar2Int(solver.convIFClauses[j]) for j in ifVars]) == rhs
)
)
# ----- Formula Consistency -----------------------------
for horizonCounter in range(1, self.horizon):
# loop consistency
# loopStart_i => (b_i <=> l_horizon)
solver.addBoolConstraint(
SMConvexSolver.IMPLIES(
solver.bVars[topLevelFormula['loopStart'][horizonCounter]],
SMConvexSolver.EQUIV(
solver.bVars[formula['boolVarsIndex'][horizonCounter-1]],
solver.bVars[formula['boolVarsIndex'][-1]]
)
)
)
# ***************************************************************************************************
# ***************************************************************************************************
#
# Encode: Constraints of AND
#
# ***************************************************************************************************
# ***************************************************************************************************
def __generateCompoundANDBooleanConstraints(self, solver, formula, topLevelFormula):
prop1 = self.LTL[formula['argument1']]
prop2 = self.LTL[formula['argument2']]
for horizonCounter in range(0, self.horizon):
solver.addBoolConstraint(
SMConvexSolver.EQUIV(
solver.bVars[formula['boolVarsIndex'][horizonCounter]],
SMConvexSolver.AND(
*[
solver.bVars[prop1['boolVarsIndex'][horizonCounter]],
solver.bVars[prop2['boolVarsIndex'][horizonCounter]]
]
)
)
)
# ------------ Formula Consistency ---------------------
for horizonCounter in range(1, self.horizon):
# loop consistency
# loopStart_i => (b_i <=> l_horizon)
solver.addBoolConstraint(
SMConvexSolver.IMPLIES(
solver.bVars[topLevelFormula['loopStart'][horizonCounter]],
SMConvexSolver.EQUIV(
solver.bVars[formula['boolVarsIndex'][horizonCounter-1]],
solver.bVars[formula['boolVarsIndex'][-1]]
)
)