plot demo for version 2
mcarfagno
parent
0f572d0caa
commit
19532431dc
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import numpy as np
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np.seterr(divide='ignore', invalid='ignore')
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from scipy.integrate import odeint
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from scipy.interpolate import interp1d
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import cvxpy as cp
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from utils import road_curve, f, df
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from mpc_config import Params
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P=Params()
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def get_linear_model(x_bar,u_bar):
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"""
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"""
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x = x_bar[0]
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y = x_bar[1]
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theta = x_bar[2]
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v = u_bar[0]
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w = u_bar[1]
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A = np.zeros((P.N,P.N))
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A[0,2]=-v*np.sin(theta)
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A[1,2]=v*np.cos(theta)
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A_lin=np.eye(P.N)+P.dt*A
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B = np.zeros((P.N,P.M))
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B[0,0]=np.cos(theta)
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B[1,0]=np.sin(theta)
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B[2,1]=1
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B_lin=P.dt*B
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f_xu=np.array([v*np.cos(theta),v*np.sin(theta),w]).reshape(P.N,1)
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C_lin = P.dt*(f_xu - np.dot(A,x_bar.reshape(P.N,1)) - np.dot(B,u_bar.reshape(P.M,1)))
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return A_lin,B_lin,C_lin
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def optimize(state,u_bar,track):
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'''
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:param state:
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:param u_bar:
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:param track:
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:returns:
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'''
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MAX_SPEED = 1.25
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MIN_SPEED = 0.75
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MAX_STEER_SPEED = 1.57/2
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# compute polynomial coefficients of the track
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K=road_curve(state,track)
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# dynamics starting state w.r.t vehicle frame
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x_bar=np.zeros((P.N,P.T+1))
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#prediction for linearization of costrains
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for t in range (1,P.T+1):
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xt=x_bar[:,t-1].reshape(P.N,1)
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ut=u_bar[:,t-1].reshape(P.M,1)
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A,B,C=get_linear_model(xt,ut)
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xt_plus_one = np.squeeze(np.dot(A,xt)+np.dot(B,ut)+C)
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x_bar[:,t]= xt_plus_one
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#CVXPY Linear MPC problem statement
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cost = 0
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constr = []
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x = cp.Variable((P.N, P.T+1))
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u = cp.Variable((P.M, P.T))
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for t in range(P.T):
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#cost += 30*cp.sum_squares(x[2,t]-np.arctan(df(x_bar[0,t],K))) # psi
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cost += 50*cp.sum_squares(x[2,t]-np.arctan2(df(x_bar[0,t],K),x_bar[0,t])) # psi
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cost += 20*cp.sum_squares(f(x_bar[0,t],K)-x[1,t]) # cte
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# Actuation rate of change
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if t < (P.T - 1):
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cost += cp.quad_form(u[:, t + 1] - u[:, t], 100*np.eye(P.M))
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# Actuation effort
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cost += cp.quad_form( u[:, t],1*np.eye(P.M))
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# Kinrmatics Constrains (Linearized model)
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A,B,C=get_linear_model(x_bar[:,t],u_bar[:,t])
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constr += [x[:,t+1] == A@x[:,t] + B@u[:,t] + C.flatten()]
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# sums problem objectives and concatenates constraints.
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constr += [x[:,0] == x_bar[:,0]] #<--watch out the start condition
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constr += [u[0, :] <= MAX_SPEED]
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constr += [u[0, :] >= MIN_SPEED]
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constr += [cp.abs(u[1, :]) <= MAX_STEER_SPEED]
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# Solve
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prob = cp.Problem(cp.Minimize(cost), constr)
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solution = prob.solve(solver=cp.OSQP, verbose=False)
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#retrieved optimized U and assign to u_bar to linearize in next step
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u_bar=np.vstack((np.array(u.value[0, :]).flatten(),
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(np.array(u.value[1, :]).flatten())))
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return u_bar
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Binary file not shown.
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After Width: | Height: | Size: 6.2 KiB |
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@ -0,0 +1,15 @@
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newmtl Material
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Ns 10.0000
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Ni 1.5000
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d 1.0000
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Tr 0.0000
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Tf 1.0000 1.0000 1.0000
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illum 2
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Ka 0.0000 0.0000 0.0000
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Kd 0.5880 0.5880 0.5880
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Ks 0.0000 0.0000 0.0000
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Ke 0.0000 0.0000 0.0000
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map_Ka cube.tga
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map_Kd checker_blue.png
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@ -0,0 +1,18 @@
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# Blender v2.66 (sub 1) OBJ File: ''
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# www.blender.org
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mtllib plane.mtl
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o Plane
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v 15.000000 -15.000000 0.000000
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v 15.000000 15.000000 0.000000
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v -15.000000 15.000000 0.000000
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v -15.000000 -15.000000 0.000000
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vt 15.000000 0.000000
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vt 15.000000 15.000000
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vt 0.000000 15.000000
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vt 0.000000 0.000000
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usemtl Material
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s off
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f 1/1 2/2 3/3
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f 1/1 3/3 4/4
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@ -0,0 +1,29 @@
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<?xml version="0.0" ?>
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<robot name="plane">
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<link name="planeLink">
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<contact>
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<lateral_friction value="1"/>
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</contact>
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<inertial>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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<mass value=".0"/>
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<inertia ixx="0" ixy="0" ixz="0" iyy="0" iyz="0" izz="0"/>
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</inertial>
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<visual>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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<geometry>
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<mesh filename="plane.obj" scale="1 1 1"/>
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</geometry>
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<material name="white">
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<color rgba="1 1 1 1"/>
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</material>
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</visual>
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<collision>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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<geometry>
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<plane normal="0 0 1"/>
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</geometry>
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</collision>
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</link>
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</robot>
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@ -0,0 +1,827 @@
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<?xml version="1.0" ?>
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<!-- =================================================================================== -->
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<!-- | This document was autogenerated by xacro from robots/kobuki_hexagons_kinect.urdf.xacro | -->
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<!-- | EDITING THIS FILE BY HAND IS NOT RECOMMENDED | -->
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<!-- =================================================================================== -->
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<!--
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- Base : kobuki
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- Stacks : hexagons
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- 3d Sensor : kinect
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-->
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<robot name="turtlebot" xmlns:controller="http://playerstage.sourceforge.net/gazebo/xmlschema/#controller" xmlns:interface="http://playerstage.sourceforge.net/gazebo/xmlschema/#interface" xmlns:sensor="http://playerstage.sourceforge.net/gazebo/xmlschema/#sensor" xmlns:xacro="http://ros.org/wiki/xacro">
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<link name="base_link">
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<visual>
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<geometry>
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<!-- new mesh -->
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<mesh filename="turtlebot/kobuki_description/meshes/main_body.dae"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0.001 0 0.05199"/>
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</visual>
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<collision>
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<geometry>
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<cylinder length="0.10938" radius="0.176"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0.0 0 0.05949"/>
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</collision>
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<inertial>
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<mass value="2.4"/>
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<!-- 2.4/2.6 kg for small/big battery pack -->
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<origin xyz="0 0 0"/>
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<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
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</inertial>
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</link>
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<joint name="wheel_left_joint" type="continuous">
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<parent link="base_link"/>
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<child link="wheel_left_link"/>
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<origin rpy="-1.57079632679 0 0" xyz="0.00 0.115 0.0250"/>
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<axis xyz="0 0 1"/>
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</joint>
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<link name="wheel_left_link">
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<visual>
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<geometry>
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<mesh filename="turtlebot/kobuki_description/meshes/wheel.dae"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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</visual>
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<collision>
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<geometry>
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<cylinder length="0.0206" radius="0.0352"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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</collision>
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<inertial>
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<mass value="0.1"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.01" ixy="0.0" ixz="0.0" iyy="0.01" iyz="0.0" izz="0.01"/>
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</inertial>
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<contact>
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<lateral_friction value="1.0"/>
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<rolling_friction value="0.0"/>
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<stiffness value="30000"/>
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<damping value="1000"/>
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</contact>
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</link>
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<joint name="wheel_right_joint" type="continuous">
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<parent link="base_link"/>
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<child link="wheel_right_link"/>
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<origin rpy="-1.57079632679 0 0" xyz="0.00 -0.115 0.0250"/>
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<axis xyz="0 0 1"/>
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</joint>
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<link name="wheel_right_link">
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<visual>
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<geometry>
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<mesh filename="turtlebot/kobuki_description/meshes/wheel.dae"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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</visual>
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<collision>
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<geometry>
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<cylinder length="0.0206" radius="0.0350"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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</collision>
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<inertial>
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<mass value="0.1"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.01" ixy="0.0" ixz="0.0" iyy="0.01" iyz="0.0" izz="0.01"/>
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</inertial>
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<contact>
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<lateral_friction value="1.0"/>
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<rolling_friction value="0.0"/>
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<stiffness value="30000"/>
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<damping value="10000"/>
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</contact>
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</link>
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<joint name="caster_front_joint" type="fixed">
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<parent link="base_link"/>
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<child link="caster_front_link"/>
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<origin rpy="-1.57079632679 0 0" xyz="0.115 0.0 0.007"/>
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</joint>
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<link name="caster_front_link">
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<collision>
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<geometry>
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<cylinder length="0.0176" radius="0.017"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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</collision>
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<inertial>
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<mass value="0.01"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.001" ixy="0.0" ixz="0.0" iyy="0.001" iyz="0.0" izz="0.001"/>
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</inertial>
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<contact>
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<lateral_friction value="0.0"/>
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<rolling_friction value="0.0"/>
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<stiffness value="30000"/>
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<damping value="10000"/>
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</contact>
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</link>
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<joint name="caster_back_joint" type="fixed">
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<parent link="base_link"/>
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<child link="caster_back_link"/>
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<origin rpy="-1.57079632679 0 0" xyz="-0.135 0.0 0.009"/>
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</joint>
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<link name="caster_back_link">
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<collision>
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<geometry>
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<cylinder length="0.0176" radius="0.017"/>
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</geometry>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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</collision>
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<inertial>
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<mass value="0.01"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.001" ixy="0.0" ixz="0.0" iyy="0.001" iyz="0.0" izz="0.001"/>
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</inertial>
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<contact>
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<lateral_friction value="0.0"/>
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<rolling_friction value="0.0"/>
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<stiffness value="30000"/>
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<damping value="1000"/>
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</contact>
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</link>
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<joint name="gyro_joint" type="fixed">
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<axis xyz="0 1 0"/>
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<origin rpy="0 0 0" xyz="0.056 0.062 0.0202"/>
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<parent link="base_link"/>
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<child link="gyro_link"/>
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</joint>
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<link name="gyro_link">
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<inertial>
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<mass value="0.001"/>
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<origin rpy="0 0 0" xyz="0 0 0"/>
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<inertia ixx="0.0001" ixy="0" ixz="0" iyy="0.000001" iyz="0" izz="0.0001"/>
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</inertial>
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</link>
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<joint name="cliff_sensor_left_joint" type="fixed">
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<origin rpy="0 1.57079632679 0" xyz="0.08734 0.13601 0.0214"/>
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<parent link="base_link"/>
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<child link="cliff_sensor_left_link"/>
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</joint>
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<link name="cliff_sensor_left_link">
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<inertial>
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<mass value="0.0001"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
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</inertial>
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</link>
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<joint name="cliff_sensor_right_joint" type="fixed">
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<origin rpy="0 1.57079632679 0" xyz="0.085 -0.13601 0.0214"/>
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<parent link="base_link"/>
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<child link="cliff_sensor_right_link"/>
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</joint>
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<link name="cliff_sensor_right_link">
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<inertial>
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<mass value="0.0001"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
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</inertial>
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</link>
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<joint name="cliff_sensor_front_joint" type="fixed">
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<origin rpy="0 1.57079632679 0" xyz="0.156 0.00 0.0214"/>
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<parent link="base_link"/>
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<child link="cliff_sensor_front_link"/>
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</joint>
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<link name="cliff_sensor_front_link">
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<inertial>
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<mass value="0.0001"/>
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<origin xyz="0 0 0"/>
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<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
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</inertial>
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</link>
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<gazebo>
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<controller:gazebo_ros_kobuki name="kobuki_controller" plugin="libgazebo_ros_kobuki.so">
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<left_wheel_joint_name>wheel_left_joint</left_wheel_joint_name>
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<right_wheel_joint_name>wheel_right_joint</right_wheel_joint_name>
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<wheel_separation>.230</wheel_separation>
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<wheel_diameter>0.070</wheel_diameter>
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<torque>1.0</torque>
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<velocity_command_timeout>0.6</velocity_command_timeout>
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<cliff_sensor_left_name>cliff_sensor_left</cliff_sensor_left_name>
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<cliff_sensor_front_name>cliff_sensor_front</cliff_sensor_front_name>
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<cliff_sensor_right_name>cliff_sensor_right</cliff_sensor_right_name>
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<cliff_detection_threshold>0.04</cliff_detection_threshold>
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<bumper_name>bumpers</bumper_name>
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<base_collision_model_link>base_link</base_collision_model_link>
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</controller:gazebo_ros_kobuki>
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</gazebo>
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<gazebo reference="wheel_left_link">
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<mu1 value="10"/>
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<mu2 value="10"/>
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<kp value="100000000.0"/>
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<kd value="10000.0"/>
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</gazebo>
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<gazebo reference="wheel_right_link">
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<mu1 value="10"/>
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<mu2 value="10"/>
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<kp value="100000000.0"/>
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<kd value="10000.0"/>
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</gazebo>
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<gazebo reference="caster_front_link">
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<mu1 value="0"/>
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<mu2 value="0"/>
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<kp value="100000000.0"/>
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<kd value="10000.0"/>
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</gazebo>
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<gazebo reference="caster_back_link">
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<mu1 value="0"/>
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<mu2 value="0"/>
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<kp value="100000000.0"/>
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<kd value="10000.0"/>
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</gazebo>
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<gazebo reference="base_link">
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<sensor:contact name="bumpers">
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<geom>base_footprint_geom_base_link</geom>
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<topic>bumpers</topic>
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<alwaysOn>true</alwaysOn>
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<updateRate>50</updateRate>
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</sensor:contact>
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</gazebo>
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<gazebo reference="cliff_sensor_left_link">
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<sensor:ray name="cliff_sensor_left">
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<alwaysOn>true</alwaysOn>
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<updateRate>50</updateRate>
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<rayCount>50</rayCount>
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<rangeCount>1</rangeCount>
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<resRange>1.0</resRange>
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<minAngle>-0.04361</minAngle>
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<maxAngle>0.04361</maxAngle>
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||||
<minRange>0.01</minRange>
|
||||
<maxRange>0.15</maxRange>
|
||||
<displayRays>true</displayRays>
|
||||
</sensor:ray>
|
||||
</gazebo>
|
||||
<gazebo reference="cliff_sensor_right_link">
|
||||
<sensor:ray name="cliff_sensor_right">
|
||||
<alwaysOn>true</alwaysOn>
|
||||
<updateRate>50</updateRate>
|
||||
<rayCount>50</rayCount>
|
||||
<rangeCount>1</rangeCount>
|
||||
<resRange>1.0</resRange>
|
||||
<minAngle>-2.5</minAngle>
|
||||
<maxAngle>2.5</maxAngle>
|
||||
<minRange>0.01</minRange>
|
||||
<maxRange>0.15</maxRange>
|
||||
<displayRays>true</displayRays>
|
||||
</sensor:ray>
|
||||
</gazebo>
|
||||
<gazebo reference="cliff_sensor_front_link">
|
||||
<sensor:ray name="cliff_sensor_front">
|
||||
<alwaysOn>true</alwaysOn>
|
||||
<updateRate>50</updateRate>
|
||||
<rayCount>50</rayCount>
|
||||
<rangeCount>1</rangeCount>
|
||||
<resRange>1.0</resRange>
|
||||
<minAngle>-2.5</minAngle>
|
||||
<maxAngle>2.5</maxAngle>
|
||||
<minRange>0.01</minRange>
|
||||
<maxRange>0.15</maxRange>
|
||||
<displayRays>true</displayRays>
|
||||
</sensor:ray>
|
||||
</gazebo>
|
||||
<gazebo>
|
||||
<controller:gazebo_ros_imu name="imu_controller" plugin="libgazebo_ros_imu.so">
|
||||
<alwaysOn>true</alwaysOn>
|
||||
<updateRate>50</updateRate>
|
||||
<bodyName>gyro_link</bodyName>
|
||||
<topicName>/mobile_base/sensors/imu_data</topicName>
|
||||
<gaussianNoise>2.89e-06</gaussianNoise>
|
||||
<xyzOffsets>0 0 0</xyzOffsets>
|
||||
<rpyOffsets>0 0 0</rpyOffsets>
|
||||
<interface:position name="gyro_link"/>
|
||||
</controller:gazebo_ros_imu>
|
||||
</gazebo>
|
||||
<joint name="pole_bottom_0_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.12 0.082 0.1028"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_bottom_0_link"/>
|
||||
</joint>
|
||||
<link name="pole_bottom_0_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0492" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_bottom_1_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.055 0.12 0.1028"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_bottom_1_link"/>
|
||||
</joint>
|
||||
<link name="pole_bottom_1_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0492" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_bottom_2_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.055 0.12 0.1028"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_bottom_2_link"/>
|
||||
</joint>
|
||||
<link name="pole_bottom_2_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0492" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_bottom_3_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.12 -0.082 0.1028"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_bottom_3_link"/>
|
||||
</joint>
|
||||
<link name="pole_bottom_3_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0492" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_bottom_4_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.055 -0.12 0.1028"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_bottom_4_link"/>
|
||||
</joint>
|
||||
<link name="pole_bottom_4_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0492" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_bottom_5_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.055 -0.12 0.1028"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_bottom_5_link"/>
|
||||
</joint>
|
||||
<link name="pole_bottom_5_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0492" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="plate_bottom_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.02364 0.0 0.1306"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="plate_bottom_link"/>
|
||||
</joint>
|
||||
<link name="plate_bottom_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/plate_bottom.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<box size="0.26727 0.340 0.006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.01"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.01" ixy="0.0" ixz="0.0" iyy="0.01" iyz="0.0" izz="0.01"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_middle_0_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.0381 0.1505 0.164"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_middle_0_link"/>
|
||||
</joint>
|
||||
<link name="pole_middle_0_link">
|
||||
<visual>
|
||||
<origin rpy="0 3.14159265359 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_middle.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0608" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_middle_1_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.0381 -0.1505 0.164"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_middle_1_link"/>
|
||||
</joint>
|
||||
<link name="pole_middle_1_link">
|
||||
<visual>
|
||||
<origin rpy="0 3.14159265359 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_middle.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0608" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_middle_2_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.0381 0.1505 0.164"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_middle_2_link"/>
|
||||
</joint>
|
||||
<link name="pole_middle_2_link">
|
||||
<visual>
|
||||
<origin rpy="0 3.14159265359 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_middle.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0608" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_middle_3_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.0381 -0.1505 0.164"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_middle_3_link"/>
|
||||
</joint>
|
||||
<link name="pole_middle_3_link">
|
||||
<visual>
|
||||
<origin rpy="0 3.14159265359 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_middle.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0608" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="plate_middle_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.01364 0.0 0.1874"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="plate_middle_link"/>
|
||||
</joint>
|
||||
<link name="plate_middle_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/plate_middle.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0.0 0.0 0.0"/>
|
||||
<geometry>
|
||||
<box size="0.28727 0.340 0.006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.01"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.01" ixy="0.0" ixz="0.0" iyy="0.01" iyz="0.0" izz="0.01"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_top_0_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.0381 0.1505 0.292"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_top_0_link"/>
|
||||
</joint>
|
||||
<link name="pole_top_0_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz=" 0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_top.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.2032" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_top_1_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0.0381 -0.1505 0.292"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_top_1_link"/>
|
||||
</joint>
|
||||
<link name="pole_top_1_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz=" 0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_top.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.2032" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_top_2_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.0381 0.1505 0.292"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_top_2_link"/>
|
||||
</joint>
|
||||
<link name="pole_top_2_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz=" 0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_top.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.2032" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_top_3_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.0381 -0.1505 0.292"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_top_3_link"/>
|
||||
</joint>
|
||||
<link name="pole_top_3_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz=" 0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_top.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.2032" radius=".006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_kinect_0_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.1024 0.098 0.2372"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_kinect_0_link"/>
|
||||
</joint>
|
||||
<link name="pole_kinect_0_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<!-- <origin xyz="0 0 0" rpy="${-M_PI/2} ${M_PI} 0"/> -->
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_kinect.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0936" radius="0.006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="pole_kinect_1_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.1024 -0.098 0.2372"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="pole_kinect_1_link"/>
|
||||
</joint>
|
||||
<link name="pole_kinect_1_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<!-- <origin xyz="0 0 0" rpy="${-M_PI/2} ${M_PI} 0"/> -->
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/pole_kinect.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<cylinder length="0.0936" radius="0.006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="plate_top_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.01364 0.0 0.3966"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="plate_top_link"/>
|
||||
</joint>
|
||||
<link name="plate_top_link">
|
||||
<visual>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/stacks/hexagons/plate_top.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<box size="0.28727 0.340 0.006"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.01"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.01" ixy="0.0" ixz="0.0" iyy="0.01" iyz="0.0" izz="0.01"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="camera_rgb_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.087 -0.0125 0.287"/>
|
||||
<parent link="base_link"/>
|
||||
<child link="camera_rgb_frame"/>
|
||||
</joint>
|
||||
<link name="camera_rgb_frame">
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="camera_rgb_optical_joint" type="fixed">
|
||||
<origin rpy="-1.57079632679 0 -1.57079632679" xyz="0 0 0"/>
|
||||
<parent link="camera_rgb_frame"/>
|
||||
<child link="camera_rgb_optical_frame"/>
|
||||
</joint>
|
||||
<link name="camera_rgb_optical_frame">
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="camera_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="-0.031 0.0125 -0.016"/>
|
||||
<parent link="camera_rgb_frame"/>
|
||||
<child link="eyes"/>
|
||||
</joint>
|
||||
<link name="eyes">
|
||||
<visual>
|
||||
<origin rpy="0 0 1.57079632679" xyz="0 0 0"/>
|
||||
<geometry>
|
||||
<mesh filename="turtlebot/turtlebot_description/meshes/sensors/kinect.dae"/>
|
||||
</geometry>
|
||||
</visual>
|
||||
<collision>
|
||||
<origin rpy="0 0 0" xyz="-0.0315 0.0 -0.017"/>
|
||||
<geometry>
|
||||
<box size="0.07271 0.27794 0.073"/>
|
||||
</geometry>
|
||||
</collision>
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="camera_depth_joint" type="fixed">
|
||||
<origin rpy="0 0 0" xyz="0 0.025 0"/>
|
||||
<parent link="camera_rgb_frame"/>
|
||||
<child link="camera_depth_frame"/>
|
||||
</joint>
|
||||
<link name="camera_depth_frame">
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
<joint name="camera_depth_optical_joint" type="fixed">
|
||||
<origin rpy="-1.57079632679 0 -1.57079632679" xyz="0 0 0"/>
|
||||
<parent link="camera_depth_frame"/>
|
||||
<child link="camera_depth_optical_frame"/>
|
||||
</joint>
|
||||
<link name="camera_depth_optical_frame">
|
||||
<inertial>
|
||||
<mass value="0.001"/>
|
||||
<origin xyz="0 0 0"/>
|
||||
<inertia ixx="0.0001" ixy="0.0" ixz="0.0" iyy="0.0001" iyz="0.0" izz="0.0001"/>
|
||||
</inertial>
|
||||
</link>
|
||||
|
||||
</robot>
|
||||
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|
|
@ -0,0 +1,6 @@
|
|||
class Params():
|
||||
def __init__(self):
|
||||
self.N = 3 #number of state variables
|
||||
self.M = 2 #number of control variables
|
||||
self.T = 20 #Prediction Horizon
|
||||
self.dt = 0.25 #discretization step
|
||||
|
|
@ -0,0 +1,207 @@
|
|||
#! /usr/bin/env python
|
||||
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
from matplotlib import animation
|
||||
|
||||
from utils import compute_path_from_wp
|
||||
from cvxpy_mpc import optimize
|
||||
|
||||
import sys
|
||||
import time
|
||||
|
||||
# Robot Starting position
|
||||
SIM_START_X=0
|
||||
SIM_START_Y=0.5
|
||||
SIM_START_H=0
|
||||
|
||||
from mpc_config import Params
|
||||
P=Params()
|
||||
|
||||
# Classes
|
||||
class MPC():
|
||||
|
||||
def __init__(self):
|
||||
|
||||
# State for the robot mathematical model [x,y,heading]
|
||||
self.state = [SIM_START_X, SIM_START_Y, SIM_START_H]
|
||||
|
||||
self.opt_u = np.zeros((P.M,P.T))
|
||||
self.opt_u[0,:] = 1 #m/s
|
||||
self.opt_u[1,:] = np.radians(0) #rad/s
|
||||
|
||||
# Interpolated Path to follow given waypoints
|
||||
#self.path = compute_path_from_wp([0,10,12,2,4,14],[0,0,2,10,12,12])
|
||||
self.path = compute_path_from_wp([0,3,4,6,10,13],
|
||||
[0,0,2,4,3,3],1)
|
||||
|
||||
# Sim help vars
|
||||
self.sim_time=0
|
||||
self.x_history=[]
|
||||
self.y_history=[]
|
||||
self.h_history=[]
|
||||
self.v_history=[]
|
||||
self.w_history=[]
|
||||
self.predicted=None
|
||||
|
||||
#Initialise plot
|
||||
plt.style.use("ggplot")
|
||||
self.fig = plt.figure()
|
||||
plt.ion()
|
||||
plt.show()
|
||||
|
||||
def predict_motion(self):
|
||||
'''
|
||||
'''
|
||||
predicted=np.zeros(self.opt_u.shape)
|
||||
x=self.state[0]
|
||||
y=self.state[1]
|
||||
th=self.state[2]
|
||||
for idx,v,w in zip(range(len(self.opt_u[0,:])),self.opt_u[0,:],self.opt_u[1,:]):
|
||||
x = x+v*np.cos(th)*P.dt
|
||||
y = y+v*np.sin(th)*P.dt
|
||||
th= th +w*P.dt
|
||||
predicted[0,idx]=x
|
||||
predicted[1,idx]=y
|
||||
|
||||
self.predicted = predicted
|
||||
|
||||
def run(self):
|
||||
'''
|
||||
'''
|
||||
|
||||
while 1:
|
||||
if self.state is not None:
|
||||
|
||||
if np.sqrt((self.state[0]-self.path[0,-1])**2+(self.state[1]-self.path[1,-1])**2)<1:
|
||||
print("Success! Goal Reached")
|
||||
return
|
||||
|
||||
#optimization loop
|
||||
start=time.time()
|
||||
self.opt_u = optimize(self.state,
|
||||
self.opt_u,
|
||||
self.path)
|
||||
|
||||
# print("CVXPY Optimization Time: {:.4f}s".format(time.time()-start))
|
||||
|
||||
self.update_sim(self.opt_u[0,1],self.opt_u[1,1])
|
||||
self.predict_motion()
|
||||
self.plot_sim()
|
||||
|
||||
def update_sim(self,lin_v,ang_v):
|
||||
'''
|
||||
Updates state.
|
||||
|
||||
:param lin_v: float
|
||||
:param ang_v: float
|
||||
'''
|
||||
|
||||
self.state[0] = self.state[0] +lin_v*np.cos(self.state[2])*P.dt
|
||||
self.state[1] = self.state[1] +lin_v*np.sin(self.state[2])*P.dt
|
||||
self.state[2] = self.state[2] +ang_v*P.dt
|
||||
|
||||
def plot_sim(self):
|
||||
|
||||
self.sim_time = self.sim_time+P.dt
|
||||
self.x_history.append(self.state[0])
|
||||
self.y_history.append(self.state[1])
|
||||
self.h_history.append(self.state[2])
|
||||
self.v_history.append(self.opt_u[0,1])
|
||||
self.w_history.append(self.opt_u[1,1])
|
||||
|
||||
plt.clf()
|
||||
|
||||
grid = plt.GridSpec(2, 3)
|
||||
|
||||
plt.subplot(grid[0:2, 0:2])
|
||||
plt.title("MPC Simulation \n" + "Simulation elapsed time {}s".format(self.sim_time))
|
||||
|
||||
plt.plot(self.path[0,:],self.path[1,:], c='tab:orange',
|
||||
marker=".",
|
||||
label="reference track")
|
||||
|
||||
plt.plot(self.x_history, self.y_history, c='tab:blue',
|
||||
marker=".",
|
||||
alpha=0.5,
|
||||
label="vehicle trajectory")
|
||||
|
||||
if self.predicted is not None:
|
||||
plt.plot(self.predicted[0,:], self.predicted[1,:], c='tab:green',
|
||||
marker=".",
|
||||
alpha=0.5,
|
||||
label="mpc opt trajectory")
|
||||
|
||||
# plt.plot(self.x_history[-1], self.y_history[-1], c='tab:blue',
|
||||
# marker=".",
|
||||
# markersize=12,
|
||||
# label="vehicle position")
|
||||
# plt.arrow(self.x_history[-1],
|
||||
# self.y_history[-1],
|
||||
# np.cos(self.h_history[-1]),
|
||||
# np.sin(self.h_history[-1]),
|
||||
# color='tab:blue',
|
||||
# width=0.2,
|
||||
# head_length=0.5,
|
||||
# label="heading")
|
||||
|
||||
plot_car(self.x_history[-1], self.y_history[-1], self.h_history[-1])
|
||||
|
||||
plt.ylabel('map y')
|
||||
plt.yticks(np.arange(min(self.path[1,:])-1., max(self.path[1,:]+1.)+1, 1.0))
|
||||
plt.xlabel('map x')
|
||||
plt.xticks(np.arange(min(self.path[0,:])-1., max(self.path[0,:]+1.)+1, 1.0))
|
||||
plt.axis("equal")
|
||||
#plt.legend()
|
||||
|
||||
plt.subplot(grid[0, 2])
|
||||
#plt.title("Linear Velocity {} m/s".format(self.v_history[-1]))
|
||||
plt.plot(self.v_history,c='tab:orange')
|
||||
locs, _ = plt.xticks()
|
||||
plt.xticks(locs[1:], locs[1:]*P.dt)
|
||||
plt.ylabel('v(t) [m/s]')
|
||||
plt.xlabel('t [s]')
|
||||
|
||||
plt.subplot(grid[1, 2])
|
||||
#plt.title("Angular Velocity {} m/s".format(self.w_history[-1]))
|
||||
plt.plot(np.degrees(self.w_history),c='tab:orange')
|
||||
plt.ylabel('w(t) [deg/s]')
|
||||
locs, _ = plt.xticks()
|
||||
plt.xticks(locs[1:], locs[1:]*P.dt)
|
||||
plt.xlabel('t [s]')
|
||||
|
||||
plt.tight_layout()
|
||||
|
||||
plt.draw()
|
||||
plt.pause(0.1)
|
||||
|
||||
|
||||
def plot_car(x, y, yaw):
|
||||
LENGTH = 1.0 # [m]
|
||||
WIDTH = 0.5 # [m]
|
||||
OFFSET = LENGTH/2 # [m]
|
||||
|
||||
outline = np.array([[-OFFSET, (LENGTH - OFFSET), (LENGTH - OFFSET), -OFFSET, -OFFSET],
|
||||
[WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]])
|
||||
|
||||
Rotm = np.array([[np.cos(yaw), np.sin(yaw)],
|
||||
[-np.sin(yaw), np.cos(yaw)]])
|
||||
|
||||
outline = (outline.T.dot(Rotm)).T
|
||||
|
||||
outline[0, :] += x
|
||||
outline[1, :] += y
|
||||
|
||||
plt.plot(np.array(outline[0, :]).flatten(), np.array(outline[1, :]).flatten(), 'tab:blue')
|
||||
|
||||
|
||||
|
||||
def do_sim():
|
||||
sim=MPC()
|
||||
try:
|
||||
sim.run()
|
||||
except Exception as e:
|
||||
sys.exit(e)
|
||||
|
||||
if __name__ == '__main__':
|
||||
do_sim()
|
||||
|
|
@ -0,0 +1,105 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
from matplotlib import animation
|
||||
|
||||
from utils import compute_path_from_wp
|
||||
from cvxpy_mpc import optimize
|
||||
|
||||
import sys
|
||||
import time
|
||||
|
||||
import pybullet as p
|
||||
import time
|
||||
|
||||
def get_state(robotId):
|
||||
"""
|
||||
"""
|
||||
robPos, robOrn = p.getBasePositionAndOrientation(robotId)
|
||||
linVel,angVel = p.getBaseVelocity(robotId)
|
||||
|
||||
return[robPos[0], robPos[1], p.getEulerFromQuaternion(robOrn)[2]]
|
||||
|
||||
def set_ctrl(robotId,v,w):
|
||||
"""
|
||||
"""
|
||||
L= 0.354
|
||||
R= 0.076/2
|
||||
|
||||
rightWheelVelocity= (2*v+w*L)/(2*R)
|
||||
leftWheelVelocity = (2*v-w*L)/(2*R)
|
||||
|
||||
p.setJointMotorControl2(robotId,0,p.VELOCITY_CONTROL,targetVelocity=leftWheelVelocity,force=1000)
|
||||
p.setJointMotorControl2(robotId,1,p.VELOCITY_CONTROL,targetVelocity=rightWheelVelocity,force=1000)
|
||||
|
||||
def plot(path,x_history,y_history):
|
||||
"""
|
||||
"""
|
||||
plt.style.use("ggplot")
|
||||
plt.figure()
|
||||
plt.title("MPC Tracking Results")
|
||||
|
||||
plt.plot(path[0,:],path[1,:], c='tab:orange',marker=".",label="reference track")
|
||||
plt.plot(x_history, y_history, c='tab:blue',marker=".",alpha=0.5,label="vehicle trajectory")
|
||||
|
||||
plt.legend()
|
||||
plt.show()
|
||||
|
||||
def run_sim():
|
||||
"""
|
||||
"""
|
||||
p.connect(p.GUI)
|
||||
|
||||
start_offset = [0,2,0]
|
||||
start_orientation = p.getQuaternionFromEuler([0,0,0])
|
||||
turtle = p.loadURDF("turtlebot.urdf",start_offset, start_orientation)
|
||||
plane = p.loadURDF("plane.urdf")
|
||||
|
||||
p.setRealTimeSimulation(1)
|
||||
p.setGravity(0,0,-10)
|
||||
|
||||
# MPC time step
|
||||
dt = 0.25
|
||||
|
||||
# starting guess output
|
||||
N = 5 #number of state variables
|
||||
M = 2 #number of control variables
|
||||
T = 20 #Prediction Horizon
|
||||
|
||||
opt_u = np.zeros((M,T))
|
||||
opt_u[0,:] = 1 #m/s
|
||||
opt_u[1,:] = np.radians(0) #rad/s
|
||||
|
||||
# Interpolated Path to follow given waypoints
|
||||
path = compute_path_from_wp([0,10,12,2,4,14],[0,0,2,10,12,12])
|
||||
x_history=[]
|
||||
y_history=[]
|
||||
|
||||
while (1):
|
||||
|
||||
state = get_state(turtle)
|
||||
x_history.append(state[0])
|
||||
y_history.append(state[1])
|
||||
|
||||
#track path in bullet
|
||||
p.addUserDebugLine([state[0],state[1],0],[state[0],state[1],0.5],[1,0,0])
|
||||
|
||||
if np.sqrt((state[0]-path[0,-1])**2+(state[1]-path[1,-1])**2)<1:
|
||||
print("Success! Goal Reached")
|
||||
set_ctrl(turtle,0,0)
|
||||
plot(path,x_history,y_history)
|
||||
p.disconnect()
|
||||
return
|
||||
|
||||
#optimization loop
|
||||
start=time.time()
|
||||
opt_u = optimize(state,opt_u,path)
|
||||
elapsed=time.time()-start
|
||||
print("CVXPY Optimization Time: {:.4f}s".format(elapsed))
|
||||
|
||||
set_ctrl(turtle,opt_u[0,1],opt_u[1,1])
|
||||
|
||||
if dt-elapsed>0:
|
||||
time.sleep(dt-elapsed)
|
||||
|
||||
if __name__ == '__main__':
|
||||
run_sim()
|
||||
|
|
@ -0,0 +1,84 @@
|
|||
import numpy as np
|
||||
from scipy.interpolate import interp1d
|
||||
|
||||
def compute_path_from_wp(start_xp, start_yp, step = 0.1):
|
||||
"""
|
||||
"""
|
||||
final_xp=[]
|
||||
final_yp=[]
|
||||
delta = step #[m]
|
||||
|
||||
for idx in range(len(start_xp)-1):
|
||||
section_len = np.sum(np.sqrt(np.power(np.diff(start_xp[idx:idx+2]),2)+np.power(np.diff(start_yp[idx:idx+2]),2)))
|
||||
|
||||
interp_range = np.linspace(0,1,np.floor(section_len/delta).astype(int))
|
||||
|
||||
fx=interp1d(np.linspace(0,1,2),start_xp[idx:idx+2],kind=1)
|
||||
fy=interp1d(np.linspace(0,1,2),start_yp[idx:idx+2],kind=1)
|
||||
|
||||
final_xp=np.append(final_xp,fx(interp_range))
|
||||
final_yp=np.append(final_yp,fy(interp_range))
|
||||
|
||||
return np.vstack((final_xp,final_yp))
|
||||
|
||||
def get_nn_idx(state,path):
|
||||
"""
|
||||
"""
|
||||
dx = state[0]-path[0,:]
|
||||
dy = state[1]-path[1,:]
|
||||
dist = np.sqrt(dx**2 + dy**2)
|
||||
nn_idx = np.argmin(dist)
|
||||
|
||||
try:
|
||||
v = [path[0,nn_idx+1] - path[0,nn_idx],
|
||||
path[1,nn_idx+1] - path[1,nn_idx]]
|
||||
v /= np.linalg.norm(v)
|
||||
|
||||
d = [path[0,nn_idx] - state[0],
|
||||
path[1,nn_idx] - state[1]]
|
||||
|
||||
if np.dot(d,v) > 0:
|
||||
target_idx = nn_idx
|
||||
else:
|
||||
target_idx = nn_idx+1
|
||||
|
||||
except IndexError as e:
|
||||
target_idx = nn_idx
|
||||
|
||||
return target_idx
|
||||
|
||||
def road_curve(state,track):
|
||||
"""
|
||||
"""
|
||||
|
||||
POLY_RANK = 3
|
||||
|
||||
#given vehicle pos find lookahead waypoints
|
||||
nn_idx=get_nn_idx(state,track)-1
|
||||
LOOKAHED = POLY_RANK + 1
|
||||
lk_wp=track[:,nn_idx:nn_idx+LOOKAHED]
|
||||
|
||||
#trasform lookahead waypoints to vehicle ref frame
|
||||
dx = lk_wp[0,:] - state[0]
|
||||
dy = lk_wp[1,:] - state[1]
|
||||
|
||||
wp_vehicle_frame = np.vstack(( dx * np.cos(-state[2]) - dy * np.sin(-state[2]),
|
||||
dy * np.cos(-state[2]) + dx * np.sin(-state[2]) ))
|
||||
|
||||
#fit poly
|
||||
return np.polyfit(wp_vehicle_frame[0,:], wp_vehicle_frame[1,:], POLY_RANK, rcond=None, full=False, w=None, cov=False)
|
||||
|
||||
def f(x,coeff):
|
||||
"""
|
||||
"""
|
||||
return round(coeff[0]*x**3 + coeff[1]*x**2 + coeff[2]*x**1 + coeff[3]*x**0,6)
|
||||
|
||||
# def f(x,coeff):
|
||||
# return round(coeff[0]*x**5+coeff[1]*x**4+coeff[2]*x**3+coeff[3]*x**2+coeff[4]*x**1+coeff[5]*x**0,6)
|
||||
|
||||
def df(x,coeff):
|
||||
"""
|
||||
"""
|
||||
return round(3*coeff[0]*x**2 + 2*coeff[1]*x**1 + coeff[2]*x**0,6)
|
||||
# def df(x,coeff):
|
||||
# return round(5*coeff[0]*x**4 + 4*coeff[1]*x**3 +3*coeff[2]*x**2 + 2*coeff[3]*x**1 + coeff[4]*x**0,6)
|
||||
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Before Width: | Height: | Size: 38 KiB After Width: | Height: | Size: 38 KiB |
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Before Width: | Height: | Size: 32 KiB After Width: | Height: | Size: 32 KiB |
Loading…
Reference in New Issue