I would like to model an omni wheel. Ideally, I would like to do this using non-uniform friction properties (see below). However, it seems like the contact algorithm is not properly accounting for the fdir1 parameter, as setting either <mu1> or <mu2> to zero causes the wheel to slip when rotating. There are a few other threads regarding omni wheels that are a few years old, but I haven't found a satisfactory answer--I have seen this method of friction modification suggested, but no examples of successful implementation.

omni-wheel macro: z-axis is axial direction.

<link name="${wheel_name}">
    <inertial>
        <mass value="${wheel_mass}"/>
        <origin xyz="0 0 0" rpy="0 0 0"/>
        <inertia ixx="${ixx}" iyy="${iyy}" izz="${izz}" ixy="${ixy}" ixz="${ixz}" iyz="${iyz}"/>
    </inertial>
    <visual name="${wheel_name}_vis">
        <origin xyz="0 0 0.05" rpy="0 0 0"/>
        <geometry name="${wheel_name}_geom">
            <!-- <cylinder length="0.025" radius="${wheel_radius}"/> -->
            <mesh filename="${wheel_visual}"/>
        </geometry>
    </visual>
    <collision name="${wheel_name}_col">
         <origin xyz="0 0.0 0" rpy="0 0 0"/>
         <geometry name="${wheel_name}_geom">
            <cylinder length="0.025" radius="${wheel_radius}"/>
            <!-- <sphere radius="${wheel_radius}"/> -->
         </geometry>
    </collision>
</link> 
<gazebo reference="${wheel_name}">
    <mu1>0</mu1>
    <mu2>1</mu2>
    <fdir1>0 0 1</fdir1>
</gazebo>

UPDATE : I actually did manage to get a physical model to "work" which is stable at 1/4th real time. However, the collision model means that the wheel looks like a ball, so any vehicle which uses it won't be able to get too close to any other object in the work (which is acceptable for my purposes right now). My robot uses three of these wheels and the following ODE parameters in the world:

  <ode>
    <solver>
      <type>quick</type>
      <iters>200</iters>
      <sor>1.2</sor>
    </solver>
    <constraints>
      <cfm>0.0</cfm>
      <erp>0.2</erp>
      <contact_max_correcting_vel>0.01</contact_max_correcting_vel>
      <contact_surface_layer>0.0001</contact_surface_layer>
    </constraints>
  </ode>
  <real_time_update_rate>2000</real_time_update_rate>
  <max_step_size>0.0005</max_step_size>

Here is the omni wheel xacro (please excuse the comments left in for debugging):

<?xml version='1.0'?>

<!-- -->

<joint name="${wheel_name}_subwheel_${subwheel_number}_j" type="${subwheel_joint_type}">
    <origin xyz="${0.05*wheel_radius * cos_pi_over_N * cos_2pi_n_over_N} ${0.05*wheel_radius * cos_pi_over_N * sin_2pi_n_over_N} 0" rpy="0 0 ${2*M_PI*subwheel_number/n_subwheels}"/>
    <!-- <axis xyz="${-sin_2pi_n_over_N} ${cos_2pi_n_over_N} 0"/> -->
    <axis xyz="0 1 0"/>
    <parent link="${wheel_name}"/>
    <child link="${wheel_name}_subwheel_${subwheel_number}_l"/>
</joint>    

<!-- <gazebo reference="${wheel_name}_subwheel_${subwheel_number}_j">
    <dynamics>
        <damping>10</damping>
        <friction>1</friction>
    </dynamics>
</gazebo> -->

<link name="${wheel_name}_subwheel_${subwheel_number}_l">
    <inertial>
        <mass value="${subwheel_mass}"/>
        <origin xyz="0 0 0" rpy="0 0 0"/>
        <inertia ixx="${2*subwheel_mass*(wheel_radius*wheel_radius*sin_pi_over_N*sin_pi_over_N)/5}" 
                 iyy="${2*subwheel_mass*(wheel_radius*wheel_radius*sin_pi_over_N*sin_pi_over_N)/5}"
                 izz="${2*subwheel_mass*(wheel_radius*wheel_radius*sin_pi_over_N*sin_pi_over_N)/5}"
                 ixy="0"
                 ixz="0"
                 iyz="0"/>
    </inertial>
    <!-- <visual name="${wheel_name}_subwheel_${subwheel_number}_vis">
        <origin xyz="0 0 0" rpy="0 0 0"/>
        <geometry name="${wheel_name}_subwheel_${subwheel_number}_geom">
            <sphere radius="${wheel_radius}"/>
        </geometry>
    </visual> -->
    <collision name="${wheel_name}_subwheel_${subwheel_number}_col">
        <origin xyz="0 0 0" rpy="0 0 0"/>
        <geometry name="${wheel_name}_subwheel_${subwheel_number}_geom">
            <sphere radius="${wheel_radius}"/>
        </geometry>
    </collision>
</link>

/xacro:macro

<!-- --> <!-- --> Gazebo/${color} <!-- 0 1 0 0 1 -->

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="0" n_subwheels="18" cos_2pi_n_over_N="1" sin_2pi_n_over_N="0" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="1" n_subwheels="18" cos_2pi_n_over_N="0.939692620785908" sin_2pi_n_over_N="0.342020143325669" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="2" n_subwheels="18" cos_2pi_n_over_N="0.766044443118978" sin_2pi_n_over_N="0.642787609686539" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="3" n_subwheels="18" cos_2pi_n_over_N="0.5" sin_2pi_n_over_N="0.866025403784439" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="4" n_subwheels="18" cos_2pi_n_over_N="0.17364817766693" sin_2pi_n_over_N="0.984807753012208" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="5" n_subwheels="18" cos_2pi_n_over_N="-0.17364817766693" sin_2pi_n_over_N="0.984807753012208" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="6" n_subwheels="18" cos_2pi_n_over_N="-0.5" sin_2pi_n_over_N="0.866025403784439" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="7" n_subwheels="18" cos_2pi_n_over_N="-0.766044443118978" sin_2pi_n_over_N="0.64278760968654" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="8" n_subwheels="18" cos_2pi_n_over_N="-0.939692620785908" sin_2pi_n_over_N="0.342020143325669" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="9" n_subwheels="18" cos_2pi_n_over_N="-1" sin_2pi_n_over_N="0.0" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="10" n_subwheels="18" cos_2pi_n_over_N="-0.939692620785908" sin_2pi_n_over_N="-0.342020143325669" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="11" n_subwheels="18" cos_2pi_n_over_N="-0.766044443118978" sin_2pi_n_over_N="-0.642787609686539" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="12" n_subwheels="18" cos_2pi_n_over_N="-0.5" sin_2pi_n_over_N="-0.866025403784438" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="13" n_subwheels="18" cos_2pi_n_over_N="-0.17364817766693" sin_2pi_n_over_N="-0.984807753012208" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="14" n_subwheels="18" cos_2pi_n_over_N="0.17364817766693" sin_2pi_n_over_N="-0.984807753012208" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="15" n_subwheels="18" cos_2pi_n_over_N="0.5" sin_2pi_n_over_N="-0.866025403784439" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="16" n_subwheels="18" cos_2pi_n_over_N="0.766044443118978" sin_2pi_n_over_N="-0.64278760968654" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

<xacro:subwheel wheel_name="${wheel_name}" wheel_radius="${wheel_radius}" subwheel_number="17" n_subwheels="18" cos_2pi_n_over_N="0.939692620785908" sin_2pi_n_over_N="-0.342020143325669" cos_pi_over_N="0.984807753012208" sin_pi_over_N="0.17364817766693" subwheel_mass="${subwheel_mass}" subwheel_joint_type="${subwheel_joint_type}"/>

/xacro:macro

Also, my ground plane is modified with the following surface parameters :

             <surface>
                <friction>
                    <ode>
                        <mu>0.8</mu>
                    </ode>
                </friction>
                <bounce>
                    <restitution_coefficient>0.0</restitution_coefficient>
                </bounce>
                <contact>
                    <ode>
                        <kp>50000</kp>
                        <kd>5000</kd>
                        <max_vel>0</max_vel>
                    </ode>
                </contact>
            </surface>