Kinematic solver for holonomic drive in moveit2

Question

I am working on a robot having a robotic arm mounted on a mobile base. The mobile base is based on holonomic drive, using 4 mecanum wheels. According to Moveit2, we need to have an kinematic solver for mobile base depending on the type of drive of the mobile base.
An example for mobile base using differential drive is available here.

I am looking for kinematic solver for mecanum wheel robot, but unable to find one. Is there any kinematic solver available for mecanum wheel(holonomic drive) on MoveIt2?
If not what other options do I have?

UPDATE:

double w_front_left_vel =
      1.0 / params_.kinematics.wheels_radius *
      (velocity_in_center_frame_linear_x_ - velocity_in_center_frame_linear_y_ -
       params_.kinematics.sum_of_robot_center_projection_on_X_Y_axis *
         velocity_in_center_frame_angular_z_);

double w_back_left_vel =
      1.0 / params_.kinematics.wheels_radius *
      (velocity_in_center_frame_linear_x_ + velocity_in_center_frame_linear_y_ -
       params_.kinematics.sum_of_robot_center_projection_on_X_Y_axis *
         velocity_in_center_frame_angular_z_);

double w_back_right_vel =
      1.0 / params_.kinematics.wheels_radius *
      (velocity_in_center_frame_linear_x_ - velocity_in_center_frame_linear_y_ +
       params_.kinematics.sum_of_robot_center_projection_on_X_Y_axis *
         velocity_in_center_frame_angular_z_);

double w_front_right_vel =
      1.0 / params_.kinematics.wheels_radius *
      (velocity_in_center_frame_linear_x_ + velocity_in_center_frame_linear_y_ +
       params_.kinematics.sum_of_robot_center_projection_on_X_Y_axis *
         velocity_in_center_frame_angular_z_);

```

Answer 1

EDIT:

Let me try and explain with greater details. Dynamics is the questions on how things move with force.

Simple Dynamic example:

A box sliding on ground with a force applied to it. Its acceleration is $\frac{\partial x^2}{\partial^2 t} = \ddot{x}$, its velocity is $\frac{\partial x}{\partial t} = \dot{x}$ and its position is $x$ and the force applied to it is $F$. Let's also assume there is friction linear $f$ to velocity and its mass is $m$. The differential equation describing this movement is:

$m\ddot{x} = -f\dot{x} + F$

which is an Ordinary Differential Equation (ODE). Since this equation is linear in all its components, there exists an algebraic (read analytical) solution. But that's not true for non-linear ODEs, e.g.:

$\ddot{x} = sin(\dot{x})$

which can only be "solved" by an approximate solver like Runge Kutta (see below).

Kinematics is the questions on how things move without considering force, but considering Kinematics will also result in a (non-linear) ODE.

Simple Kinematic example:

A 2-Dimensional "car" with a driven wheel. The wheel with radius $r$ turns at rotational velocity $\dot{\phi}$ without slipping and the body of the car therefore moves forward. Then the car's velocity $\dot{x}$ will be

$\dot{x} = 2\pi r\dot{\phi}$

as you can see we did not consider any force (and therefore not acceleration), but the resulting equation is still an ODE. For more complex systems, also Kinematics become non-linear ODEs. Example is the kinematics of a 2D-arm. which again need to be solved using an approximate ODE-solver like the ones I suggested in my old answer.

OLD ANSWER BEFORE EDIT:

Have you looked into Ascent which implements ODE-solvers via Runge-Kutta

e.g. by Agilex Robotics see Agilex Github Header file

Another popular choice is to implement Runge-Kutta yourself using open-source tool for nonlinear optimization and algorithmic differentiation: Casadi like in this example, see this code snippet:

dt = T/N; % length of a control interval
for k=1:N % loop over control intervals
   % Runge-Kutta 4 integration
   k1 = f(X(:,k),         U(:,k));
   k2 = f(X(:,k)+dt/2*k1, U(:,k));
   k3 = f(X(:,k)+dt/2*k2, U(:,k));
   k4 = f(X(:,k)+dt*k3,   U(:,k));
   x_next = X(:,k) + dt/6*(k1+2*k2+2*k3+k4);
   opti.subject_to(X(:,k+1)==x_next); % close the gaps
end

where essentially you "only" need to know the differential equations for your kinematics.