How to implement direct dynamics equations using Euler-Lagrange for an RRP/SCARA robot in Robotics Toolbox?

Hello MATLAB community,

I'm currently working on the dynamic modeling of an RRP-type (SCARA) robot and I'm looking for guidance on how to implement direct dynamics equations using the Euler-Lagrange method within Robotics Toolbox in MATLAB.

I've already defined the Denavit-Hartenberg parameters for the robot, the forward and inverse kinematics. Now I want to derive the equations of motion that relate applied torques/forces to joint accelerations.

My problem is when I'm calculating the link center of mass in link one, the robot has a "L" type form, so I split the link in La and Lb, and calculate both center, I don't know if it's well calculated or if I put all the mass center right.

Is there any built-in function in Robotics Toolbox or similar that helps formulate Euler-Lagrange equations?

[Torsten]

Multibody mechanical systems are handled by "Simscape Multibody". But I doubt you can go down to the equation level.

[dpb]

The Robotics TB uses a rigidbody tree object and internal numeric methods to solve the forward kineatics problem with forwardDynamics. The formulation used is shown in the "More About" section although the details of the techniques used are only referenced.

The only way you would be able to get to create and solve the actual Euler-Lagrange equations would be to set them up for one of the differential equation solvers provided in MATLAB.

You might want to look into <Euler Lagrange Tool Package> on the FEX. I know nothing about it, just saw the link that looked to be pertinent.

Answer 1

[William Rose]

@José Maximiliano,

Even if the first link has an "L" shape, it still has a well-defined (i.e calculatable) center of mass and moment of inertia matrix. I recommend that you do not split link 1 into two links. Calculate the CoM and MoI of the complete link 1, and treat link 1 like every other link.

I think @dpb is right that the Euler-Langrange tool does what you are asking for.