Symbolic Derivation of Manipulator Dyn. Denavit-Hartenberg

This single MATLAB file generates the nonlinear dynamics of any manipulator which obeys Denavit-Hartenberg parameters.

To use the code, just run and enter a number between 1-9 to select one of the predefined robots in the code. They are rotary beam, planar 2 DoF manipulator, SCARA, Spherical robot, etc. The degree of freedom of them varies from 1 to 6, but it must be compatible with the case number. The dynamics of robots lower than 4 DoF are computed fast though, above 4, you should expect more time to see the results.

The notation of the code could be followed in [1] or [2].

The robots are defined between lines 109-354, you may add your own in the proposed format.

The derivation of dynamics is coded between 357-437.

The presentation of the dynamics is the rest of the code between 439-460. For robotic arms with lower than 5 DoF, you can see the output in the command screen and use it. For manipulators with higher than 5 DoF, the command window is not able to print all of them. So, you may find the dynamics in the saved output text file “Output_Manipulator_Dynamics.txt”

For the sake of speed of computations, the simplify command was removed from the codes for manipulators with more than 4 DoF, lines 445-448. If you want to see the compact form of the output, you may add a “simplify” command for them as well, but you should remember it is so time-consuming.

[1] Korayem, M.H. and S.R. Nekoo, "Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control," ISA Transactions, 54, pp. 125-144, 2015.

[2] Korayem, M.H. and S.R. Nekoo, "State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities," ISA Transactions, 57, pp. 117-135, 2015.

This code is one of the attachments of Ref. [2]. It is provided for free use.

More sophisticated codes, linked to SDRE and SDDRE regulation and tracking can be found in the attachment of Ref. [2] on the journal website.