MATLAB Source Code for Fourth-Order MHM Hyper-State Computation of the KUKA LBR iiwa 7 R800
Year: 2026
Type: software
Abstract: This software record contains the MATLAB implementation associated with the CODIT 2026 manuscript “Fourth-Order Automatic Differentiation for Robotic Kinematics via Nilpotent Hypercomplex Algebra”. The code evaluates the fourth-order multidual homogeneous-matrix hyper-state of the KUKA LBR iiwa 7 R800 serial manipulator. The formulation uses screw-Jacobian columns and local product-of-exponentials factors, while the prescribed joint trajectory is lifted to a finite nilpotent multidual algebra through joint increments containing derivatives up to order four. At each evaluation instant, the multidual end-effector transformation is normalized by the corresponding real pose. The invariant rotational and translational field coefficients are then extracted from the normalized hyper-state using factorial-scaled coefficient extraction. The script reports Phi_j and a_j for j = 1, 2, 3, 4, corresponding to velocity, acceleration, jerk, and snap. The archive includes the standalone MATLAB source file, the generated MATLAB diary output, README, manifest, citation metadata, and license file. Internal implementation checks are included for the screw-axis representation, multidual orthogonality, first-order skew-symmetry, and coefficient-level consistency of the local exponential factors.
Authors: Condurache, Daniel, Cojocari, Mihail
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162525182