A Lie-Theory-Based Dynamic Parameter Identification Methodology for Serial Manipulators

Accurate estimation of the dynamic parameters comprising a robot's dynamics model is of paramount importance for simulation and real-time model-based control. The conventional approaches for obtaining the identification model are extremely cumbersome, and incapable of offering universal applicability, as well as physical feasibility of dynamic parameter identification. To this end, the work presented herein proposes a novel and generic identification methodology, for retrieving the dynamic parameters of serial manipulators with arbitrary degrees of freedom (DOFs), based on the Lie theory. In this approach, the robot dynamics model that includes frictional terms is analytically represented as a closed-form matrix equation, by rearranging the classical recursive Newton-Euler formulation. The link inertia matrix that comprises inertia tensors, masses, and Center of Mass (CoM) positions, together with the joint friction coefficients, are extracted from the regrouped linear dynamics model by means of the Kronecker product. Meanwhile, the introduced Kronecker-Sylvester identification equation is formulated as an optimization problem involving dynamic parameters with physical feasibility constraints, and is ultimately estimated via linear matrix inequality techniques and semidefinite programming using joint position, velocity, acceleration, and torque data. Identification results of dynamic parameters are accurately procured through a series of practical tests that entail providing a seven-DOF Rokae xMate robot, with optimized Fourier-series-based excitation trajectories. Experimental validation serves the purpose of demonstrating the proposed method's efficacy, in terms of accurately retrieving a serial manipulator's dynamic parameters.

Automated summary

Accurate estimation of dynamic parameters is crucial for simulation and real-time control of robots. Traditional approaches for identification models are cumbersome and lack universal applicability, but a novel method based on Lie theory is proposed here for serial manipulators with arbitrary DOFs. Frictional terms in the robot dynamics model are represented as a closed-form matrix equation, extracting link inertia matrix and joint friction coefficients using Kronecker product. The introduced Kronecker-Sylvester identification equation is formulated as an optimization problem with physical constraints, ultimately estimated via linear matrix inequality techniques and semidefinite programming.