Generation of Periodic Trajectories for Optimal Robot Excitation

Abstract

This paper describes the parameterization of robot excitation trajectories for optimal robot identification based on finite Fourier series. The coefficients of the Fourier series are optimized for minimal sensitivity of the identification to measurement disturbances, which is measured as the condition number of a regression matrix, taking into account motion constraints in joint and cartesian space. This approach allows obtaining small condition numbers with few coefficients for each joint, which simplifies the optimization problem significantly. The periodicity of the resulting trajectories and the fact that one has total control over their frequency content, are additional features of the presented parameterization approach. They allow further optimization of the excitation experiments through time domain data averaging and optimal selection of the excitation bandwidth, which both help the reduction of the disturbance level on the measurements, and therefore improve the identification accuracy.

Identification of dynamic parameters of a 3-DOF RPS parallel manipulator

“…As mentioned in the introduction, parameterizing the trajectory in the form of finite Fourier series analytical functions brings many advantages. It was initially introduced by Swevers et al [15] and widely implemented afterwards. It has the following analytical form:…”

“…To discard these disadvantages, Swevers et al [15] suggested considering the configurations governed by a single global trajectory. This trajectory is parameterized using a finite Fourier series function, its coefficients being the variables of the optimization process.…”

Identification of dynamic and friction parameters of a parallel manipulator with actuation redundancy

“…For the robotic manipulator, the identification results of the dynamic parameters rely on excitation trajectories [28,29]. In our identification experiment, the excitation trajectory of the parallel manipulator is designed in the workspace.…”

An inertial parameter identification method of eliminating system damping effect for a six-degree-of-freedom parallel manipulator

“…18 However, their optimization process requires a set of optimized sampled configurations that must obey the kinematic constraints of the mechanical structure at all levels, which is difficult to achieve. Swevers et al 19 then proposed a dynamic parameter identification method using a single global trajectory that is parameterized using a finite Fourier series function. Because of the advantage of obtaining the velocities and accelerations in the frequency domain from the analytical derivation of the designed Fourier series trajectory and reducing the noise-to-signal ratio by averaging the measurement data obtained for more than one cycle, this method has received more attention in recent identification processes; see for example.…”