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Uncertainties in Robot Machine Dynamics Characterisation

Name Affiliation Phone Number Email Address
Silvia Estelles-Martinez The Manufacturing Technology Centre
Industrial Sector:

A computer assisted system modeling deterministic approach has been recently implemented at the MTC for estimating the dynamic stiffness of an industrial parallel robot machine, the Exechon Parallel Kinematic Machine (PKM) – see Fig 1. For modeling purposes, it is treated as a multi-body system externally excited at the tooltip position. The ultimate objective of this modeling work is to identify the dynamic stiffness of the machine to improve its accuracy via real-time feedback control design. Likewise in a CNC machine, it is normally affected by machining process loads, machine calibration and environmental variables. The aim of this use case is to increase the maturity of the model by quantifying the effects of known sources of uncertainty Time domain measurement data was used to estimate a model for the robot drives. Experimental acceleration data of vibration transmissibility at certain locations on the machine (i.e. tool holder, machine’s head, legs and structure), whilst exciting it with random forces was recorded. Forces were applied through a shaker table via the tooltip (Fig 1) and the recorded data corresponds to only two machine positions along the X-axis. The model assessment variables are the accelerations predicted at the vibration measurement locations, used to estimate the transmissibility of the vibrations at the tooltip. The correspondence between the location of the modeled sensors and the actual accelerometers is naturally a source of uncertainty, not considered in the current model. Frequency domain data of the accelerations was used to validate the model, showing good qualitative agreement in the Bode plots for the highest transmissibility key process variables, i.e. tool holder and machine’s head – see Fig. 2 for a reference. [caption id="attachment_1274" align="aligncenter" width="633"]Figure 1. Image of the Exechon Parallel Kinematic Machine (PKM) and experimental set up. Figure 1. Image of the Exechon Parallel Kinematic Machine (PKM) and experimental set up.[/caption] [caption id="attachment_1275" align="aligncenter" width="530"]Figure 2. Bode diagram for predicted vs. experimental data (tool holder) Figure 2. Bode diagram for predicted vs. experimental data (tool holder)[/caption] Apart from sensor location, there are other sources of uncertainty associated to the model simplification. The model does not account for body flexibility or frictional effects in the machine joints. Additionally, internal mechanisms and drives control are represented via mathematical deterministic models The assessment of the machine vibrations focused on the dynamic response of the machine to a force excitation with a burst random frequency characteristic and a pre-set power value. This should suffice for designing advanced dynamic control algorithms, with no need for modeling the machining process, which reduces the number of uncertainties of the model for control design purposes.

2.1 Process Inputs

The uncertain inputs in the robot machine dynamics model are:

  • Accuracy of the inertial properties of the multibody system elements.
  • Drives’ mechanism / mathematical description and control algorithms.
  • Dynamic properties of other components such as joint damping, stiffness and friction
  • Mechanical properties of the robot parts
  • Accuracy of the accelerometers location
  The effects of the uncertainties are evidenced in the use case described here through the natural vibration frequency values, and magnitude and phase of the frequency characteristic of the machine vibration model when subjected to the same burst random external excitations as used experimentally to emulate machining process loads.   Only deterministic approaches have been used so far and there is no current characterisation of the inputs above variability. There are however, experimental measurements that can be used in conjunction with the output from the dynamics model to quantify the effect of the uncertainty on the dynamics behaviours of the robot machine. Some additional test data could be collected prior tot the Study group if required.

2.2 Propagation

The dynamics modeling an frequency response characterization was performed using a multibody modeling approach in Matlab / Simscape Multibody, which has much lower computational requirements compared with other approaches such as FEM. FEM and experimental data could be used in the future to estimate the effects of body deformation through modal analysis   Furthermore, the model does not consider stochastic modeling and no propagation of uncertainties has been carried out at this stage o the dynamics characterisation process.

2.3 Interpretation and Communication of Results

The ambition is to obtain an estimation of uncertainties on the parameters described above. It is expected that the results will provide a better understanding on how the variations of these parameters may modify the frequency response of the machines model and increase its predictive capabilities.   This would allow a more robust frequency-based control design in the future based on a more accurate estimation of the dynamic stiffness of the machine.


The multibody dynamics model of an Exechon PKM machine was developed at the MTC as part if the Simulation and Systems Integration Readiness Scale Development (SimReady) project, which aims to crate a maturity scale for integration and simulation studies. The dynamics model, still in validation stage, has a Readiness Level 2 based on SimReady’s maturity scale [1,2], with good qualitative agreement w.r.t the experimental data and potentialities to demonstrate feasibility of control concepts. This comes from the outputs of SimReady’s assessment tool [2], which exhaustively scores the maturity of seven key factors associated with the model, the modeling process, cost and usage (see outcomes in Fig. 3).   An uncertainty quantification modeling / analysis could help to increase rhe Readiness Level of the machine dynamics model to 3 – 4 by providing some characterisation / quantification of either the parameter uncertainty and / or directly in the robot dynamic stiffness mathematical model. This would also raise the confidence levels of the model and its usability for control design purposes, hence the cost-benefit factor of this modeling use case.   [caption id="attachment_1276" align="aligncenter" width="489"]Figure 3: Readiness Level Chart applied to the evaluation of dynamics model validation developed within the SimReady project. Figure 3: Readiness Level Chart applied to the evaluation of dynamics model validation developed within the SimReady project.[/caption]   References:

  1. The Manufacturing Technology Centre. Simulation and Systems Integration Readiness Scale Development report for WP4. Use Case 2 – PKM Dynamics Model Validation (Internal Report). UK (2016)
  2. The Manufacturing Technology Centre. SimReady (white paper in preparation). UK (2017)