Improving Operational Accuracy of a Mobile Manipulator by Modeling Geometric and Non-Geometric Parameters

Thanh D. V. Nguyen1,2, Vincent Bonnet1,3, Pierre Fernbach2, Thomas Flayols1, Florent Lamiraux1
1LAAS-CNRS, CNRS, Université Paul Sabatier, Toulouse, France 2TOWARD S.A.S, Toulouse, France 3IPAL, CNRS-UMI, Singapore
Paper Code

Abstract

This paper addresses two intrinsic phenomena encountered in mobile manipulator robots, but often neglected, with the objective of improving the overall accuracy of end-effector pose estimation. Firstly, after performing state-of-the-art geometric calibration of the arm, we propose two identifiable mathematical models to account for non-geometric effects: a model for the mobile base suspension system and a model of non-linear inaccuracies of joint angles estimates. The latter is due to backlash and misaligned encoders mounting. Then, the proposed models were experimentally validated on the mobile manipulator TIAGo using a stereophotogrammetric system. Overall, the end-effector pose accuracy was improved by 60% when compared to the nominal manufacturer model, with root mean square errors (RMSE) of 5.7mm and 2.7deg for positional and orientational errors, respectively.

Experimental setup with motion capture and force plate
Figure 1: Experimental setup showing the TIAGo robot, motion capture system, and force plate.

Problem Statement

The agility and adaptability of mobile base collaborative robots make them invaluable in applications ranging from manufacturing to healthcare. However, their relatively light and often inexpensive construction compromises their operational accuracy, posing significant challenges for applications requiring precise positioning and manipulation.

Sources of Inaccuracy in Mobile Manipulators

Mobile manipulators suffer from positioning inaccuracies caused by multiple factors:

  • Lack of Geometric Calibration: Users often rely on manufacturer specifications without recalibration after extended use
  • Joint Flexibility and Encoder Misalignment: Transmission flexibility and imperfect encoder mounting introduce measurement errors
  • Gear Backlash: Clearance between mating gear teeth causes lost motion and positioning errors, especially as gears wear over time
    Shaft encoder and backlash illustration
    Figure 2: Illustration of the drive chain including motor, shaft, and relative/absolute encoders with backlash phases
  • Suspension Dynamics: Unknown base suspension behavior affects pose estimation during arm movements
    Base suspension illustration
    Figure 3: Illustration of caster and driving wheels inducing flexibilities at the base of the robot

This paper addresses these neglected phenomena by developing comprehensive models for both geometric and non-geometric effects, validated through experimentation on the TIAGo mobile manipulator.

Key Contributions

This paper addresses two intrinsic phenomena in mobile manipulator robots that are often neglected but significantly impact operational accuracy: base suspension dynamics and non-geometric joint transmission effects.

1. Suspension Model for Mobile Base

Models each wheel as a linear and torsional spring-damper system to account for base flexibility during arm movements. The 6D spatial suspension model captures how external wrenches cause base displacement, affecting end-effector positioning accuracy.

Mathematical Model:

Linear spring-damper force:

0Fi = Kti · Δri + Cti · d(Δri)/dt

where Kti is the linear stiffness matrix and Cti is the linear damping matrix

Torsional spring-damper moment:

0Mi = Kθi · θ + Cθi · dθ/dt + ri × 0Fi

where Kθi is the torsional stiffness matrix and Cθi is the torsional damping matrix

2. Non-Geometric Joint Phenomena Model

Addresses backlash in mechanical transmissions, joint flexibility, and encoder mounting misalignments using a combination of sigmoid functions (for hysteresis behavior) and multivariate polynomials (for configuration-dependent effects).

Hypothesized Model:

Joint position discrepancy model:

Δθ̂LMk = Cr(θMk, τk) · S(dθMk/dt) + Cl(θMk, τk) · (1 - S(dθMk/dt))

where Δθ̂LMk represents the discrepancy between motor-side and link-side encoder measurements

Right-side polynomial (engaged teeth):

Cr(θMk, τk) = ∑i=1m ∑j=1n Akij · θMki · τkj

polynomial approximating backlash gap when teeth are engaged

Left-side polynomial (disengaged teeth):

Cl(θMk, τk) = ∑i=1m ∑j=1n Bkij · θMki · τkj

polynomial approximating backlash gap when teeth are disengaged

Sigmoid activation function:

S(dθMk/dt) = 1 / (1 + e(-ρ · dθMk/dt))

smooth hysteresis function activated by direction changes, where ρ is the sigmoid gain

3. Integrated Framework with Geometric Calibration

Combines the proposed models with state-of-the-art geometric calibration using the FIGAROH toolbox, providing a comprehensive approach to mobile manipulator accuracy improvement.

Experimental Results

Experiments were conducted on the TIAGo mobile manipulator using stereophotogrammetric motion capture and force plate measurements. Four models were compared:

  • Nominal Model: Manufacturer's default geometric parameters
  • Model 1: Nominal model + suspension compensation
  • Model 2: Model 1 + geometric calibration
  • Model 3: Model 2 + non-geometric joint phenomena compensation
Overview of the models proposed for improving mobile manipulator accuracy

Figure 4: Overview of the models proposed for improving mobile manipulator accuracy

Accuracy Improvements

The integrated approach achieved significant improvements in end-effector pose estimation:

  • Position Accuracy: RMSE reduced from 13.3mm to 5.7mm (57% improvement)
  • Orientation Accuracy: RMSE reduced from 8.57° to 2.71° (68% improvement)
Boxplot comparing end-effector errors by model

Figure 5: Boxplot comparing end-effector position and orientation errors for each model.

These results demonstrate the importance of accounting for both geometric and non-geometric phenomena in mobile manipulator modeling, particularly when the robot handles heavy objects or experiences significant external wrenches.

Citations

If you use FIGAROH in your research, please cite the following papers:

Main Reference

@inproceedings{nguyen2024improving,
  title={Improving Operational Accuracy of a Mobile Manipulator by Modeling Geometric and Non-Geometric Parameters},
  author={Nguyen, Thanh D. V. and Bonnet, V. and Fernbach, P. and Flayols, T. and Lamiraux, F.},
  booktitle={2024 IEEE-RAS 23rd International Conference on Humanoid Robots (Humanoids)},
  pages={965--972},
  year={2024},
  address={Nancy, France},
  doi={10.1109/Humanoids58906.2024.10769790}
}

Related Work

@inproceedings{nguyen2023figaroh,
            title={FIGAROH: a Python toolbox for dynamic identification and geometric calibration of robots and humans},
            author={Nguyen, Dinh Vinh Thanh and Bonnet, Vincent and Maxime, Sabbah and Gautier, Maxime and Fernbach, Pierre and others},
            booktitle={IEEE-RAS International Conference on Humanoid Robots},
            pages={1--8},
            year={2023},
            address={Austin, TX, United States},
            doi={10.1109/Humanoids57100.2023.10375232},
            url={https://hal.science/hal-04234676v2}
          }