Derivation and analysis of a dynamic model of a robotic manipulator on a moving base

doi:10.1016/j.robot.2011.05.010

Robotics and Autonomous Systems

Volume 59, Issue 10, October 2011, Pages 758-769

https://doi.org/10.1016/j.robot.2011.05.010 Get rights and content

Abstract

A dynamic model of a robotic manipulator mounted on a moving base is derived using the Euler–Lagrange approach. It is assumed that the base inertia is large enough not to be influenced by the manipulator motion and therefore can be treated as a time-varying parameter in the dynamic equations. The presented derivation is applied to a Mitsubishi PA10-6CE robotic manipulator mounted on a 2-DOF platform. The model is analysed by comparing simple closed-loop control results of the simulated model with experimental data from the manipulator mounted on the platform.

Highlights

► We derive a dynamic model of a robotic manipulator mounted on a moving base. ► We apply it to a Mitsubishi PA10-6CE robotic manipulator mounted on a 2-DOF platform. ► The model is analysed by comparing simulated model results with experimental data. ► The approach is useful for controlling a robotic manipulator on a moving base.

Introduction

There are numerous situations where the base of a robotic manipulator is attached to a non-inertial coordinate system, such as a manipulator mounted on a ship or a floating oil rig, or a manipulator mounted on a vehicle driving on uneven terrain. Consider for example a vessel on the sea with a manipulator attached to it. The vessel would be stabilised; however, it is not possible to completely dampen the motion induced by the sea waves. Although this motion would mostly occupy the lower part of the frequency range of the manipulator motion, it could affect the control quality due to unmodelled dynamics.

In this paper a full derivation of a generic model of a robotic manipulator on a moving platform is presented (assuming that the platform is not affected by the manipulator motion and its trajectory is considered to be a time-varying parameter of the obtained model). An analysis of the significance of the model terms is performed by a comparison with the static base model. An actual symbolic derivation is performed for the PA10 manipulator on a 2-DOF base with roll and pitch angles as time-varying parameters of the model. Simulation and experimental results are presented and compared. This paper contributes the following results:

•
the consideration of the base motion as a time-varying parameter of the manipulator on a non-inertial base and resulting simplifications in the dynamic equations,
•
a broad analysis (using a comparison of model simulations and manipulator experiments) of the obtained model for the PA10 manipulator with various types of base trajectory by assessing the relative significance of the dynamic model terms for each joint.

The merit of this approach is that designers employing model-based control methods for a manipulator on a moving base could simplify their algorithms by omitting non-significant dynamics terms.

The following assumptions apply to the system under consideration:

•
the base motion is not used to control the manipulator,
•
the manipulator motion is unconstrained.

The remainder of the paper is organised as follows. Section 2 presents past and current research efforts addressing similar problems. The mathematical derivation of the dynamic model is performed in Section 3. Remarks on the implementation of the derived model to the Mitsubishi PA10 manipulator mounted on a moving platform are presented in Section 4. Section 5 presents the comparison of simulation and experimental results to verify the derived model and analyses the significance of the model terms by means of feedback control torque comparisons. The paper is concluded in Section 6.

Section snippets

Background

The majority of manipulator dynamic and kinematic modelling work applies to fixed base cases, where the manipulator is attached to an inertial coordinate system and no external forces influence its motion. Multiple dynamic models have been developed for the PA10 manipulator on a fixed base.

Model derivation

The dynamic model of a manipulator on a mobile platform is derived using the Euler–Lagrange approach.

Implementation

In order to use the analytical formulae defining the dynamic model in numerical simulations the explicit equations for the PA10 manipulator mounted on a platform need to be derived. The schematic of the PA10 kinematics with the coordinate systems for each link and base coordinate system bound to the centre of the platform mounting plate is presented in Fig. 1.

Model evaluation

Due to the high complexity of the platform related dynamics elements, the model cannot be verified by hand. Therefore, to quantitatively assess the model, the PA10 model behaviour is compared with the experimental results recorded from the robotic arm. The manipulator, installed on a moving platform, is driven with a PID controller, and all the joint configuration and control variables and the platform trajectory are recorded. The derived equations of the PA10 dynamics on a moving platform

Conclusions

In this paper a generic model of a robotic manipulator on a moving platform (not dynamically influenced by the manipulator) has been derived.

The derived equations have been used to obtain a model of the PA10 manipulator on a 2-DOF (roll and pitch) platform. However, the model derivation procedure is general and applies to any rigid manipulator on a 6-DOF moving base.

The obtained model has been compared with the experimental results from the actual PA10 manipulator mounted on a moving platform

C.M. Wronka has an M.Sc. in Electronics (Robotics) and an MSc in Mathematics (Statistics) from the Technical University of Wroclaw, Poland. He was awarded his Ph.D. in Electrical, Electronic and Computer Engineering from Heriot-Watt University (Edinburgh) in 2010 where his research was concerned with manipulator control. He is currently a software team leader at Optos and works on image recognition/enhancement techniques.

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M.W. Dunnigan received the B.Sc. degree in electrical and electronic engineering (with First-Class Honors) from Glasgow University, Glasgow, UK, in 1985 and the M.Sc. and Ph.D. degrees from Heriot-Watt University, Edinburgh, UK, in 1989 and 1994, respectively. He was employed by Ferranti from 1985 to 1988 as a Development Engineer in the design of power supplies and control systems for moving optical assemblies and device temperature stabilization. In 1989, he became a Lecturer at Heriot-Watt University, where he was concerned with the evaluation and reduction of the dynamic coupling between a robotic manipulator and an underwater vehicle. He is currently a Senior Lecturer and his research grants and interests include the areas of hybrid position/force control of an underwater manipulator, coupled control of manipulator-vehicle systems, nonlinear position/speed control and parameter estimation methods in vector control of induction machines, frequency domain self-tuning/adaptive filter control methods for random vibration, and shock testing using electrodynamic actuators.

View full text

Derivation and analysis of a dynamic model of a robotic manipulator on a moving base

Abstract

Highlights

Introduction

Section snippets

Background

Model derivation

Implementation

Model evaluation

Conclusions

Modeling and control of the Mitsubishi PA-10 robot arm harmonic drive system

Mechatronics, IEEE/ASME Transactions on 10

Simulation of cooperating robot manipulators on a mobile platform

Robotics and Automation, IEEE Transactions on 7

A simple active damping control for compliant base manipulators

Mechatronics, IEEE/ASME Transactions on 6

Motion control of non-fixed base robotic manipulators

Robotica

Efficient dynamic simulation of an underwater vehicle with a robotic manipulator

Systems, Man and Cybernetics, IEEE Transactions on 25