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Planning and control of under-actuated mobile manipulators using differential flatness

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Abstract

Mobile manipulators are intrinsically nonholonomic systems since the mobile base is subject to nonholonomic constraints that result from no-slip constraints on the wheels. The highly nonlinear dynamic coupling between the mobile base and the manipulator arm, in addition to the nonholonomic constraints at the base, makes these systems difficult to plan and control. If the system is under-actuated, the problem becomes even more difficult.

In this paper, using a special inertia distribution on the manipulator arm, the differential flatness property of mobile manipulators is achieved. An integrated planning and control methodology is presented for two different types of under-actuated planar mobile manipulators, with a two-wheeled differentially driven mobile base and with a car-like mobile base, respectively. A mobile manipulator with either of the two bases is shown to be differentially flat. In addition, this paper shows that a wide range of under-actuated arm designs results in differential flatness. Through illustrative examples of under-actuated two-link planar mobile manipulators, it is demonstrated that with the differential flatness property, the trajectory planning and feedback controller design problem can be solved in an efficient and simplified way.

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Abbreviations

TWMB:

Two-Wheeled Mobile Base

CLMB:

Car-Like Mobile Base

m 0 :

mass of the TWMB

I 0 :

moment of inertia of the TWMB

r :

radius of the TWMB’s wheel

b :

half the distance between the TWMB’s two wheels

m b :

mass of the CLMB except for the front wheel

I b :

moment of inertia of the CLMB except for the front wheel

m w :

mass of the CLMB’s front wheel

I w :

moment of inertia of the CLMB’s front wheel

R :

radius of the CLMB’s front wheel

I 1 :

moment of inertia of the first link of the arm

I 2 :

moment of inertia of the second link of the arm

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Delaware, Newark, DE, 19716, USA

    Ji-Chul Ryu & Sunil K. Agrawal

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  1. Ji-Chul Ryu
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  2. Sunil K. Agrawal
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Correspondence to Sunil K. Agrawal.

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Ryu, JC., Agrawal, S.K. Planning and control of under-actuated mobile manipulators using differential flatness. Auton Robot 29, 35–52 (2010). https://doi.org/10.1007/s10514-010-9185-0

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