Research Papers

Minimum Energy Control of Redundant Linear Manipulators

[+] Author and Article Information
Yoram Halevi

Faculty of Mechanical Engineering,
Haifa 32000, Israel
e-mail: yoramh@technion.ac.il

Emanuele Carpanzano

Istituto di Tecnologie Industriali
e Automazione (ITIA),
Consiglio Nazionale delle Ricerche (CNR),
Milano 20133, Italy
e-mail: emanuele.carpanzano@itia.cnr.it

Giuseppe Montalbano

Istituto di Tecnologie Industriali
e Automazione (ITIA),
Consiglio Nazionale delle Ricerche (CNR),
Milano 20133, Italy
e-mail: giuseppe.montalbano@itia.cnr.it

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 12, 2012; final manuscript received April 9, 2014; published online July 9, 2014. Assoc. Editor: Nariman Sepehri.

J. Dyn. Sys., Meas., Control 136(5), 051016 (Jul 09, 2014) (8 pages) Paper No: DS-12-1299; doi: 10.1115/1.4027419 History: Received September 12, 2012; Accepted April 09, 2014; Revised April 09, 2014

In redundant manipulation systems, the end-effector path does not completely determine the trajectories of all the individual degrees of freedom (dof) and the additional dofs can be used to enhance the performance in some sense. The paper deals with utilizing the redundancy to minimize energy consumption. A full linear electromechanical model is used, and the exact energy consumption is calculated. The optimization includes also displacement limits via penalty functions that are included in the cost function. The optimal trajectory is feasible in the sense that it can be obtained by a finite input voltage and all the velocities are continuous. The solution is based on projections that separate the system and the input into two parts. One that is completely determined by the end-effector path and the other that is free for optimization. The important and delicate issue of boundary conditions is resolved accordingly. Simulation results show that redundancy, even with limited joint motion, can lead to a considerable reduction in energy consumption.

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Grahic Jump Location
Fig. 1

A redundant XY system

Grahic Jump Location
Fig. 2

The responses q1(t), q3(t), and the reference signal r(t) (x-direction) in fixed-free configuration with qm = 0.15

Grahic Jump Location
Fig. 6

The end-effector path (dashed) and the main system motion (solid) in example 2 with qm = 0.35



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