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Research Papers

On Global, Closed-Form Solutions to Parametric Optimization Problems for Robots With Energy Regeneration

[+] Author and Article Information
Poya Khalaf

Department of Mechanical Engineering,
Cleveland State University,
Cleveland, OH 44122
e-mail: p.khalaf@vikes.csuohio.edu

Hanz Richter

Mem. ASME
Department of Mechanical Engineering,
Cleveland State University,
Cleveland, OH 44122
e-mail: h.richter@csuohio.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 8, 2016; final manuscript received August 10, 2017; published online November 8, 2017. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 140(3), 031003 (Nov 08, 2017) (12 pages) Paper No: DS-16-1436; doi: 10.1115/1.4037653 History: Received September 08, 2016; Revised August 10, 2017

Parametric optimization problems are considered for serial robots with regenerative drive mechanisms. A subset of the robot joints are conventional, in the sense that external power is used for actuation. Other joints are energetically self-contained passive systems that use (ultra)capacitors for energy storage. Two different electrical interconnections are considered for the regenerative drives, a distributed and a star configuration. The latter allows for direct electric energy redistribution among joints, a novel idea shown in this paper to enable higher energy utilization efficiencies. Closed-form expressions are found for the optimal manipulator parameters (link masses, link lengths, etc.) and drive mechanism parameters (gear ratios, etc.) that maximize regenerative energy storage between any two times, given motion trajectories. A semi-active virtual control strategy previously proposed is used to achieve asymptotic tracking of trajectories. Optimal solutions are shown to be global and unique. In addition, closed-form expressions are provided for the maximum attainable energy. This theoretical maximum places limits on the amount of energy that can be recovered. The results also shed light on the comparative advantages of the star and distributed configurations. A numerical example with a double inverted pendulum and cart system is provided to demonstrate the results.

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Figures

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Fig. 1

Fully active and semiactive JMs

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Fig. 2

Distributed configuration for semiactive JMs

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Fig. 3

Star configuration for semiactive JMs

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Fig. 4

Bond graph of electromechanical semiactive JM in the distributed and star configurations

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Fig. 5

Double inverted pendulum and cart system with fully active and semiactive JMs

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Fig. 6

Desired reference trajectories for the fully active and semiactive JMs

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Fig. 7

Simulation results for initial parameters: change in capacitor energy (distributed: solid lines, star: dotted lines), modulation index, power flows for JM1 (lower left), power flows for JM2 (lower right)

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Fig. 8

Simulation results for first case: change in capacitor energy (distributed: solid lines, star: dotted lines), modulation index, power flows for JM1 (lower left), and power flows for JM2 (lower right)

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Fig. 9

Sankey diagram for case 1

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Fig. 10

Simulation results for case 3: change in capacitor energy (distributed: solid lines, star: dotted lines), modulation index, power flows for JM1 (lower left), and power flows for JM2 (lower right)

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Fig. 11

Sankey diagram for case 3

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Fig. 12

Simulation results for case 4: change in capacitor energy (distributed: solid lines, star: dotted lines), modulation index, power flows for JM1 (lower left), and power flows for JM2 (lower right)

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Fig. 13

Sankey diagram for case 4

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Fig. 14

Current flows for case 4. Positive current is from JM to the capacitor.

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Fig. 15

Simulation results for case 5: change in capacitor energy (distributed: solid lines, star: dotted lines), modulation index, power flows for JM1 (lower left), and power flows for JM2 (lower right)

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Fig. 16

Sankey diagram for case 5

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