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Research Papers

Multivariable Extremum Seeking for Joint-Space Trajectory Optimization of a High-Degrees-of-Freedom Robot

[+] Author and Article Information
Mostafa Bagheri

Department of Mechanical
and Aerospace Engineering,
San Diego State University
San Diego, CA 92115;
Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mails: mbagheri@sdsu.edu;
mstfbagheri@eng.ucsd.edu

Miroslav Krstić

Daniel L. Alspach Endowed Chair in Dynamic
Systems and Control,
Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: krstic@ucsd.edu

Peiman Naseradinmousavi

Dynamic Systems and
Control Laboratory (DSCL),
Department of Mechanical Engineering,
San Diego State University,
San Diego, CA 92115
e-mails: pnaseradinmousavi@sdsu.edu;
peiman.n.mousavi@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 24, 2017; final manuscript received June 29, 2018; published online August 1, 2018. Assoc. Editor: Tesheng Hsiao.

J. Dyn. Sys., Meas., Control 140(11), 111017 (Aug 01, 2018) (13 pages) Paper No: DS-17-1483; doi: 10.1115/1.4040752 History: Received September 24, 2017; Revised June 29, 2018

In this paper, a novel analytical coupled trajectory optimization of a seven degrees-of-freedom (7DOF) Baxter manipulator utilizing extremum seeking (ES) approach is presented. The robotic manipulators are used in network-based industrial units, and even homes, by expending a significant lumped amount of energy, and therefore, optimal trajectories need to be generated to address efficiency issues. These robots are typically operated for thousands of cycles resulting in a considerable cost of operation. First, coupled dynamic equations are derived using the Lagrangian method and experimentally validated to examine the accuracy of the model. Then, global design sensitivity analysis is performed to investigate the effects of changes of optimization variables on the cost function leading to select the most effective ones. We examine a discrete-time multivariable gradient-based ES scheme enforcing operational time and torque saturation constraints in order to minimize the lumped amount of energy consumed in a path given; therefore, time-energy optimization would not be the immediate focus of this research effort. The results are compared with those of a global heuristic genetic algorithm (GA) to discuss the locality/globality of optimal solutions. Finally, the optimal trajectory is experimentally implemented to be thoroughly compared with the inefficient one. The results reveal that the proposed scheme yields the minimum energy consumption in addition to overcoming the robot's jerky motion observed in an inefficient path.

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Figures

Grahic Jump Location
Fig. 1

The 7DOF Baxter's arm

Grahic Jump Location
Fig. 2

The joints' configuration: (a) sagittal view and (b) top view

Grahic Jump Location
Fig. 3

Comparison between the experimentally measured and nominal analytical torques used in driving the joints (a) S0, (b) E0, (c) W0, and (d) W1; the non-zero torques at the initial point (t = 0) stand for holding torques against gravity

Grahic Jump Location
Fig. 4

The global sensitivity analysis with respect to B's

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Fig. 5

The global sensitivity analysis with respect to C's

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Fig. 6

Discrete-time multivariable gradient-based ES using washout filter

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Fig. 7

The optimal values of B's using the ES

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Fig. 8

The optimal values of B's using the GA

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Fig. 9

The (a) actual and (b) mean value of energy optimized using the ES

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Fig. 10

(a) The energy optimized using the GA and (b) the convergence history of the GA

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Fig. 11

The actual (inefficient), nominal fitted to the actual, and optimal trajectories using the ES and GA: (a) S0, (b) S1, (c) E0, (d) E1, (e) W0, (f) W1, and (g) W2

Grahic Jump Location
Fig. 12

The experimental nominal and optimal trajectories using the ES in sample times of (a) t = 1 s, (b) t = 3 s, (c) t = 5 s, and (d) t = 6 s; at t = 6 s, the robot's end effector through the nominal trajectory collides with another object due to the jerky motion, while the optimal one avoids such a collision throughout the whole operational time. The shadow frames present the nominal trajectory.

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