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Technical Brief

On Constrained and Energy Efficient Balance Control of a Standing Biped: Experimentation and Stability Analysis

[+] Author and Article Information
Yuming Sun

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB, R3T 5V6, Canada
e-mail: umsun82@cc.umanitoba.ca

Mansoor Alghooneh

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB, R3T 5V6, Canada
e-mail: umalghoo@cc.umanitoba.ca

Yun-Hsiang Sun

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB, R3T 5V6, Canada
e-mail: suny3411@myumanitoba.ca

Christine Qiong Wu

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg, MB, R3T 5V6, Canada
e-mail: Christine.Wu@umanitoba.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 4, 2013; final manuscript received March 20, 2014; published online July 9, 2014. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 136(5), 054504 (Jul 09, 2014) (8 pages) Paper No: DS-13-1260; doi: 10.1115/1.4027288 History: Received July 04, 2013; Revised March 20, 2014

Balancing control is important for biped standing. In spite of large efforts, it is very difficult to design balancing control strategies satisfying three requirements simultaneously: maintaining postural stability, improving energy efficiency, and satisfying the constraints between the biped feet and the ground. To implement such a control, inclusion of the actuators' dynamics is necessary, which complicates the overall system, obstructs the control design, and makes stability analysis more difficult. In this paper, a constrained balancing control meeting all three requirements is designed for a standing bipedal robot. The dynamics of the selected actuators has been considered for developing the motion equations of the overall control system, which has usually been neglected in simulations. In addition, stability analysis of such a complex biped control system has been provided using the concept of Lyapunov exponents (LEs), which shows the significance of actuators' dynamics on the stability region. The paper contributes to balancing standing biped in both the theoretical and the practical sense.

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Figures

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Fig. 3

Experimental setup: (a) the control system, (b) the Bertec's fully instrumented treadmill [15], and (c) a side view of the treadmill and the standing robot

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Fig. 2

Block diagram of GA-based PID control

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Fig. 4

Performance of the convergence test

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Fig. 5

Evolution of (a) the angle and the angular speed of the lower link; (b) the angle and the angular speed of the upper link; (c) two control torques applied at the ankle joint and the hip joint, respectively; and (d) two voltage signals generated by the PID controllers

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Fig. 1

(a) The simplified biped model; (b) the free body diagram of the two-link inverted pendulum; and (c) the free body diagram of the foot-link

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Fig. 7

Evolution of the system Lyapunov exponents. The converged value of each exponent has been shown as the Y reading of the datatip in the corresponding subplot, while the X reading reflects the time the system has progressed over.

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Fig. 6

Evolution of (a) the vertical ground reaction force; (b1) and (b2) the horizontal ground reaction force; and (c) the location of COP

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Fig. 8

Stability regions of the controlled robot: The area surrounded by blue circles is the stability region for the real one-legged robot actuated by the GA-based controller, the area encompassed by green squares is the stability region for the simulation model with the identical mass geometry and the same controller, but without incorporation of the motor dynamics

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