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Research Papers

Decentralized Passivity-Based Control With a Generalized Energy Storage Function for Robust Biped Locomotion

[+] Author and Article Information
Mark Yeatman

Department of Mechanical Engineering,
University of Texas at Dallas,
Richardson, TX 75080

Ge Lv

Department of Electrical Engineering,
University of Texas at Dallas,
Richardson, TX 75080

Robert D. Gregg

Department of Bioengineering;
Department of Mechanical Engineering,
University of Texas at Dallas,
Richardson, TX 75080
e-mail: rgregg@ieee.org

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 9, 2018; final manuscript received May 14, 2019; published online June 13, 2019. Assoc. Editor: Inna Sharf.

J. Dyn. Sys., Meas., Control 141(10), 101007 (Jun 13, 2019) (11 pages) Paper No: DS-18-1419; doi: 10.1115/1.4043801 History: Received September 09, 2018; Revised May 14, 2019

This paper details a decentralized passivity-based control (PBC) to improve the robustness of biped locomotion in the presence of gait-generating external torques and parametric errors in the biped model. Previous work demonstrated a passive output for biped systems based on a generalized energy that, when directly used for feedback control, increases the basin of attraction and convergence rate of the biped to a stable limit cycle. This paper extends the concept with a theoretical framework to address both uncertainty in the biped model and a lack of sensing hardware, by allowing the designer to neglect arbitrary states and parameters in the system. This framework also allows the control to be implemented on wearable devices, such as a lower limb exoskeleton or powered prosthesis, without needing a model of the user's dynamics. Simulations on a six-link biped model demonstrate that the proposed control scheme increases the convergence rate of the biped to a walking gait and improves the robustness to perturbations and to changes in ground slope.

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Figures

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Fig. 1

Kinematic model of the biped. COP denotes the center of pressure. The solid links denote the stance leg and the dashed links denote the swing leg.

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Fig. 2

Generalized energy (E) of the PD controlled (inner-loop) biped system while traversing the limit cycle. There are three constant energy levels with discrete jumps between them.

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Fig. 3

Centralized storage function for the perturbed system with PBC and without PBC, over five steps. The transition between steps is marked by a large decrease in storage, caused by heel impact.

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Fig. 4

Torque over time for the centralized controller U for the first three steps

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Fig. 5

Maximum absolute value of the eigenvalues of the linearization of the Poincaré map as the gain k is varied from 0 to 10

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Fig. 6

Generalized energy of all three systems while traversing the limit cycle. There is a break in the y-axis of the graph to accommodate the difference in average magnitude of the energy trajectories.

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Fig. 7

System storage function across PBC implementations

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Fig. 8

System storage function for a decentralized PBC with perfect model parameters versus a decentralized PBC with random ±30% error in the model parameter

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Fig. 9

Robustness of decentralized control versus model parameter error norm with k =1

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Fig. 10

System storage function for the centralized PBC with various adaptation gains. The scaling gain k =1 is used across all cases. The PD control by itself is given for comparison.

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