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2024 | OriginalPaper | Buchkapitel

Efficiency Study of the Non-instantaneous Double Support Phase in HZD Controlled Bipedal Robot

verfasst von : Yinnan Luo, Ulrich J. Römer, Marten Zirkel, Lena Zentner, Alexander Fidlin

Erschienen in: Advances in Nonlinear Dynamics, Volume II

Verlag: Springer Nature Switzerland

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Abstract

A study on the influence of a non-instantaneous double support phase on the energy efficiency and the stability of a bipedal walking robot with hybrid zero dynamics control is performed. The planar robot model consists of five rigid body segments and four actuated revolute joints. The periodic gait includes two alternating continuous single and double support phases as well as two discrete transition events. Two virtual actuators are introduced to create one degree of under-actuation in the double support phase. Periodic solutions of the gait are found via the numerical optimization, which minimizes the energy consumption of locomotion. The resulted efficiency and stability are compared against the common model approach with instantaneous double support phase. Despite the less efficiency, the extended controller with non-instantaneous double support phase improves the gait stability, which could be beneficial for the experimental validation on a robot prototype.

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Vorheriges Kapitel Image-Based Aerial Grasping of a Moving Target Using Model Predictive Control

Nächstes Kapitel Aeroelastic Limit Cycle Oscillations Due to Multi-element Control Surface with Freeplay

Here, the straight line connecting the hip joint and the front stance foot represents the virtual leg to define the absolute body orientation \(\theta \) in the DSP, as depicted in Fig. 1 left. In the SSP, however, the virtual leg is defined by the straight line that connects the hip joint and the stance foot.

The projection \({\mathbf {P}}_{\mathrm {d}} = [{\mathbf {P}}_{\mathrm {d,1}},\, {\mathbf {P}}_{\mathrm {d,2}}]\) is regarded as gait parameters with the restrictions \(|{\mathbf {P}}_{\mathrm {d,1}}|-1=0\), \(|{\mathbf {P}}_{\mathrm {d,2}}|-1=0\), and \({\mathbf {P}}_{\mathrm {d,1}} \cdot {\mathbf {P}}_{\mathrm {d,2}}=0\), which are formulated as equality constraints in the numerical optimization in the efficiency study.

Note that this projection is not related in the SSP, since the system has five DoF and all four actuators are required for creating the under-actuation of one DoF.

This implicitly means that \({\mathbf {P}}_{\mathrm {d,opt}}^{(i,\,2)} \approx 0\) for \(i \in [1,2,3]\), due to the requirement \(|{\mathbf {P}}_{\mathrm {d,2}}|-1=0\) from Sect. 2. After the DSP is terminated, however, all actuators provide driving torques for the walking motion in the following SSP.

The method for determining the solution as well as calculating the Floquet multiplier is developed in [9, 11]. The solution is stable if \(0 < \Lambda < 1\).

This comparison considers the simplest control law with the linear PD feedback to study the stability. Introducing nonlinear feedback laws could enhance the convergence towards the limit cycle. This is, however, not the focus of the presented work.

Also, using all actuators in the over-actuated DSP provides many possibilities to formulate other control tasks, such as the direct control on the generalized momentum for even better stability [11].

Reher, J., Ames, A.D.: Dynamic walking: toward agile and efficient bipedal robots. Annu. Rev. Control Robot. Auton. Syst. 4. 535–572 (2021)

Tran Thien, H., Van Kien, C., Anh, H.P.H.: Optimized stable gait planning of biped robot using multi-objective evolutionary JAYA algorithm. Int. J. Adv. Robot. Syst. 17(6), 1729881420976344 (2020)CrossRef

Rajendra, R., Pratihar, D.: Analysis of double support phase of biped robot and multi-objective optimization using genetic algorithm and particle swarm optimization algorithm. Sadhana 40, 549–575 (2015)MathSciNetCrossRef

Li, T., et al.: Stability control for biped walking based on phase modification during double support period. In: 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), pp. 1290–1295 (2014)

Westervelt, E.R., Grizzle, J.W., Koditschek, D.: Hybrid zero dynamics of planar biped walkers. IEEE Trans. Autom. Control 48(1), 42–56 (2003)MathSciNetCrossRef

Westervelt, E.R., Grizzle, J.W., Chevallereau, C., Choi, J.H., Morris, B.: Feedback Control of Dynamic Bipedal Robot Locomotion. Boca Raton, CRC Press. (2007)

Bauer, F., Römer, U.J., Fidlin, A., Seemann, W.: Optimization of energy efficiency of walking bipedal robots by use of elastic couplings in the form of mechanical springs. Nonlinear Dyn. 83(3), 1275–1301 (2015)MathSciNetCrossRef

Bauer, F., Römer, U.J., Fidlin, A., Seemann, W.: Optimal elastic coupling in form of one mechanical spring to improve energy efficiency of walking bipedal robots. Multibody Syst. Dyn. 38(3), 227–262 (2016)MathSciNetCrossRef

Römer, U.J., Kuhs, C., Krause, M.J., Fidlin, A.: Simultaneous optimization of gait and design parameters for bipedal robots. In: c2016 IEEE International Conference on Robotics and Automation (ICRA) pp. 1374–1381 (2016)

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Hamed, K.A., Sadati, N., Gruver, W.A., Dumont, G.A.: Stabilization of periodic orbits for planar walking with noninstantaneous double-support phase. IEEE Trans. Syst. Man Cybern. A: Syst. Hum. 42, 685–706 (2012)CrossRef

11.

Luo, Y., Römer, U.J., Dyck, A., Zirkel, M., Zentner, L., Fidlin, A.: Hybrid zero dynamics control for bipedal walking with a non-instantaneous double support phase (2023). arXiv. Preprint available: https://arxiv.org/abs/2303.05165

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Luo, Y., Römer, U.J., Zentner, L., Fidlin, A.: Improving energy efficiency of a bipedal walker with optimized nonlinear elastic coupling. In: Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series, pp. 253–262 (2022)

Titel: Efficiency Study of the Non-instantaneous Double Support Phase in HZD Controlled Bipedal Robot
verfasst von: Yinnan Luo
Ulrich J. Römer
Marten Zirkel
Lena Zentner
Alexander Fidlin
Verlag: Springer Nature Switzerland
Buch: Advances in Nonlinear Dynamics, Volume II
Print ISBN: 978-3-031-50638-3

Electronic ISBN: 978-3-031-50639-0

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-50639-0_7

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