Design, analysis, and neural control of a bionic parallel mechanism

doi:10.1007/s11465-021-0640-8

Front. Mech. Eng.

2021, Vol. 16

Issue (3) : 468-486 https://doi.org/10.1007/s11465-021-0640-8

RESEARCH ARTICLE

Design, analysis, and neural control of a bionic parallel mechanism

Yaguang ZHU^1,^2,³(

), Shuangjie ZHOU¹, Manoonpong PORAMATE^3,⁴, Ruyue LI‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬‬¹

¹. The Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an 710064, China
². State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
³. Embodied Artificial Intelligence & Neurorobotics Laboratory, SDU Biorobotics, The Mærsk Mc-Kinney Møller Institute, The University of Southern Denmark, Odense 5230, Denmark
⁴. The College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; The School of Information Science & Technology, Vidyasirimedhi Institute of Science & Technology, Rayong 21210, Thailand

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Abstract

Although the torso plays an important role in the movement coordination and versatile locomotion of mammals, the structural design and neuromechanical control of a bionic torso have not been fully addressed. In this paper, a parallel mechanism is designed as a bionic torso to improve the agility, coordination, and diversity of robot locomotion. The mechanism consists of 6-degree of freedom actuated parallel joints and can perfectly simulate the bending and stretching of an animal’s torso during walking and running. The overall spatial motion performance of the parallel mechanism is improved by optimizing the structural parameters. Based on this structure, the rhythmic motion of the parallel mechanism is obtained by supporting state analysis. The neural control of the parallel mechanism is realized by constructing a neuromechanical network, which merges the rhythmic signals of the legs and generates the locomotion of the bionic parallel mechanism for different motion patterns. Experimental results show that the complete integrated system can be controlled in real time to achieve proper limb–torso coordination. This coordination enables several different motions with effectiveness and good performance.

Keywords neural control behavior network rhythm motion pattern

Corresponding Author(s): Yaguang ZHU

Just Accepted Date: 11 June 2021 Online First Date: 26 July 2021 Issue Date: 24 September 2021

Cite this article:

Yaguang ZHU,Shuangjie ZHOU,Manoonpong PORAMATE, et al. Design, analysis, and neural control of a bionic parallel mechanism[J]. Front. Mech. Eng., 2021, 16(3): 468-486.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0640-8
https://academic.hep.com.cn/fme/EN/Y2021/V16/I3/468

Fig.1 Mechanical structure of the parallel mechanism. (a) 3D model; (b) picture of the platform; and (c) geometric configuration.

Tab.1 Structure parameters of the parallel mechanism

Fig.2 Structural constraint on the spherical hinge.

Fig.3 Effect of different size spherical hinges. (a) r_s = 3 mm, r_b = 5.6 mm, and h = 6 mm; (b) r_s = 3.5 mm, r_b = 6.4 mm, and h = 6.7 mm; and (c) r_s = 4.5 mm, r_b = 7.9 mm, and h = 9 mm. The red area is the ideal workspace, and the blue area is the actual workspace with constraints.

Fig.4 Structural parameters affecting the workspace. (a) Workspace influence of γ_m; (b) workspace influence of r; (c) workspace influence of R; (d) workspace influence of L; (e) workspace influence of L₁; and (f) workspace influence of R₀.

Fig.5 Range of motion of the parallel platform. (a) Rotation around the Z axis; (b) rotation around the Y axis; (c) rotation around the X axis; (d) movement along the Z axis; (e) movement along the Y axis; (f) movement along the X axis; (g) comparison with horses and cats; (h) comparison with horses in different gaits, A is for the rotation around the Y axis, B is for the rotation around the X axis, and C is for the rotation around the Z axis.

Fig.6 Unbalance degree of force in different motion patterns. F_Z = 200 N along the Z axis. (a) Pitch around the Y axis under F_X = 50 N; (b) lateral movement along the X axis under F_X = 50 N; (c) twist movement around the Z axis under F_X = 50 N; (d) pitch around the Y axis under F_X = 100 N; (e) lateral movement along the X axis under F_X = 100 N; (f) twist movement around the Z axis under F_X = 100 N; (g) pitch around the Y axis under F_X = 200 N; (h) lateral movement along the X axis under F_X = 200 N; (i) twist movement around the Z axis under F_X = 200 N.

Fig.7 Joint torque analysis of the parallel mechanism; i represents the ith joint.

Fig.8 Structural parameters affecting the joint torque. (a) workspace influence of ξ_i with motor inclination angles; (b) workspace influence of δ_i with motor inclination angles; (c) joint torque influence of ξ_i and δ_i with different motor inclination angles. F_i = 50 N along the coupler link.

Fig.9 Locomotion control network for the parallel mechanism. Φ_i is an oscillation phase of the ith joint. O_i is the control signal of the ith joint. Every limb is composed of two links, two spherical hinges, one actuator, and one force sensor. The geometric structure is shown in Fig. 1.

Fig.10 Phase configuration of the network for different motion patterns. Phase factors (ψ_i = Φ_i/(2π)) are marked. (a) Stretching and flexing along the Z axis; (b) lateral movement along the X axis; (c) turning around the X axis; and (d) pitching around the Y axis.

Fig.11 The limb–torso network (two oscillators) coordinates the locomotion control network of the legs (four oscillators) and the motion control network of the parallel mechanism (six oscillators).

Fig.12 Position trajectory of typical motion patterns. α is the pitch angle around the X axis, and β is the pitch angle around the Y axis. The solid line is the designed trajectory, and the dashed line is the actual trajectory of the parallel mechanism. (a) Movements and rotations; (b) synthesis movements. ψ₁= [0, 0.5, 0.2, 0.3, 0, 0.5], ψ₂= [0, 0.5, 0.3, 0.2, 0, 0.5], ψ₃= [0, 0.5, 0.4, 0.1, 0, 0.5], ρ₁= [3/4, 1/4, 0.55, 0.45, 3/4, 1/4], and ρ₂= [1/4, 3/4, 0.45, 0.55, 1/4, 3/4]. ρ₁ and ρ₂ correspond to limb 3 and Δ₁₃, respectively.

Fig.13 Ratio of motion range. A is for stretching and flexing along the Z axis, B is for lateral movement along the X axis, C is for turning around the X axis, and D is for pitching around the Y axis. (a) Positive directions A (from 260 to 292 mm), B (from 0 to 71.9 mm), C (from 0° to 20.54°), D (from 0° to 15.64°), and (b) negative directions A (from 260 to 240 mm), B (from 0 to −66.2 mm), C (from 0° to −13.5°), and D (from 0° to −15.47°).

Fig.14 Rhythmic signals of neuromechanical control for different gaits. (a) Different gaits; (b) network output of O₅, O₆ and O₁₂; (c) network output of O₆ and O₁₁; (d) amplitude frequency characteristics of O₅; (e) movement of moving platform; (f) rotation of moving platform. Walking gait (φ_p = 1 s, ρ_leg= [0.75, 0.75, 0.75, 0.75], ψ_leg= [0, 0.25, 0.5, 0.75]) is in 0–5 s, trotting gait (φ_p= 1 s, ρ_leg= [0.5, 0.5, 0.5, 0.5], ψ_leg= [0, 0.5, 0.5, 0]) is in 5–10 s, and bounding gait (φ_p= 0.5 s, ρ_leg= [0.25, 0.25, 0.25, 0.25], and ψ_leg= [0, 0.5, 0, 0.5]) is in 10–15 s. Phase factors ψ_i = Φ_i/(2π). α, β, and γ present rotations around the Z, Y, and X axes, respectively.

Fig.15 Movement snapshots of the parallel mechanism during the experiments.

Fig.16 Rhythmic signals and motions of different running gaits. (a) Gaits at different running speeds; (b) network output of four legs; (c) network output of O₅, O₆,_{O₁₂and O₁₃; (d) network output of the torso; (e) movement of moving platform; (f) rotation of moving platform; (g) compound movement of moving platform. Cantering gait (φ_p = 1 s, ρ_leg= [1/3, 1/3, 1/3, 1/3], ψ_leg= [0, 1/3, 2/3, 0]) is in 3–7 s, galloping gait (φ_p = 1 s, ρ_leg = [1/3, 1/3, 1/3, 1/3], ψ_leg= [0, 1/3, 6/5, 1/6]) is in 7–11 s, and bounding gait (φ_p= 0.5 s, ρ_leg = [0.25, 0.25, 0.25, 0.25], and ψ_leg= [0, 0.5, 0, 0.5]) is in 11–15 s. Phase factors ψ_i= Φ_i/(2π). α, β, and γ present rotations around the Z, Y, and X axes, respectively.}

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