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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2014, Vol. 9 Issue (4) : 295-307    https://doi.org/10.1007/s11465-014-0317-7
RESEARCH ARTICLE
Motion capability analysis of a quadruped robot as a parallel manipulator
Jingjun YU(),Dengfeng LU,Zhongxiang ZHANG,Xu PEI
School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
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Abstract

This paper presents the forward and inverse displacement analysis of a quadruped robot MANA as a parallel manipulator in quadruple stance phase, which is used to obtain the workspace and control the motion of the body. The robot MANA designed on the basis of the structure of quadruped mammal is able to not only walk and turn in the uneven terrain, but also accomplish various manipulating tasks as a parallel manipulator in quadruple stance phase. The latter will be the focus of this paper, however. For this purpose, the leg kinematics is primarily analyzed, which lays the foundation on the gait planning in terms of locomotion and body kinematics analysis as a parallel manipulator. When all four feet of the robot contact on the ground, by assuming there is no slipping at the feet, each contacting point is treated as a passive spherical joint and the kinematic model of parallel manipulator is established. The method for choosing six non-redundant actuated joints for the parallel manipulator from all twelve optional joints is elaborated. The inverse and forward displacement analysis of the parallel manipulator is carried out using the method of coordinate transformation. Finally, based on the inverse and forward kinematic model, two issues on obtaining the reachable workspace of parallel manipulator and planning the motion of the body are implemented and verified by ADAMS simulation.
Keywords quadruped robot      actuated joints selection      kinematics analysis      motion planning      parallel manipulator     
Corresponding Author(s): Jingjun YU   
Online First Date: 11 December 2014    Issue Date: 19 December 2014
 Cite this article:   
Jingjun YU,Dengfeng LU,Zhongxiang ZHANG, et al. Motion capability analysis of a quadruped robot as a parallel manipulator[J]. Front. Mech. Eng., 2014, 9(4): 295-307.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0317-7
https://academic.hep.com.cn/fme/EN/Y2014/V9/I4/295
Fig.1  A quadruped robot MANA
Fig.2  Structural diagram of the robot MANA
Structural parameters Value/mm
L (Body length) 210
W (Body width) 160
H (Body height)d (Pelvis width)l1 (Pelvis length) 2103040
l2 (Thigh length)l3 (Shank length)S (Displacement)D (Diameter of robot feet) 75105515
Tab.1  Structural parameters of MANA robot
Fig.3  Leg posture and coordinate frames. (a) Initial posture; (b) general posture
Fig.4  Four-limb parallel manipulator and coordinate frames
Fig.5  A general configuration of the parallel manipulator
Actuated joints Joint 1, 2, 3 Joint 2, 3 Joint 1, 3 Joint 1, 2
Constraints of the moving platform provided by the limb
Actuated joints Joint 1 Joint 2 Joint 3
Constraints of the moving platform provided by the limb
Tab.2  Constraint distribution of the moving platform provided by the limb
Distributions of actuators Actuated joints of each leg
Leg 1 Leg 2 Leg 3 Leg 4
3+3+0+0 No feasible combinations
3+2+0+1 Joints 1, 2 and 3 Joint 3(2) – Joints 1 and 3(2)
Joints 1, 2 and 3 Joints 2 and 3 Joint 3(2)
3+1+1+1 Joints 1, 2 and 3 Joint 3(2) Joint 3(2) Joint 1
2+2+0+2 Joints 1 and 3(2) Joints 2 and 3 – Joints 1 and 3(2)
Joints 2 and 3 Joints 2 and 3 – Joints 1 and 3(2)
2+2+1+1 Joints 2 and 3 Joints 2 and 3 Joint 1 Joint 3(2)
Joints 2 and 3 Joints 1 and 3(2) Joint 1 Joint 3(2)
Tab.3  Some feasible combinations for actuated joints
Fig.13  Four-limb parallel manipulator and coordinate frames
Leg number Hip 1 joint/rad Hip 2 joint/rad Knee joint/rad
1 0 ???0.94 -1.6143
2 0 -0.94 ???1.6143
3 0 ???0.94 -1.6143
4 0 -0.94 ???1.6143
Tab.4  Angular displacements of all joints in its initial posture
Body position and orientation Value
X-axis rotation (roll) 15°
Y-axis rotation (pitch) 10°
Z-axis rotation (yaw) 15°
X-axis translation 20 mm
Y-axis translation 20 mm
Z-axis translation -20 mm??
Tab.5  Body position and orientation with respect to the initial body coordinates
Leg number Hip 1 joint/rad Hip 2 joint/rad Knee joint/rad
1 -0.61946 ???1.12860 -2.1264
2 ???0.59703 -1.39350 ???1.8965
3 ???0.16013 ??0.87966 -1.7571
4 -0.18813 -0.99065 ???1.4017
Tab.6  Results of inverse displacement analysis
Body position and orientation Value
X-axis rotation (roll) 15.030°
Y-axis rotation (pitch) 10.354°
Z-axis rotation (yaw) 15.068°
X-axis translation 20.071 mm
Y-axis translation 19.774 mm
Z-axis translation -19.830 mm??
Tab.7  Simulation results using ADAMS
Solution number X-axis rotation/(° ) Y-axis rotation/(° ) Z-axis rotation/(° ) X-axis translation/mm Y-axis translation/mm Z-axis translation/mm
1 -8.6092?? -53.5960????? 25.437 -48.030????? 20.001 -26.594??
2 -13.7780????? -59.0860????? 29.745 -44.272????? 20.001 -42.933??
3 10.7380 -6.0426?? 14.854 -13.585????? 20.001 100.314
4 15.0020 10.0010 15.003 20.005 20.001 130.004
5 -13.7780????? -59.0860????? 29.745 -44.272????? 20.001 -42.933??
6 10.7380 -6.0426?? 14.854 -13.585????? 20.001 100.314
7 15.0020 10.0010 15.003 20.005 20.001 130.004
8 -8.6092?? -53.5960????? 25.437 -48.030????? 20.001 -26.594??
Tab.8  Numerical solutions using MATLAB
Fig.14  Workspace resulted by the translational motion. (a) Workspace without considering stability; (b) workspace considering stability
Minimum value/(° ) Maximum value/(° )
X-axis rotation -52 52
Y-axis rotation -27 27
Z-axis rotation -49 49
Tab.9  Angular displacement of the body rotation
Fig.15  Comparisons of simulation trajectory and theoretical trajectory
Fig.16  Variation of the translational displacement with respect to time. (a) Variation of the X-axis translational displacement with respect to time; (b) variation of the Y-axis translational displacement with respect to time; (c) variation of the Z-axis translational displacement with respect to time
Fig.17  Variation of the angular displacement with respect to time. (a) Variation of the X-axis angular displacement with respect to time; (b) variation of the Y-axis angular displacement with respect to time; (c) variation of the Z-axis angular displacement with respect to time
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