Different manipulation mode analysis of a radial symmetrical hexapod robot with leg–arm integration

Abstract

With the widespread application of legged robot in various fields, the demand for a robot with high locomotion and manipulation ability is increasing. Adding an extra arm is a useful but general method for a legged robot to obtain manipulation ability. Hence, this paper proposes a novel hexapod robot with two integrated leg–arm limbs that obtain dexterous manipulation functions besides locomotion ability without adding an extra arm. The manipulation modes can be divided into coordinated manipulation condition and single-limb manipulation condition. The former condition mainly includes fixed coordinated clamping case and fixed coordinated shearing case. For the fixed coordinated clamping case, the degrees of freedom (DOFs) analysis of equivalent parallel mechanism by using screw theory and the constraint equation of two integrated limbs are established. For the fixed coordinated shearing case, the coordinated working space is determined, and an ideal coordinated manipulation ball is presented to guide the coordinated shearing task. In addition, the constraint analysis of two adjacent integrated limbs is performed. Then, mobile manipulation with one integrated leg–arm limb while using pentapod gait is discussed as the single-limb manipulation condition, including gait switching analysis between hexapod gait and pentapod gait, different pentapod gaits analysis, and a complex six-DOF manipulation while walking. Corresponding experiments are implemented, including clamping tasks with two integrated limbs, coordinated shearing task by using two integrated limbs, and mobile manipulation with pentapod gait. This robot provides a new approach to building a multifunctional locomotion platform.

Graphical abstract

Keywords

leg–arm integration / hexapod robot / fixed coordinated manipulation / mobile manipulation

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Nomenclature

Variables
Ch1	Maximum stability of robot with three-limb support in hexapod gait
Ch2	Maximum stability of robot with six-limb support in hexapod gait
Cp1	Maximum stability of robot with three-limb support in pentapod gait
Cp2	Maximum stability of robot with five-limb support in pentapod gait
CR	Radius of the regular hexagon circumcircle in hexapod gait and pentapod gait
d	Order of the mechanism
fiz	Component force along the z-axis ({Ci}) that is effected on the object of each limb end
df	DOF of equivalent PM
Fg	Gravity of object
{}_{E_i}^{O_{\mathrm{g}}}\mathit{g}	Expected pose of ith limb end-effector in {Og}
{}_{COB}^{O_{\mathrm{g}}}\mathit{g}	Position and attitude of robot body in {Og}
{}_{O_i}^{COB}\mathit{g}	Pose of the ith limb coordinate in {COB}
{}_{E_i}^{O_i}\mathit{g}(0)	Initial pose of the ith limb end-effector in the ith limb coordinate
k	Number of kinematic pairs
l3k (k = 1, 2)	Lengths of Shanks 1 and 2
ll, ls, lJ, lK	Lengths of E1L, SK, JK, and KE2 in Fig. 11
l_m (m=1,2,...,5)	Lengths of hip, thigh, shank, Arm 1, and Arm 2
dl	Unknown position compensation
n	Total number of links
P	Position vector
d{\mathit{P}}_{COB}^{O_{\mathrm{g}}}	Position compensation of robot body in {Og}
{\mathit{P}}_{COB,0}^{O_{\mathrm{g}}}	Initial position of robot body without compensation in { O_{\mathrm{g}}}
{\mathit{P}}_{COB}^{O_{\mathrm{g}}}	Real position of robot body
R_{\mathrm{B}}	Radius of robot body
R_{\mathrm{i}}	Diameter of ideal coordinated manipulation ball
\mathit{R}	Rotation matrix
{\mathit{S}}_{\mathrm{b}\mathrm{r}}i	Twist system of branch i
{\mathit{S}}_{\mathrm{b}\mathrm{r}i}^{\mathrm{r}}	Constrained wrench system of branch i
{\mathit{S}}_{\mathrm{m}}	Twist system of equivalent PM
{\mathit{S}}^{\mathrm{c}}	Constrained wrench system of equivalent PM
{\mathit{S}}^{\mathrm{r}}	Constrained wrench system of moving platform
\alpha	Angle between E_1{E}_2 and E_{1}L in Fig. 11
\epsilon	Number of virtual constraints
\zeta	Passive DOF
\rho	Number of branches
\lambda	Number of independent common constraints
\mu \left(\mu \in \left[1,4\right]\right)	Static friction coefficient between limb end and object
{\theta }_{\mathrm{b}}^{O_{\mathrm{g}}}	Known angle between robot movement direction and x-axis in { O_{\mathrm{g}}}
{\theta }_{ij} (i=3,4,5,6;j=1,2,3)	Rotation angle of every joint in normal leg
{\theta }_{ij} (i=1,2;j=1,2,...,5)	Rotation angle of every joint in integrated leg–arm limb
{\phi }_i	DOF of the ith kinematic pair
{\text{\$}}_{ij}	Twist of the jth joint in the ith limb
{\text{ξ}}_{ij}	Screw motion of the jth joint in the ith limb

Acknowledgements

This paper was funded by the National Key R&D Program of China (Grant No. 2019YFB1309600) and the National Natural Science Foundation of China (Grant Nos. 51775011 and 91748201).

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