Design, Analysis, and Applications of Mobile Manipulators

Design, Analysis, and Applications of Mobile Manipulators

Tao Song (Shanghai University, China), Feng Feng Xi (Ryerson University, Canada) and Shuai Guo (Shanghai University, China)
Copyright: © 2019 |Pages: 40
DOI: 10.4018/978-1-5225-5276-5.ch002

Abstract

Presented in this chapter is a method for design and analysis of a mobile manipulator. The wrench induced by the movement of the robot arm will cause system tip-over or slip. In tip-over analysis, three cases are considered. The first case deals with the effect of the link weights and tip payload on the horizontal position of the CG. The second case deals with the effect of the joint speeds through the coupling terms including centrifugal forces and gyroscopic moments. The third case deals with the effect of the joint accelerations through the inertia forces and moments. In slip analysis, the first case considers the reaction force in relation to the stand-off distance between system and work-piece. The second and third cases investigate the effects of the joint speeds and accelerations. Then, the mobile platform is optimized to have maximum tip-over stability which optimizes the placement of the robot arm and accessory on the mobile platform. The effectiveness of the proposed method is demonstrated.
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Wrench Modeling

Manipulator Kinematics

Figure 1.

Manipulator kinematic modeling with static and motion parts

978-1-5225-5276-5.ch002.f01

Figure 1 shows a kinematic model of the manipulator under this study. The method presented in (Xi, 2009; Lin, Xi, Mohamed, & Tu, 2010) is used here for kinematic modeling. This method formulates the manipulator kinematics through two parts. The first is a static part to represent the initial configuration of each link and the second is a motion part to represent the movement of each joint. For the static part, a set of initial configuration set-up (ICSU) are defined including a static rotation matrix 978-1-5225-5276-5.ch002.m01 and a static body vector 978-1-5225-5276-5.ch002.m02, for each link, that is

978-1-5225-5276-5.ch002.m03
(1)
978-1-5225-5276-5.ch002.m04
(2) where 978-1-5225-5276-5.ch002.m05, 978-1-5225-5276-5.ch002.m06, 978-1-5225-5276-5.ch002.m07 are three rotation matrices about X, Y, and Z axis of local frame 978-1-5225-5276-5.ch002.m08 relative to local frame 978-1-5225-5276-5.ch002.m09, and 978-1-5225-5276-5.ch002.m10, 978-1-5225-5276-5.ch002.m11, 978-1-5225-5276-5.ch002.m12 are the three unit vectors of local frame 978-1-5225-5276-5.ch002.m13 attached to the 978-1-5225-5276-5.ch002.m14th joint. 978-1-5225-5276-5.ch002.m15 is a vector representing the 978-1-5225-5276-5.ch002.m16th link at the initial configuration. In this chapter, a bold vector is expressed with respect to the base frame, and a bold vector with an apostrophe is expressed with respect to a local frame.

The total translation 978-1-5225-5276-5.ch002.m17 and total rotation 978-1-5225-5276-5.ch002.m18 of the 978-1-5225-5276-5.ch002.m19th link is expressed by including the motion part as

978-1-5225-5276-5.ch002.m20
(3)
978-1-5225-5276-5.ch002.m21
(4) where 978-1-5225-5276-5.ch002.m22 and 978-1-5225-5276-5.ch002.m23 are the motional rotation matrix and motional body vector, respectively. In practice, 978-1-5225-5276-5.ch002.m24 corresponds to a rotational joint driven by a rotary motor and 978-1-5225-5276-5.ch002.m25 corresponds to a prismatic joint driven by a linear motor. In case of revolution joint, 978-1-5225-5276-5.ch002.m26 is equal to 978-1-5225-5276-5.ch002.m27, and 978-1-5225-5276-5.ch002.m28 is the rotation angle of the 978-1-5225-5276-5.ch002.m29th joint.

To this end, the end-effector’s position 978-1-5225-5276-5.ch002.m30 and orientation 978-1-5225-5276-5.ch002.m31, can be expressed with respect to the base frame of the mobile platform as

978-1-5225-5276-5.ch002.m32
(5)
978-1-5225-5276-5.ch002.m33
(6) where 978-1-5225-5276-5.ch002.m34 represents the rotation matrix of link 978-1-5225-5276-5.ch002.m35 with respect to the base frame, which is multiplied sequentially by a number of 978-1-5225-5276-5.ch002.m36. In eqn. (5), subscript 978-1-5225-5276-5.ch002.m37 indicates the tip of the last link where the end-effector is located, and the end-effector’s orientation coincides with the last link, expressed by 978-1-5225-5276-5.ch002.m38.

Taking the time derivative of eqn. (5) and (6) leads to the following forward recursive velocity equations

978-1-5225-5276-5.ch002.m39
(7)
978-1-5225-5276-5.ch002.m40
(8) where 978-1-5225-5276-5.ch002.m41 is the velocity vector at the 978-1-5225-5276-5.ch002.m42th joint and 978-1-5225-5276-5.ch002.m43 is the angular velocity vector of the 978-1-5225-5276-5.ch002.m44th link. Note that the following holds

978-1-5225-5276-5.ch002.m45
(9)
978-1-5225-5276-5.ch002.m46
(10)

Furthermore, taking the time derivative of eqn. (7) and (8) results in the following forward recursive acceleration equations

978-1-5225-5276-5.ch002.m47
(11)
978-1-5225-5276-5.ch002.m48
(12) where 978-1-5225-5276-5.ch002.m49 is the acceleration vector at the 978-1-5225-5276-5.ch002.m50th joint and 978-1-5225-5276-5.ch002.m51 is the angular acceleration vector of the 978-1-5225-5276-5.ch002.m52th link.

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