Tham khảo tài liệu 'mobile robots - moving intelligence part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Dynamics and Control for Nonholonomic Mobile Modular Manipulators 31 2. An Integrated Modelling Method Kinematics analysis A mobile modular manipulator is normally composed of an m-wheeled holonomic or nonholonomic mobile platform and an n-DOF onboard modular manipulator as shown in Fig. 1 a . In this chapter we analyze the 3-wheeled nonholonomic mobile platform which has two driving wheels and one castor wheel. The two driving wheels are coaxial and mounted in front of the platform and the castor wheel in the rear is orientable with respect to the cart. The robot is assumed to move on a horizontal plane then the motion of the mobile platform can be illustrated as shown in Fig. 1 b . An arbitrary inertial base frame ObXbYbZb is fixed on the motion plane while a frame OmXmYmZm is attached to the mobile platform. In frame O X Y Z O x y is selected as the midpoint of the line segment connecting the two driving-wheel centres OmYm is along the coaxial of the two driving wheels OX is perpendicular to OmYm and passes through O . The heading angle Ộ determines the posture of the mobile platform. a Prototype b coordinate system definition Fig. 1. Prototype and coordinate system definition for a mobile modular manipulator. 32 Mobile Robots moving intelligence Since the modular manipulator is mounted on the mobile platform it can be assumed that the relative position of frame O X Y Z and the frame O0X0Y0Z0 is steady here O0X0Y0Z0 is the frame attached to the 1st module of the modular manipulator. Therefore the mobile platform can be treated as a special module added to the bottom of the modular manipulator which can both move on the motion plane and rotate about the vertical axis. From Fig. 1 b transformation matrices between the frames OBXBYBZB O X Y Z and OữXữYữZữ are given by cos ẻ - sin ẻ 0 x r 1 0 0 m m m G Bt sin K cos ộ 0 ym mT 0T 0 1 0 0 1 m 0 0 1 rf 0 0 1 ha 0 0 0 1 _ 0 0 0 1 _ where r is the radius for the driving wheels lG and hG denote offsets of the 1st .