Tham khảo tài liệu 'mobile robots -towards new applications 2008 part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A Novel Autonomous Climbing Robot for Cleaning an Elliptic Half-shell 591 5. Climbing dynamics Kinematics analysis The robot autonomously climbs and cleans the elliptic surface. From the safety point of view the process of climbing from one strip to another is very dangerous because the robot has to adapt to the shape of the building. Additionally this robot has to be quite large in order to realize all necessary functions. Therefore in designing the mechanism of this system and its controls an equilibrium between safety and size has to be reached. In this section the climbing dynamics of the robot are calculated based on the Lagrange formulation. We only discuss the process of ascending because the process of descending is similar. There are two phases during the process of ascending. First the auxiliary frame moves along the main frame then the main frame ascends. The first part is very safe due to the clutches holding the sliding-rod and the abdominal plate inserted into two sets of sliding-rods. We will only discuss the second part in detail. The climbing dynamics of the robot are analyzed by the application of the Lagrange equation described as 1 Fu . et al. 1987 . 4 U- L F j 1 2 3 1 dt dq dq j J Where Fj is the generalized forces L is the Lagrange function as shown in 2 . L T - V 2 Where T is the kinetic energy of the system and V is the potential energy. We can change 1 into the following format 3 . M q q C q q q N q q F 3 Where F is the generalized driving force q is the generalized coordinate C q q q described with 4 is decided by the factors of the Coriolis force and the centrifugal force N q q is decided by the nonconservative and conservative forces. Furthermore it can be described as 5 when the friction is neglected. r. Iv1 ỈdMij . dMik dMkj Ị . Cq q q -y 1 J ik -Hi- q 2 i Fk ikij ik i J dV Ni q q ỳýý-dq i 4 5 The kinematics model of the robot during climbing is shown in Figure 18. Where oxyz is the world coordinate and the xoy plane is .