TAILIEUCHUNG - Complex Robotic Systems - Pasquale Chiacchio & Stefano Chiaverini (Eds) Part 2

Tham khảo tài liệu 'complex robotic systems - pasquale chiacchio & stefano chiaverini (eds) part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Derivation of task vectors 7 vector for a task of carrying an object in the workspace for example. For more complicated tasks that include constrained motion it has to be defined not only as position orientation of the object but also as forces moments acting on the object. In this section we derive task vectors to describe a task performed by the multi-arm robot. The constraint forces moments fi are those applied to the object by the arm i and are obtained from Equation when the joint torques or forces Ti are given. Since fị is 6-dimensional the forces moments applied to the object by the two arms are altogether 12-dimensional six of which are for driving the object and the rest of which do not contribute to the motion of the object but yield internal forces moments on the object. Noting this intuition we derive the task vector for the cooperative two arms 12 13 24 . External and internal forces moments First the external forces moments on the object are defined as those to drive the object. That is fa f 1 f 2 I6 I6 fĩ fĩ T wx 1-12 where w is a 6 X 12 matrix with range of 6-dimension and null space of 6-dimension. In is the unit matrix of n-dimension. This relation is shown in Figure a . A solution for A when fa is given is A w fa I12 - w w z w fa l6 -I6 Tfr W fa Vfr where w is the Moore-Penrose inverse of w given by z is an arbitrary vector of 12-dimension. The second term of the right hand side of Equation represents the null space of w and V represents its bases by which the vector fr is represented. The relation is shown in Figure b . It is apparent when viewing V that fr represents forces moments being applied by the two arms in opposite directions. 8 Chapter 1. Multi-arm robot systems A survey a External forces moments Figure External and internal forces moments. We call the forces moments represented by fr internal forces moments. Solving Equation for fa and fr we have fa fl Ỉ2 fr j fr-f2 - 1-15 1-16 External

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