tailieunhanh - Multi-Robot Systems Trends and Development 2010 Part 9

Tham khảo tài liệu 'multi-robot systems trends and development 2010 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 312 Multi-Robot Systems Trends and Development a b Fig. 5. Examples of undesired effects a robots swapping red move 1 0 0 AT green move -1 0 0 AT b robot passing through the wall red move 2 0 0 AT To be consistent with the Shannon s Theorem it is sufficient to apply a sampling of the time at a twice frequency . the timeline must have a time unit half of the other timelines. In particular the twice sampling has to be applied in the space where the collisions are detected the Coordination Space. This guarantees an adequate representation of all the obstacles along the time static . walls and dynamical . other robots opening doors etc. . This assumption also ensures to avoid the problem of Fig. 5 of robots tunneling the walls or other robot through. Fig. 6. The Motion Silhouette for the translational move 2 0 0 AT 313 Time-Invariant Motion Planner in Discretized C-Spacetime for MRS Robot discrete kinematics the spatiotemporal discrete move To define properly the behavior of a robot in a discretized world is mandatory to define accurately its kinematics. A discretized kinematics is a set of atomic moves defined on the base of single moves along the coordinate axes. In a discretized spatiotemporal space Z4 for a robot moving on a 2D manifold the definition of spatiotemporal move is the 4-tuple Ax Ay A0 At where A is a finite variation Ax Ay e Z2 A0 e S1 At e Z and with the obvious constraint At 0 an example in Fig. 8 . This definition has two main interpretations Ax Ay A0 are finite increments of the spatial coordinates during the finite time interval At. It entails the following space metrics As move U- yAe As2 Ax2 Ay2 r2 -AỚ2 At Ax Ay A0 At are finite increments of the spatiotemporal coordinates inducing the following metrics move Ax Ay AỚ At AS2 Ax2 Ay2 r2 AỚ2 vr2 At2 As2 vr2 At2 Where AS is the distance between two events of the spacetime r is a dimensional constant vTis the speed of spontaneous translation along the time axis. It is easier to see it if