tailieunhanh - Climbing and Walking Robots part 17

Tham khảo tài liệu 'climbing and walking robots part 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The Rh-1 full-size humanoid robot Control system design and Walking pattern generation 473 The footprints Fig. 27 for doing an n-th step can be computed as follows pn pn R 0 T .Ln 46 Where T P ÍÍ py p L L - -WL L. T n n-1 n 1 p p p World and feet frames pn pn 1 pn l feet position T-n 1 j-n 1 j-n 1 L Ly Lz swing foot displacements Ỡ n 1 oy x 0 rotations about world frame The walking patterns developed are introduced into the inverse kinematics algorithm Arbulu et al. 2005 to obtain the angular evolution of each joint those are the reference patterns of the humanoid robot. Goal swing foot configuration Fig. 27. Footprint location. 474 Climbing and Walking Robots Inverse Kinematics model In order to compute the robot s joint motion patterns some kinematics considerations must be made. Due to the fact that the kinematics control is based on screw theory and Lie logic techniques it is also necessary to present a basic explanation. Lie logic background Lie groups are very important for mathematical analysis and geometry because they serve to describe the symmetry of analytical structures Park et. al. 1985 . A Lie group is an analytical manifold that is also a group. A Lie algebra is a vectorial space over a field that completely captures the structure of the corresponding Lie group. The homogeneous representation of a rigid motion belongs to the special Euclidean Lie group SE 3 Abraham et. al. 1999 . The Lie algebra of SE 3 denoted se 3 can be identified with the matrices called twists ế eq. 47 where the skew symmetric matrix eq. 48 is the Lie algebra so 3 of the orthogonal special Lie group SO 3 which represents all rotations in the three-dimensional space. A twist can be geometrically interpreted using screw theory Paden 1986 as Charles s theorem proved that any rigid body motion could be produced by a translation along a line followed by a rotation around the same line this is a screw motion and the infinitesimal version of a screw motion is a twist. ế w V 0 0 0

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