A riemannian-geometry approach for dynamics and control of object manipulation under constraints

A Riemannian-geometry approach for control and stabilization of dynamics of object manipulation under holonomic or non-holonomic (but Pfaffian) constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a nonholonomic constraint is reinterpreted in terms of "submersion" in Riemannian geometry. A force control signal constructed in the image space spanned from the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability on a manifold for a redundant system under holonomic constraints is discussed. Second, control and stabilization of dynamics of two-dimensional object grasping and manipulation by using a pair of multi-joint robot fingers are tackled, when a rigid object is given with arbitrary shape. Then, it is shown that rolling contact constraint induce the Euler equation of motion...

• Type: Journal
• Year: 2009
• Where: ICRA
• Authors: Suguru Arimoto, Morio Yoshida, Masahiro Sekimoto, Kenji Tahara
• Keywords: Degrees-of-freedom Redundancy Problem, Grasping, ICRA 2009, Multi-joint Robot Fingers, Robotics