Trajectory design for formations of robots by kinetic energyshaping
Belta, C.; Kumar, V.
Robotics and Automation, 2002. Proceedings. ICRA apos;02. IEEE International Conference on
Volume 3, Issue , 2002 Page(s):2593 - 2598
Digital Object Identifier 10.1109/ROBOT.2002.1013622
Summary:We develop a method for generating smooth trajectories for a set
of mobile robots. Given two end configurations, by tuning one parameter,
the user can choose an interpolating trajectory from a continuum of
curves varying from that corresponding to maintaining a rigid formation
to motion of the robots toward each other The idea behind our method is
to change the original constant kinetic energy metric in the
configuration space and can be summarized into three steps. First, the
energy of the motion as a rigid structure is decoupled from the energy
of motion along directions that violate the rigid constraints. Next, the
metric is "shaped" by assigning different weights to each term. Finally,
geodesic flow is constructed for the modified metric. The optimal
motions generated on the manifolds of rigid body displacements in 3D
space or in plane, and the uniform rectilinear motion of each robot
corresponding to a totally uncorrelated approach are particular cases of
our general treatment
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