  We present object handling and transporting by a multi-robot team with a
deformable sheet as a carrier. Due to the deformability of the sheet and the
high dimension of the whole system, it is challenging to clearly describe all
the possible positions of the object on the sheet for a given formation of the
multi-robot system. A complete forward kinematics (FK) method is proposed for
object handling by an $N$-mobile robot team with a deformable sheet. Based on
the virtual variable cables model (VVCM), a constrained quadratic problem (CQP)
is formulated by combining the geometric constraints and minimum potential
energy conditions of the system. Analytical solutions to the CQP are presented
and then further verified with the force closure condition. We present an FK
algorithm based on the FK method to obtain all possible solutions with the
given initial sheet shape and the robot team formation. We demonstrate the
effectiveness, completeness, and efficiency of the FK algorithm with
experimental results and case study examples.
