  This paper considers the simultaneous position and orientation planning of
nonholonomic multirobot systems. Different from common researches which only
focus on final position constraints, we model the nonholonomic mobile robot as
a rigid body and introduce the orientation as well as position constraints for
the robot's final states. In other words, robots should not only reach the
specified positions, but also point to the desired orientations simultaneously.
The challenge of this problem lies in the underactuation of full-state motion
planning, since three states need to be planned by mere two control inputs. To
this end, we propose a dynamic vector field (DVF) based on the rigid body
modeling. Specifically, the dynamics of the robot orientation are brought into
the vector field, implying that the vector field is not static on the 2-D plane
anymore, but a dynamic one varying with the attitude angle. Hence, each robot
can move along the integral curve of the DVF to arrive at the desired position,
and in the meantime, the attitude angle can converge to the specified value
following the orientation dynamics. Subsequently, by designing a circular
vector field under the framework of the DVF, we further study the obstacle
avoidance and mutual-robot-collision avoidance in the motion planning. Finally,
numerical simulation examples are provided to verify the effectiveness of the
proposed methodology.
