Convergence and Collision Avoidance in Formation Control: A Survey of the Artificial Potential Functions Approach

Hybrid Architecture for Coordination of AGVs in FMS

“…Thus, at a low level some motion control laws must be designed to achieve formations and to follow prescribed trajectories in the FMS. A brief introduction about the standard formation and marching control [30] is presented in the next subsection.…”

“…Assume that N � � �α � �, N � � �α � �, N � � �α � �, i.e., the robots communicate to form a cyclic pursuit configuration [30], and they need to achieve a triangle-shaped formation pattern given by c �� � �0,11�, c �� � �5.5, �5.5�, c �� � ��5.5, �5.5�. In Figure 12, for 0 � � � �50, three robots are moved from their given home positions to the position of RM �� in the triangle formation using the formation control law with collision avoidance (8).…”

“…Note that in the closed-loop system ( 5)-( 6), the dynamics of are reduced to α� � � f � , and the behaviour of the front point is similar to the case of a simple point robot moving in the plane, cancelling all the non-linearities of the original kinematic model. Note that the control law (6) does not influence directly the orientation angles θ � , but these could converge, as mentioned in [30]. The main objective of the control law is to design the functions f � to achieve (1) formation, (2) convergence to a point, and (3) marching behaviour, avoiding inter-robot collisions in the three cases.…”