Pose control of multi‐rigid‐body systems with distance‐dependent topologies

Abstract

Abstract This paper investigates the pose control problem of multi‐rigid‐body systems, where the distance‐dependent graphs are adopted to describe the interaction relations between rigid bodies. The authors design distributed control laws for torque and force of rigid bodies, with back‐stepping technique and potential function method being utilized. An admissible set for initial states of rigid bodies is presented, on which the theoretical results about attitude synchronization, collision avoidance and connectivity maintenance are established without relying on the prior connectivity assumption of the dynamical neighbour graphs. The authors introduce the initial neighbourhoods or the neighbourhoods corresponding to a minimum spanning tree extracted from the initial neighbour graph into the controller, to reduce the communication pressure on system and the constraints on motion of rigid bodies. Furthermore, a leader is introduced into the system to guide all rigid bodies to a desired attitude. Simulation examples are given to verify the theoretical results.

Keywords

• Spatial variables control
• Combinatorial mathematics
• Control system analysis and synthesis methods
• Multivariable control systems