Stability Analysis of Decentralized Motion and Force Control for Multiple Robots

When multiple robots collaboratively transport or manipulate a load, both motion and force need to be considered. This is especially true when the load is fragile or needs to be moved rapidly. Tight force coordination is possible if all robots share their force information and the grasp geometry is completely known. When this is not the case, a common approach is to use the leader/follower strategy, where the leader provides the position control for the load and other robots comply based on the individual contact force measurements. This paper considers an alternate decentralized motion and force control method, where all robots participate in the control of the load without sharing any position and force information. To demonstrate the stability of this scheme, we first consider decentralized motion control and centralized force control. We show that the decentralized motion control is semi-globally exponentially stable. The centralized force control does not affect the robot motion due to the move/squeeze decomposition. When the force control is decentralized, a perturbation term is added to the motion control loop. Because of robustness provided by the exponential stability, the closed loop system remains stable. In the case that the load starts from rest, both position and force errors converge to zero exponentially.