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In this paper, we consider cooperative manipulation of a planar rigid body using multiple actuator agents— unilateral  thrusters, each attached to the body and each able to apply an unilateral force to the body. Generally, the dynamics of the body manipulated with uncoordinated forces of thrusters is nonlinear. The problem we consider is  how to design the unilateral force  each agent applies to ensure the decoupling and linearity of the linear and angular (i.e., translational and rotational) accelerations of the body and thus allow a controller to be designed in a simpler manner, instead of developing sophisticated nonlinear control techniques. Here consider two types of unilateral thrusters with (i) all fixed directions, and (ii) all non-fixed directions, respectively. To address the problem, we design two decomposition frameworks, each with its advantages, on the structure of the forces and control policy such that (i) the linear and angular accelerations of the body are decoupled and controlled independently, and (ii) the control that ensures the forces to be unilateral (only for thrusters with non-fixed directions) is independent from the linear and angular accelerations. As a result, the closed-loop dynamics of the body is linear with respect to both the linear and angular accelerations; thus the control of the body becomes trivial, which may provide a convenient and alternative methodology for design of a physical system with a quick estimation and reference of the manipulated forces required.

Decomposition frameworks for cooperative manipulation of a planar rigid body with multiple unilateral thrusters