Quaternion-based attitude synchronisation for multiple rigid bodies in the presence of actuator saturation

This paper concentrates on the quaternion-based attitude synchronisation problems of networked rigid bodies under fixed and undirected communication topology without relative angular measurements in the presence of actuator saturation. We first consider the leaderless attitude synchronisation problem with zero final angular velocity. In this case, we not only discuss the performance under the acyclic communication topology with the proposed bounded control algorithm, but also analyse that if there exist cycles in the topology, the proposed bounded algorithm guarantees that all equilibrium points are unstable except that the attitudes of networked rigid bodies achieve synchronisation. We also expand the result to the case of attitude tracking synchronisation with a static leader in the presence of actuator saturation. Next, the tracking synchronisation problem with the desired time-varying attitude is addressed in the presence of actuator saturation. Numerical examples are provided to validate the effectiveness of the proposed bounded schemes and illustrate the performances of multiple rigid bodies.