Coordination control of underactuated ODINs in three-dimensional space

• Coordination controllers for ODINs in 3D space are designed.
• Both Euler angles and unit-quaternion are used for attitude representation.
• New disturbance observers and pairwise collision avoidance functions are proposed.
• Tracking errors asymptotically converge to zero.
• There is no collision between ODINs.

A constructive design of distributed coordination controllers for a group of NN underactuated omni-directional intelligent navigators (ODINs) in three-dimensional space under the environmental disturbances induced by ocean currents is presented. To make the control design effective and avoid singularities in the ODIN’s dynamics, a combination of Euler angles and unit-quaternion is used for the attitude representation of the vehicle. The coordination control design is based on an exponential disturbance observer, a non-zero convergent result for a first-order differential inequality, and new pairwise collision avoidance functions. The pairwise collision functions are functions of both relative positions and relative velocities between the ODINs instead of only their relative positions as in the literature. To overcome the inherent underactuation of the ODIN, the roll and pitch angles of the ODIN are considered as immediate controls. Simulations illustrate the results.