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This paper presents a coordinating and stabilizing control law for a group of underwater vehicles with unstable dynamics. The coordinating law is derived from a potential that only depends on the relative configuration of the underwater vehicles. Being coordinated,the group behaves like one mechanical system with symmetry,and we focus on stabilizing a family of coordinated motions,called relative equilibria. The stabilizing law is derived using energy shaping to stabilize the relative equilibria which involve each vehicle translating along its longest(unstable) axis without spinning,while maintaining a relative configuration within the group. The proposed control law is physically motivated and avoids the linearization or cancellation of nonlinearities.
This paper presents a coordinating and stabilizing control law for a group of underwater vehicles with unstable dynamics. The coordinating law is derived from a potential that only depends on the relative configuration of the underwater vehicles. Being coordinated, the group behaves like one mechanical system with symmetry, and we focus on stabilizing a family of coordinated motions, called relative equilibria. The stabilizing law is derived using energy shaping to stabilize the relative equilibria which involve each vehicle translating along its longest (unstable) axis without spinning, while maintaining a relative configuration within the group. The proposed control law is physically motivated and avoids the linearization or cancellation of nonlinearities.