This paper proposes a nonlinear robust adaptive control strategy to force a six degrees of freedom underactuated underwater vehicle with only four actuators to follow a predefined path at a desired speed despite of the presence of environmental disturbances and vehicle's unknown physical parameters. The proposed controller is designed using Lyapunov's Direct Method, the popular backstepping and parameter projection techniques. The closed-loop path following error can be made arbitrarily small. Numerical simulations are provided to illustrate the effectiveness of the proposed methodology for path following of underactuated underwater vehicles.
This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation. The controllers guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on an algebraic separation condition between ellipses, Lyapunov's method, and smooth or p-times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need of switchings under the agents' limited sensing ranges.
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