In this paper, a distributed shell-space decomposition (DSSD) scheme is proposed for rendezvous trajectory planning of multiple autonomous marine vehicles (AMVs); this category of vehicle includes both autonomous underwater vehicles and autonomous surface vessels. The DSSD extends the concept of shell-space decomposition (SSD) by generating multiple sets of shells radiating out from the starting position of each vehicle to the rendezvous destination, enabling each vehicle to generate its trajectory within its own SSD subset. This scheme is combined with an optimized mass-center rendezvous-point selection scheme, together with a B-spline-based quantum particle swarm optimization technique to find optimal rendezvous trajectories for multiple AMVs with minimal travel time and simultaneous time of arrival for all the participating vehicles. The path planner identifies the optimal rendezvous location and generates the corresponding rendezvous trajectories based on the capabilities of each vehicle and the dynamics of the ocean environment. Simulation results show that the proposed DSSD method, combined with a novel optimized mass-center rendezvous-point selection scheme, is able to find trajectories for multiple AMVs that ensure that they reach their common destination simultaneously and with optimized time/energy consumption. A set of representative Monte Carlo simulations were run to analyze the performance of these path planners for multiple AMVs rendezvous. The results demonstrate the inherent robustness and superiority of the proposed planner based on the combined DSSD method and optimized mass-center rendezvous-point selection scheme, in comparison with other techniques.

In this paper, a control method that combines linear and nonlinear-velocity feedback control is proposed to suppress the principal parametric resonance in a flexible cantilever beam structure. Linear-velocity feedback is employed for bifurcation control, and cubic-velocity feedback is employed to suppress high-amplitude vibration. A unified bifurcation parameter 2 that includes both the excitation frequency and amplitude is defined for the stability analysis, so that bifurcations under quasi-stationary frequency-response and quasi-stationary force-response can be treated uniformly when 2 is quasi-statically varied. This unified bifurcation parameter simplifies the system stability analysis as well as the controller design procedure. Numerical simulation and experimental results show that the combined bifurcation control and nonlinear feedback control strategy performs better than linear-velocity or cubic-velocity feedback control alone, and is less susceptible to actuator saturation.