  Battery-hybrid power source architectures can reduce fuel consumption and
emissions for ships with diverse operation profiles. However, conventional
control strategies may fail to improve performance if the future operation
profile is unknown to the controller. This paper proposes a guidance,
navigation, and control (GNC) function that integrates trajectory generation
and hybrid power source supervisory control. We focus on time and fuel optimal
path-constrained trajectory planning. This problem is a nonlinear and nonconvex
optimal control problem, which means that it is not readily amenable to
efficient and reliable solution onboard. We propose a nonlinear change of
variables and constraint relaxations that transform the nonconvex planning
problem into a convex optimal control problem. The nonconvex
three-degree-of-freedom dynamics, hydrodynamic forces, fixed pitch propeller,
battery, and general energy converter (e.g., fuel cell or generating set)
dissipation constraints are expressed in convex functional form. A condition
derived from Pontryagin's Minimum Principle guarantees that, when satisfied,
the solution of the relaxed problem provides the solution to the original
problem. The validity and effectiveness of this approach are numerically
illustrated for a battery-hybrid vessel in model scale. First, the convex
hydrodynamic hull and rudder force models are validated with towing tank test
data. Second, optimal trajectories and supervisory control schemes are
evaluated under varying mission requirements. The convexification scheme in
this work lays the path for the employment of mature, computationally robust
convex optimization methods and creates a novel possibility for real-time
optimization onboard future smart and unmanned surface vehicles.
