Online Utility-Optimal Trajectory Design for Time-Varying Ocean Environments

This paper considers the problem of online optimal trajectory design under time-varying environments. Of particular interest is the design of energy-efficient trajectories under strong and uncertain disturbances in ocean environments and time-varying goal location. We formulate the problem within the constrained online convex optimization formalism, and a modified online gradient descent algorithm is motivated. The mobility constraints are met using a carefully chosen step-size, and the proposed algorithm is shown to incur sublinear regret. Different from the state-of-the-art algorithms that entail planning and re-planning the full trajectory using forecast data at each time instant, the proposed algorithm is entirely online and relies mostly on the current ocean velocity measurements at the vehicle locations. The trade-off between excess delay incurred in reaching the goal and the overall energy consumption is examined via numerical tests carried out on real data obtained from the regional ocean modelling system. As compared to the state-of-the-art algorithms, the proposed algorithm is not only energy-efficient but also several orders of magnitude computationally efficient.