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This paper uses Pontryagin methods to analyze pulse-and-glide driving for different nominal vehicle speeds. There is significant literature supporting the fact that pulse-and-glide has the potential to reduce fuel consumption compared to driving at a constant speed, but the benefits at a variety of nominal speeds remain relatively unexplored. Building on the literature, we formulate a speed trajectory optimization problem where the objective is a linearly-scalarized Pareto combination of fuel consumption and average vehicle speed, in addition to a quadratic penalty on jerk. By analyzing this optimization problem using Pontryagin methods, we show that (i) for each nominal speed, there is a critical penalty on jerk below which the optimal solution is pulse-and-glide, (ii) without any penalty on jerk, the optimal pulse-and-glide trajectory switches infinitely fast, and (iii) above a critical nominal velocity, the optimal solution is steady-speed driving rather than pulse-and-glide, regardless of the penalty on jerk.

This paper addresses the problem of trajectory optimization for an unmanned surface vehicle while considering direction-dependent ocean currents and flexible refueling constraints. This work is motivated by the rising interest in developing autonomous navigation technology for commercial, scientific, and military applications for ocean-bound unmanned surface vehicles. Relevant literature on such vehicles has addressed energy-efficient trajectory optimization and time-efficient trajectory optimization. However, the application of trajectory optimization techniques which include refueling stops and multi-objective optimization remains relatively unexplored. We address this open challenge by formulating the trajectory design problem as a nonconvex mixed-integer optimization program with a multi-objective cost function. Then, we apply dynamic programming to solve this optimization program for fuel and time optimal trajectories. We synthesize these results into a series of Pareto fronts which demonstrates the tradeoff between fuel consumption and trip time for a prototypical route with direction-dependent ocean currents. Furthermore, the optimal trajectories for which we solve illustrate the changes in the vehicle's behavior as the fuel level becomes low, and as the vehicle encounters counterproductive ocean currents. Our results indicate several meaningful insights about the overall trajectory optimization process., Comment: 6 pages