Approximate Dynamic Programming for Platoon Coordination under Hours-of-Service Regulations

Abstract

Freight drivers of electric trucks need to design charging strategies for where and how long to recharge the truck in order to complete delivery missions on time. Moreover, the charging strategies should be aligned with drivers' driving and rest time regulations, known as hours-of-service (HoS) regulations. This letter studies optimal charging problems of electric trucks with delivery deadlines under HoS constraints. We assume that a collection of charging and rest stations are given along a pre-planned route with known detours and the problem data are deterministic. The goal is to minimize the total cost associated with the charging and rest decisions during the entire trip. This problem is formulated as a mixed integer program with bilinear constraints, resulting in a high computational load when applying exact solution approaches. To obtain real-time solutions, we develop a rollout-based approximate scheme, which scales linearly with the number of stations while offering solid performance guarantees. We perform simulation studies over the Swedish road network based on realistic truck data. The results show that our rollout-based approach provides near-optimal solutions to the problem in various conditions while cutting the computational time drastically.

Event-Triggered Distributed Model Predictive Control for Platoon Coordination at Hubs in a Transport System

“…In contrast, the computation of the planned charging time at the station requires consideration of various factors. We cast the charging problem addressed by the trucks as mixedinteger linear programs, which are modified in part from our previous work [8]. In what follows, we provide a brief account of the model for the charging problems faced by trucks, as well as the optimization problem upon receiving the anticipated waiting time at the present station.…”

“…In what follows, we provide a brief account of the model for the charging problems faced by trucks, as well as the optimization problem upon receiving the anticipated waiting time at the present station. For simplicity, constraints related to drowsy driving discussed in [8] are not considered here. However, they can be incorporated into the present framework without modification of any part discussed earlier.…”

“…However, they can be incorporated into the present framework without modification of any part discussed earlier. Interested readers are referred to [8] for further details.…”

“…Denote by {(b * ℓ , t * ℓ )} N ℓ=k the values that attain the minimum of the problem, then the anticipated charging time sending to S k is the product of b * k and t * k . In our previous work [8], we have developed a rolloutbased method for solving the charging problems approximately. It enables real-time solutions with cheap hardware at little loss of solution quality.…”

“…To date, there have been extensive works developing viable charging strategies. For instance, [7] and [8] investigated the optimal planning of charging stops for electric trucks, which also integrate with the mandatory rest schedules of drivers. Some other works, such as [9]- [11], transformed the optimal charging problem into the wellknown vehicle routing problem, where optimality can refer to consuming the least amount of energy, cost, or time.…”