Optimal Speed Trajectories Under Variations in the Driving Corridor

Abstract

The optimal speed trajectory for a heavy-duty truck is calculated using the Pontryagin's maximum principle. The truck motion depends on controllable tractive and braking forces and external forces such as air and rolling resistance and road slope. The velocity of the vehicle is restricted to be within a driving corridor which consists of an upper and a lower boundary. Simulations are performed on data from a test cycle commonly used for testing distribution driving. The data include road slope and a speed reference, from which the driving corridor is created automatically. The simulations include a sensitivity analysis on how changes in the parameters for the driving corridor influence the energy consumption and trip time.For the widest driving corridor tested, 15.8 % energy was saved compared to the most narrow corridor without increasing the trip time. Most energy was saved by reducing the losses due to braking and small amounts of energy were saved by reducing the losses due to air resistance. Finally, optimal trajectories with the same trip time derived from different settings on the driving corridor are compared in order to analyse energy efficient driving patterns.

Optimal powertrain control of a heavy-duty vehicle under varying speed requirements

“…The same problem as in [9] is treated, but with more thorough simulations in order to investigate how variations in the driving corridor influence the energy consumption and trip time. The work in this paper extends [9] and [11] by including powertrain components such as an engine and a gearbox in the vehicle model. This is a step towards more implementable solutions, since the tractive force is replaced by the injected fuel and the gear selection is added as a control signal.…”

“…For any velocity of the truck, the set of feasible gears is thus given by the gears satisfying (11).…”

“…The velocity is at all positions bounded by the driving corridor such that v l,k ≤ v k ≤ v u,k , where v l and v u are the lower and upper bound of the driving corridor. As discussed in [11], the driving corridor is created from a reference speed trajectory v r and from real truck operation data. The main idea of using traffic data is to restrict the truck to decelerate in a way that does not deviate too much from a normal way of driving.…”

“…The transition cost from one stage to the next is denoted by ζ k (x k , u k ). The algorithm becomes: 1) At the last stage N of the driving mission, the velocity v N is fixed while the gear g N is only restricted by the requirements for the engine speed (11). The optimal costto-go is equal to zero for all feasible states at this stage.…”

“…The same principle is used in [10], where gear changes are also considered. In [11], the concept of a driving corridor is used, i.e., an upper and a lower limit that the velocity of the vehicle must lie within. The same problem as in [9] is treated, but with more thorough simulations in order to investigate how variations in the driving corridor influence the energy consumption and trip time.…”