Elsevier

Applied Soft Computing

Volume 13, Issue 1, January 2013, Pages 247-258
Applied Soft Computing

Effect of a risk factor in convoy merging manoeuvres considering uncertainty in travelling times

https://doi.org/10.1016/j.asoc.2012.08.011Get rights and content

Abstract

Cooperative guiding, and especially in convoys, for automated, non-contaminating transport units is a line of research for sustainable urban transport. In this paper we propose a strategy for facilitating the merging manoeuvre between independent units travelling in a transport scenario (usually a city) and a convoy following a pre-defined peripheral trajectory in the same scenario. The proposal consists of an inexpensive computational cost algorithm, which is able to calculate the optimal merging point and the efficient route to reach it. An optimal merging node is the one on the periphery which minimises the merging time. In addition to the complexity of the problem is the uncertainty associated to travelling times, as is habitual in a real urban setting. Sources of uncertainty include weather conditions, the effect of the zone (proximity to centres of social services or cultural interest), the day and time on traffic density, etc. All this justifies the variability in the time taken by any vehicle moving along a section in the transport scenario.

In order to delimit the randomness inherent to the problem, the authors incorporate a novel “risk factor” parameter, which conditions the solution. This risk factor limits the probability of a convoy reaching the merging node before the pursuer (failed merging manoeuvre).

The possibility of having the travelling experiences from any unit moving in the transport scenario means that the statistics (mean and variance) associated to the expected travelling times can be updated dynamically. This task is executed in a remote centre which communicates with all the units in the transport scenario. This dynamic updating means that the objectives (optimal merging node and efficient routing) can be re-evaluated, and makes it possible to adapt to the changing conditions of the transport scenario, each time the pursuing unit reaches an intermediate node.

In order to validate the algorithm described in this paper and evaluate the effect of the aforementioned novel risk factor, we have tested them on a simulated transport scenario using Player/Stage. The results and conclusions are also shown.

Highlight

► Solving of a dynamic routing problem in an urban scenario in which there are transport units trying to join a constantly moving convoy. ► The uncertainty inherent to the travelling times of all the transport units moving in the urban scenario is considered (Gaussian model). ► A risk factor is used to limit the probability of unsuccessful manoeuvres due to the stochastic nature of the problem. ► All the transport units are wirelessly connected to a remote centre which runs the routing algorithms and updates the statistic parameters. ► The routing algorithms and the impact of the risk factor are experimentally validated using the Player&Stage simulation software.

Introduction

The countless hours lost in traffic jams have become so common, especially in large cities that they have ceased to be newsworthy. Safety and respect for the environment are other aspects which promote the search for new solutions, thus facilitating mobility within cities, enhancing both competitiveness and convenience [1]. There are special settings in which environmental, safety and traffic congestion reasons may come to restrict or even prohibit conventional traffic. Cases in point are historical town centres (e.g. UNESCO's World Heritage Cities), theme parks, university campuses, etc. For these settings, transport solutions have been proposed based on electrical units travelling independently and/or in convoys [2], [3], [4], [5]. Basically, we can picture a group of electric vehicles moving in a coordinated way along a specific route (convoy formation), so that when an individual unit is required, it would leave the convoy to collect passengers, would drive them to a specific destination and, once the mission is finished, would return to the convoy as quickly as possible. Nevertheless, the return of the transport unit to the convoy (merging manoeuvre) is very challenging since the convoy is moving continuously. Even when the map of the environment is known beforehand, the problem is still doubly complex. On one hand, when the pursuer decides to carry out the manoeuvre, the convoy is in constant movement; on the other hand, there are sources of uncertainty which make difficult the evaluation of the time needed to travel along different sections in the transport scenario. Sources of uncertainty include all those that determine the traffic intensity at a certain point at a given moment in time, such as the weather conditions, the type of road and the speed limit thereof, whether it is a working day or a public holiday, proximity to public centres (education, healthcare, administration, etc.) and the state of the vehicle itself (load level, maintenance, etc.), to name but a few. The amassing of experiences by the various units driving round the scenario will contribute to the modelling of uncertainty and error minimisation in decision-making. Therefore, in this paper we will describe a routing strategy that is able to find the appropriate merging point amongst a convoy that is constantly moving and a transport unit that desires to return to it. On the other hand, this routing strategy will need to be able to cope with the uncertainty inherent to the travelling times along the streets of the city, and even evaluate the risk of the solution achieved.

Classic search algorithms are based on graphs for finding the optimal route between and initial position and a destination, both of which are static and known. These proposals are extremely precise, but they entail excessive convergence times when conducting the search, hampering their real-time application. Worthy of note among the classic routing algorithms are Dijkstra [6], [7], [8], A* [9], [10], [11], [12], [13], RTA* [14], LRTA* [15], LPA* [16] and D* Lite [17], [18]. Only a small number of proposals, such as MTS [19], tackle the case of routing towards a known but non-static destination, for which on-line adaptation algorithms are proposed. Following this last proposal, the pursuing vehicle is able to react to the changes in the destination point, and it will be able to reach it provided that these changes have a lower speed than the speed of the pursuer.

The numerous studies on route re-planning in the presence of obstacles [20], or searching for less congested alternatives [21], [22], or the well known travelling salesman problem [23], [24], are not considered in the present paper.

Among those studies dealing with uncertainty in travelling times, worthy of special mention is that by Ambrose et al. [25], who describe a routing solution derived from A*, between known points in the city of Virginia (USA), taking into account the mean travelling values of each section and their variances – statistics which contemplate a 24 h log –. The resulting application provides users with information on the likely time of and variance in the different alternative routes, so that users themselves can decide on the most suitable one. In the study by Lecluyse et al. [26], the stochastic behaviour (mean value and variance) of the travelling time in a setting is modelled on the basis of rush hours and environmental conditions, so that the expected value and the risk associated to the variance in the recorded times distribution is considered.

The remainder of the paper is structured as follows: In Section 2, the problem to be solved is presented, along with the intervening elements. Section 3 presents the routing strategy proposed by the authors for executing the merging manoeuvre. Section 4 shows the experimental validation thereof. Section 5 includes the conclusions of the paper. There are also three appendices, which provide further details concerning the algorithms described in the rest of the paper: Estimation of times between consecutive and non-consecutive nodes, Calculation of the optimal merging node, and Efficient routing.

Section snippets

Problem setup

As it was mentioned in the introduction, in this paper we want to describe the solution we propose for a complex routing problem amongst a convoy of vehicles constantly moving and a transport unit which is trying to merge with the convoy. The basic approach is that of a vehicle, located at a fixed point on the map of the transport setting, whose objective is to merge with a convoy of vehicles travelling around a peripheral circuit. By way of example, Fig. 1 shows part of the historical quarter

Merging manoeuvre routing strategy

The solution proposed by the authors is based on three key aspects, already shown in Fig. 2, and explained in Fig. 3:

  • Recording of the real travelling times required by the units when moving along the different sections of the map.

  • Calculation of statistics (mean and variance) for the travelling times. Application of dynamic programming for estimating times between non-consecutive nodes.

  • Execution of algorithms in the pursuing unit, in order to obtain the optimal merging node and the efficient

Experimental validation

This section is devoted to verify the validity of the proposal presented in this paper. To this end, we designed a topological map and we considered two study cases. In both the analysis, the initial locations of the convoy and of the pursuing unit were the same, but the risk factor assumed for the linking manoeuvre was different.

The software used to simulate the movement of the convoy leader and pursuing units in a city and thus evaluate the goodness of the present work, was Player&Stage. The

Conclusions

This work has been conducted in the context of strategies for facilitating the merging manoeuvre of a pursuing unit with a convoy. The convoy of vehicles is assumed to be moving continuously along the periphery of a transport scenario, while the pursuing unit is located inside this scenario.

The principal contribution of the paper is to analyse the effect of a novel risk factor that we have included in the calculation of the optimal meeting node and of the most efficient route to be followed by

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