1. Introduction
In the last years, sea protection and monitoring have been central topics for the underwater community. However, because of the difficulties and risks involved in underwater missions, most part of the marine environment still remains unexplored. Thanks to recent developments in technology and automation,
Autonomous Underwater Vehicles (AUVs) can now play a key role in underwater exploration. Indeed, AUVs represent effective tools for very different purposes, such as glacier inspection [
1], monitoring of marine habitats [
2] and climate changes effects [
3], and for seafloor mapping [
4]. In particular, the exploitation of AUVs for monitoring purposes makes data collection faster and certainly safer [
5].
Traditionally, in
Information Gathering (IG) operations, where underwater exploration entails environmental data collection, AUVs follow predefined geometric routes, typically with lawnmower patterns. However, this approach is not efficient as the AUV moves along a path which can lead to areas of low interest, wasting time and energy. On the contrary, optimal path planning algorithms generate paths that optimise an objective function representing specific criteria, such as energy consumption, survey duration or distance travelled [
6]. Moreover, by benefiting from the measurements coming from the sensors on-board the vehicle, the planner can employ online replanning strategies to avoid collisions with potential obstacles along the way. Among the various optimal planning strategies,
Informative Path Planning (IPP) focuses on increasing the knowledge about environmental variables of interest while respecting some constraints on the robot and path features [
7].
A model of the environmental variable of interest, based on the
a priori knowledge about the area to be inspected, is crucial to achieve efficient informative paths and a successful completion of missions. An efficient way for modelling the environment is applying a
Gaussian Process (GP) [
8]. GPs are powerful nonparametric techniques that can handle a large variety of problems, having the ability to learn spatial correlation with noisy measured data [
9]. The key feature of GPs for IG scenarios is their capability to handle both data uncertainty and data incompleteness effectively. Thus, they allow to perform dense estimation of environmental variables for coverage-based exploration purposes, giving a clear idea of which are the places that need to be inspected to reduce model uncertainty. However, the weakness of these techniques is related to their high computational time. Some works overcome this issue by proposing the use of a sparse version of the GP [
10,
11], or local maps fusion using Bayesian Committee Machine (BCM) [
12], to reduce computational costs and enable online execution.
The estimate of the variable of interest provided by the GP, in terms of mean and covariance, can be exploited to quantitatively describe the informativeness associated with each position within the target area, using the so called information function. In particular, higher values on the covariance map indicate points where the GP estimates are more uncertain and, thus, more informative: collecting data in those areas means reducing the uncertainty of the model, and thus increasing knowledge about the environmental variable of interest. While the authors of [
13] propose the use of an interpolated version of the GP model predicted variance, most of the methods use either
Differential Entropy (DE) or
Mutual Information (MI) as information function. Using DE results in lower computation time and higher uncertainty reduction than using MI, when computed from GP predictions of stationary setups [
14]. Despite the submodularity property of MI [
15], the computational time of such information function results prohibitive in many applications.
The IPP approaches used for IG purposes can be categorised into two groups: myopic and non-myopic. Myopic strategies only plan one step forward and they work following greedy heuristics [
16]. Conversely, non-myopic strategies look several steps ahead, providing paths that may result better on the long run, and are usually based on graphs [
10,
17,
18], random trees [
14,
19,
20,
21,
22], or evolutionary algorithms [
23,
24,
25]. In the framework of non-myopic strategies, a Rapidly-exploring Information Gathering (RIG) tree [
20] approach was presented by Hollinger et al. in 2014, where the vertices in RIG-tree represent a tuple of location, cost, and information. In 2019, Viseras et al. improved the RIG approach in [
14], proposing a two-stage planning process. In the first step, the planner finds the target position providing the highest information spot under a budget constraint through Rapidly-exploring Random Tree (RRT) [
26]. In the second step, it provides an optimised path to the goal. Among the category of the evolutionary algorithms are the
Genetic Algorithms (GA), which are commonly employed in classical cost-optimisation planning. GA are inspired by genetics and survival concepts [
27,
28], ensuring flexibility in multiple scenarios, such as terrestrial [
29], aerial [
30], and marine [
31,
32]. However, the above applications of GAs suffer from some problems, such as a high computational cost, the need to discretise the environment [
33] or the necessity to have a fixed end point [
34]. Furthermore, GAs are rarely used in IPP strategies for IG purposes in underwater environments.
The innovation introduced by the work presented in this paper consists in the application of a GA-based IPP algorithm, renamed
Genetic Path Planner (GPP), with the aim of generating a path that simultaneously maximises the information gathered and the coverage of the inspected area. In particular, the analysed scenario is the monitoring of
Posidonia Oceanica (PO), which is an endemic low-growing Mediterranean sea grass with a high ecological value. Indeed, it is essential for the stability of coastal ecosystems, currents and waves energy attenuation, and carbon absorption, and it is a source of food and refuge for numerous animal species. Many studies show how human activity is causing the continuous decline of this species [
35], and how monitoring the ecosystems that they form is essential to plan strategies for its control and maintenance. The authors’ final goal is to employ an AUV capable of finding and replanning autonomously the best path to carry out PO monitoring activities. In this paper, a GP trained on data describing the presence of PO, in probabilistic terms, has been utilised to create a model of the PO meadow extension and shape in the area of interest, through Equations (
A2) and (
A3) [
11] (details in
Appendix A.1). To obtain the dataset, used for the training of the GP, a collection of images, acquired by the AUV in previous missions over the target area, were segmented using a pre-trained
Convolutional Neural Network (CNN) [
36]. The uncertainty of the estimate provided by the GP has then been used as input of the GPP algorithm to compute the informativeness of a given position within the inspected area. As a further step towards the final goal, the new data collected by the AUV along the planned path will be exploited to retrain the GP, and hence update the environmental model. This way, the GPP method will be able to re-plan a path according to the updated covariance map of the GP prediction.
Within this work, the proposed GPP algorithm has been tested offline using GPs trained on real marine data relative to three different geographical areas covered by PO. Moreover, a comparison with other two IPP strategies has been carried out.
The manuscript is organised as follows. The proposed path planner, together with the alternative planning strategies and the metrics used for the comparative analysis, are presented in
Section 2. Results analysis and comparative evaluation are described in
Section 3.
Section 4 reports a discussion regarding the results reported in the previous Section. Finally, paper conclusions and possible future works are presented in
Section 5.
4. Discussion
The results of the comparative study show that the proposed GPP generally performs better than the S-B and Random planners. In terms of ME, the GPP algorithm statistically outperforms the others for all the studied cases (area and scenario). It is worth discussing the case of Area 2-Scenario 1 and 2, in which the percentage of times the S-B planner performs better than the other approaches results to be greater than the other areas, as represented in
Table 5 and
Figure 8b. This is because the starting point of the first and second scenarios is located in an area characterised by a high variance of the GP. Therefore, the S-B planner is likely to find its
Station point close to the starting point, resulting in a short path with high information content. This situation could occur whenever the most informative point is located near the starting point, despite the amount of target area investigated by the
Station Search phase of the S-B planner. Consequently, the ME metric could result in a higher value for the S-B planner in similar scenarios, potentially leading to misleading considerations if not associated to the other two metrics. In fact, the standard deviation of the ME for the results of S-B planner in Area 2-Scenario 1 is much higher than the one obtained by GPP, as reported in
Table 3 and
Figure 8b, and that highlights a statistic inconsistency in the S-B planner results. On the contrary, the other two approaches generate paths with a higher mean value of ME and lower standard deviation over the 40 offline executions.
Moreover, the proposed GPP algorithm results to generate paths with a good coverage of the area under inspection. In particular, as shown in
Figure 9 and
Figure 10, the PL and O2E metrics obtained by the GPP strategy result to be significantly better than the ones of the S-B planner, allowing to explore a wider portion of the target area as well as gathering more useful data about PO along the path. The PL and O2E metrics result comparable between the GPP and the Random planner. This is reasonable since the two planners exploit the same distributions and parameters for the chromosome generation. However, as reported in
Table 5, the ME of the GPP approach is statistically higher than that of the Random planner, thus justifying the use of the iterative part of the GPP algorithm. Furthermore,
Figure 11 shows the improvement obtained thanks to the optimisation phase performed in the GPP algorithm, and not included in the Random planner instead. The mean trend of the utility value, represented in red in the plot, is strictly increasing but does not reach convergence in the defined planning time
. Thus, the choice of utilising a stop condition based on time become more relevant, since the convergence of the algorithm could require an amount of time which will make the algorithm not exploitable online. An analogous result is reported also in [
14], which shows the evolution of the utility value over an extended planning time of 180 s for the S-B planner. The reader is there addressed, as a S-B characterisation is beyond the scope of the authors’ manuscript.
Last, it is worth pointing out that the results obtained by the GPP algorithm, utilising the parameters configuration discussed in
Section 3.2, have similar performance over the three different target areas, although obtained through optimisation on a specific area (Area 1). This confirms that the considered set of parameters has a validity independent from the specific area and scenario.
5. Conclusions
This work presents a novel IPP algorithm based on GA theory, renamed GPP, to address the path planning problem in underwater environments. The strategy relies on the concepts of genetic operations, namely crossover and mutation, to generate the optimal path in terms of informativeness and coverage of the inspected area. The proposed approach has been tested offline, exploiting real marine data, within the context of PO monitoring, where the GPP aims at generating an optimal path for an AUV to investigate the presence of PO in a target area. To this aim, the GPP algorithm exploits the uncertainty of a GP prediction, which is employed to provide an a priori knowledge about the presence of PO in the area of interest. The algorithm uses such uncertainty to compute the DE in the points belonging to each generated path, which is adopted to represent their information content. Afterwards, the GPP method retrieves the path that maximises an utility function, consisting of an averaged version of the DE along the path and a geometric index representing the coverage of the inspected area. A comparative study with other two IPP strategies has been carried out to evaluate the performance of the proposed GPP method. The first one is a S-B algorithm, which is considered, to the extent of the authors’ knowledge, as one of the main state of the art IPP approaches for IG operations. The second strategy is instead a Random planner, which has been taken into account to assess whether the genetic iterative operations performed in the GPP algorithm provide improvements to the path performance, or they can be avoided to reduce planning time. Thus, this planner implements only the first phase of the GPP method, generating random chromosomes for all the available planning time, without applying any crossover or mutation transformations, and in the end the best chromosome in terms of utility value among all the generated ones is selected.
The comparative analysis has been performed over 3 different areas, located in Mallorca Island (Spain), and considering 3 starting points for each area. The result of the tests showed that the GPP generally performs better than the S-B planner in terms of all the metrics used for the comparison: ME, PL, and O2E. The performance of GPP and Random planner result similar in terms of PL and O2E, but the GPP usually generates more informative paths (higher ME).
As a future work, the issue of retraining the GP exploiting the data acquired by the AUV along the planned path will be addressed. This will allow the AUV to update the model of the environment and to replan its path according to the newly acquired information. Moreover, alternative methods to perform the consistency check on the genes of the chromosome will be investigated, e.g., a cost factor in the utility function could be introduced to penalise those genes which are outside . Furthermore, strategies to avoid the issue of overlapping path sections will be studied. Indeed, the presence of loops within a path implies that the same point will be visited multiple times. Therefore, the information acquired by the AUV along such path will be conditioned by the redundant points, which will contribute more than once to the global information content of the path. This issue cannot be addressed by updating the GP model every time a new data is available, due to the computational cost of this operation. However, the problem could be solved imposing some penalties in the utility function when a path has overlapping sections. Finally, the proposed GPP algorithm will be implemented on an AUV and tested on field experiments to assess its performance in a real marine scenario.