A constrained A* approach towards optimal path planning for an unmanned surface vehicle in a maritime environment containing dynamic obstacles and ocean currents

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About: This article is published in Ocean Engineering.The article was published on 2018-12-01 and is currently open access. It has received 169 citations till now.

Summary

1. Introduction

• Recent advances in electronic navigation and intelligent robots have become an imperative aid to navigate marine vehicles effectively for applications ranging from reconnaissance in hostile areas to operations in dangerous weather conditions (Loe, 2008).
• Ocean environmental effects and moving obstacles play the most significant role in path planning of USVs and very few literatures have covered their effect on path planning in the last decade (Tam et al., 2009, Statheros et al., 2008).
• In the subsequent section, simulation studies conducted in various environmental scenarios are reported and the proposed approach is benchmarked.
• The conclusions of the current study are reported in the final section.

1.1. Related work

• Many studies have been conducted on the subject of grid based path planning in the area of marine vehicles from different perspectives of collision avoidance, heading constraint, environmental disturbances and energy consumption.
• AUVs cannot operate in all environmental conditions due to limited speed and onboard capabilities against USVs which are more suited for operation in areas of high military, shipping or fishing activity, due to acoustic interference, collision risk, and net entanglement.
• The International Maritime Organization (IMO) ((IMO, 1988, 1995, 2007)) has suggested certain regulations for navigation in a marine environment for collision avoidance commonly known as International Regulations for Preventing Collisions at Sea.
• A modified A* algorithm, Theta*, for search in 3D Euclidean space at all orientation was implemented for USV path planning complying with heading angle of USV and compared with conventional grid based 3D path planners (Kim et al., 2012).

1.2. Problem definition and major contribution

• In the present context of autonomy required in the marine environment, autonomous navigation of USVs in a practical marine environment needs to be cognizable of three important issues, namely, safety, reliability of the mission and likelihood of the success (Statheros et al., 2008, LaValle, 2006).
• Central to the path planning algorithms, two approaches are widely adopted namely, a waypoint approach and a trajectory based approach.
• Hence there is a challenge to conserve energy as well as consider safety of USVs in USV path planning for USVs designed with heterogeneous mission requirements in mind.
• Ocean environmental effects can be bifurcated into three streams, as the additive and multiplicative disturbances on vehicle hull, namely, wind, waves and ocean currents (Fossen, 1995).
• Another major challenge is to understand the steady non uniform headwind and tailwind (Knight, 2008, Belcher, 2007) currents effect on way-point generation and optimality in grid-based path planners.

2.1. Environmental mapping

• The abstraction of path planning for USVs is shown in Fig.3.
• In order to implement path planning algorithms, mapping the environment becomes the initial step.
• Environmental mapping converts world space into Configuration space which helps in quick implementation of algorithms and manageable storage in computers (Mooney et al., 2010).
• Portsmouth harbour is among the busiest harbours in United Kingdom and is a perfect area for understanding path planning of USVs.

2.2. A* Algorithm

• In the present study, the A* approach with safety distance constraints has been adopted.
• Since the current study considers an USV, Springer, developed with primary purpose of monitoring sea pollution, generation of safer way points with conservation of optimality for higher endurance becomes the highest priority.
• No approach has been able to compute path with a better computational time than the conventional A* approach in simulation studies.
• Each adjacent cell of actually reached cell is evaluated by value of f(n) and the one with lowest value of f(n) is chosen as the next one in sequence.
• This advantage of modifying distance in A* gives wide range of modifications which can be applied in the algorithm in form of energy consumption and safety distance (Duchoň et al., 2014).

2.3. Assumptions

• The complexity of USV path planning is massive and a number of simplifications have been recommended to reduce the intricacies of the problem (Azariadis and Aspragathos, 2005).
• Here, the following assumptions have been made: 1. The map (study area) is considered to be in a confined sea environment near to Portsmouth harbor.
• Kalman filter and other sensor measurements are used on a USV to determine the obstacle position over time.
• Overlapping of elliptical shape with grid cell boundary is neglected.
• The deliberative systems help in determining global waypoints while reactive systems are responsible for collision avoidance when dynamic obstacles come in the USV safety domain described in Fig.

2.4. Challenges of incorporating COLREGs in path planning algorithms

• The COLREGs serves as a handbook for selecting avoidance manoeuvres.
• Recently, several efforts have been made to integrate COLREGs in path planning algorithms for USVs (Svec et al., 2013, Kuwata et al., 2014).
• These studies work safely in a scenario with very few complexities with an assumption that each vessel in the operational domain has the same amount of information about the current COLREGs situation and reacts in same way.
• This hypothesis does not hold true in real time where each sailor interprets COLREGs based on speed, size and heading of the other vessel (Shah, 2016).
• In addition to that, various external factors such as limited field of view, ocean currents and seamanship in case of breaching the COLREGs make it non-trivial to incorporate COLREGs rules into path planning framework used in complex scenarios.

2.5. Incorporating Guidance and Control System with Path Planning Algorithm

• The general architecture of an USV operation in a maritime environment has basically three subsystems, namely, control and path planning, obstacle detection and avoidance (ODA) and communication and monitoring as shown in Fig.6.
• The current study proposes an computationally effective and safer approach for generation of optimal waypoints for USV navigation in the desired environment.
• Guidance is responsible to achieve motion control objectives in the physical environment in which the vehicle moves (Bibuli et al., 2009).
• The easiest way is to use a classical autopilot system, so that commanded yaw angle generated from a line-of-sight (LOS) guidance algorithm can be controlled (assuming sufficient bandwidth) and cross track error is minimized.
• In terms of autopilot and control system development, a detailed review of studies con- ducted on USVs has been discussed by Roberts (2008).

2.6. Collision avoidance in close encounter situation

• The general architecture for a USV operation in a maritime environment described in Fig.6 shows that high level planners send waypoints to low level decision makers i.e. local control systems and obstacle avoidance subsystems to execute the waypoint following task.
• When a time variant moving obstacle enters the working domain of the operating USV, it is expected that high level planners quickly regenerates new set of way points based on the current information of the environment.
• Many other factors like relative velocity of the USV and the obstacle , the sensing horizon etc also plays an important role in such regeneration process.
• In such transition, it is hereby required to have a quick response time from the high level planners which is one of the main objectives of the current study.
• To enable the safe and secure operation of autonomous surface ships within the existing IMO requirement, a code of practice has been prepared by the UK Maritime Autonomous Systems Working Group and published by Maritime UK through the Society of Maritime Industries (UK, 2017).

3. Simulation Results

• The proposed approach is simulated using C++ and OpenCV.
• The simulations were repeated for 500 times, especially in terms of computational time, to account for variable computational power in OS Windows.
• The average time from all repetitions was calculated for proper verification of the proposed approach.

3.1. Comparing A* approach with and without safety distance

• The proposed study deals with inclusion of a safety distance criteria in the A* approach towards USV path planning.
• In order to benchmark the safety distance approach and to decide upon an optimum value of safety distance, four arbitrary values, 10, 20, 30 and 40 pixels are taken as safety distance on a grid map (as shown in Fig. 2) and compared against an A* approach without safety distance in terms of computational time.
• In terms of path length, simulations shows that the A* approach with and without safety distance constraint produces path of equal length i.e. 1.043 km although a difference in resultant path can be seen in Fig.11.
• This leads to the fact that optimality remains conserved in path planning with decrease in computational effort in the proposed approach unlike ones adopted in literature towards path planning of USVs where an increase in computational cost has been observed with increase in path length for proposed approaches.
• This value also provides enough time for local reactive techniques for collision avoidance in case where one or more moving obstacles are detected in the operational domain of the USV.

3.2. Constrained A* approach under static and partially dynamic environment

• In order to understand the effectiveness of the proposed approach, simulations are conducted in binary maps of Portsmouth harbour comprising of static obstacles as well as moving obstacles.
• The computational time again increases once the moving obstacle escapes out of the safety domain of the USV.
• The results shown in Fig.18 shows path generated by proposed approach in different scenarios of an maritime environment with two moving obstacles.
• In this case also the same pattern as found with the single moving obstacle scenario is observed.
• The comparison of path length and computational time is shown in Fig.19 and Fig.20 respectively.

3.3. Constrained A* approach with environmental disturbances

• Ocean currents generated in the upper layer of the ocean environment by atmospheric wind system are referred as sea surface currents (Fossen, 1995).
• Real ocean currents are multi-directional and irregular, spatially and temporally.
• Path length and computational time are compared for both scenarios shown in Fig.21 and results are presented in Fig.22 and Fig.23 respectively.
• Along the same line, currents of 2.5 m/s are considered to understand the path planning pattern of USV under influence of strong ocean currents.
• Fig.24 shows the path obtained by the proposed approach with currents moving in anti-clockwise and clockwise direction with intensity of 2.5 m/s.

3.4. Constrained A* approach with single moving obstacle and environmental disturbance

• Since the complexity of the environment has increased, a more flexible safety distance constraint of 15 pixel has been adopted for this study in order to keep a proper trade off between optimal way points and environmental complexity.
• Fig.28 shows the generated paths for different start time in the environment comprising of static obstacle, sea surface currents of 1.4 m/s moving in anticlockwise direction and moving obstacle (where each dynamic position is considered static).
• Comparison of path length and computational time for all scenarios presented in Fig.28 are shown in Fig.27 and Fig.29 respectively.
• In addition to that, most cases have been able to generate path within a reasonable computational time.
• These results show that the proposed algorithm can generate safer way points for the USV voyage for long and short duration missions in a cluttered complex environment.

4. Conclusions

• The objective of generating safer way points by keeping a safe distance from the obstacle was evaluated in simulations, conducted in various environments comprising of static obstacle, moving obstacle and sea surface currents of different intensities.
• The upstream and effects of sea surface currents was evaluated and effect of sea surface currents with moving obstacle was also analysed.
• The simulation results shows that the present approach generates safer way points for USV voyage in a computationally efficient manner against the conventional A* approach with no loss of optimality.
• Another extension of the present work lies in considering heading angle constraint for USV, in such cases, where, path length is more important than computational time.
• Most leading companies in USV operations are looking for the integration of COLREGs with optimal path planners to abide the working guidelines of the IMO.

Figures

Table 1: Specifications of Springer

Figure 6: General architecture of USV operation in a maritime environment (Campbell and Naeem, 2012)

Figure 23: Comparison of computational time to determine path obtained for currents moving with intensity of 1.4 m/s in anticlockwise (AC) and clockwise (C) directions. The interval on each bar denotes the standard deviation of the computational time.

Figure 24: Comparison of paths obtained for currents moving with intensity of 2.5 m/s in (a) anti-clockwise and (b) clockwise direction. The start and goal states are same as shown in Fig.12. The safety distance constraint of 20 pixels is maintained for both scenarios.

Figure 26: Comparison of computational time to determine path obtained for currents moving with intensity of 2.5 m/s in anticlockwise (AC) and clockwise (C) directions. The interval on each bar denotes the standard deviation of the computational time.

Figure 25: Comparison of path length obtained for currents moving with intensity of 2.5 m/s in anticlockwise (AC) and clockwise (C) directions. The interval on each bar denotes the standard deviation of the path length.

Figure 9: Binary Map with Start and Goal States

Figure 18: Comparison of paths obtained with different start time (a) 0 (b) 10 (c) 20 (d) 30 (e) 40 (f) 100 seconds. A safety distance constraint of 20 pixel is maintained for all scenarios in the figure.Position of both moving obstacles is plotted at each start time on the binary map, based on the velocity and direction mentioned in Fig.13.

Figure 2: A schematic showing the path generated by a conventional grid based path planner compared against the path generated by a grid based path planner by considering safety distance and sea surface currents (clockwise). In case of anti clockwise currents, the sea surface currents push the USV towards the obstacle and the proposed algorithm makes sure that a safety distance is maintained to ensure no collision

Figure 29: Comparison of path length obtained for scenario with sea surface currents of 1.4 m/s moving in anti-clockwise direction having a moving obstacle for different start time of 0, 10, 20, 30, 40, 50, 60, 80 and 100 seconds. The interval on each bar denotes the standard deviation of the path length.

Figure 19: Comparison of path length obtained with different start time 0, 10, 20, 30, 40 and 100 seconds.The interval on each bar denotes the standard deviation of the path length

Figure 20: Comparison of computational time obtained with different start time of 0, 10, 20, 30, 40 and 100 seconds. The interval on each bar denotes the standard deviation of the computational time

Figure 8: Schematic of the proposed path planning system

Figure 14: Dimension of the elliptical domain representing the encapsulation of a moving obstacle in a static one in the binary map. The dimensions of ellipse are chosen in accordance with the dimensions of high speed craft having operational velocity range from 6 to 9 knots

Figure 13: Binary map of the simulation area (Portsmouth harbour) showing velocity and direction of moving obstacles. In this study, 20 pixels has been chosen as the safety distance around an USV.

Figure 21: Comparison of paths obtained for currents moving with intensity of 1.4 m/s in (a) anti-clockwise and (b) clockwise direction. The start and goal states are same as shown in Fig.12. The safety distance constraint of 20 pixels is maintained for both scenarios.

Figure 28: Comparison of paths obtained for scenario with sea surface currents of 1.4 m/s moving in anticlockwise direction having a moving obstacle for different start time of (a) 0 (b) 10 (c) 20 (d) 30 (e) 40 (f) 50 (g) 60 (h) 80 (i) 100 seconds. The start and goal states are same as shown in Fig.12. The safety distance constraint of 15 pixels is maintained for all scenarios.

Figure 3: Path planning abstraction for USVs (Singh et al., 2016)

Figure 15: Comparison of paths obtained with different start time (a) 0 (b) 10 (c) 20 (d) 30 (e) 40 (f) 50 (g) 60 (h) 100 (i) 120 seconds. Position of the single moving obstacle is plotted at each start time on the binary map, based on the velocity and direction mentioned in Fig.13

Figure 11: Resultant path with safety distance of (a) 0 (b) 10 (c) 20 (d) 30 (e) 40 pixels

Figure 12: Binary map with start and goal states for simulating A* approach under static and partially dynamic environment

Frequently asked questions

Q1. What are the contributions in "A constrained a* approach towards optimal path planning for an unmanned surface vehicle in a maritime environment containing dynamic obstacles and ocean currents" ?

Unlike existing work on USV navigation using graph based methods, this study extends the implementation of the proposed A * approach in an environment cluttered with static and moving obstacles and different current intensities. The study also examines the effect of headwind and tailwind currents moving in clockwise and anti clockwise direction respectively of different intensities on optimal waypoints in a partially dynamic environment. 

Q2. What are the future works mentioned in the paper "A constrained a* approach towards optimal path planning for an unmanned surface vehicle in a maritime environment containing dynamic obstacles and ocean currents" ?

The approach is found to be robust, computationally efficient and can be extended for real time path planning of USVs in confined water. In future work, it is planned to extend the work in development of a path follower approach working in conjugation with proposed approach for a reactive path planning in scenarios involving close encounters. A challenging 28 extension of the current work lies in fact of finding a heuristic cost function which can take into account rules of the COLREGs without compromising the optimality and computational effort required to find a feasible trajectory.