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A potential field approach for reactive navigation of autonomous sailboats
Robotics and Autonomous Systems 60 (2012) 1520–1527
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A potential field approach for reactive navigation of autonomous sailboats✩ C. Pêtrès ∗ , M.-A. Romero-Ramirez, F. Plumet Intelligent Systems and Robotics Institute, (ISIR-CNRS-UMR 7222, Pierre et Marie Curie University), France
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Article history: Received 20 May 2012 Received in revised form 3 August 2012 Accepted 17 August 2012 Available online 23 August 2012 Keywords: Reactive navigation Artificial potential field Autonomous sailboat
abstract Navigation techniques for autonomous sailboats are faced with two inherent difficulties. The uncontrollable and partially unpredictable nature of thrust forces on one hand and the complex kinematics of sailboats on the other hand. This paper proposes a new reactive navigation approach, based on artificial potential fields, that addresses these two problems simultaneously. Environment and specific sailboat navigation constraints are represented by a local potential built around the vehicle location. Changes of wind direction and detected obstacles affect this periodically updated potential, which guarantees the real-time computation of a feasible heading for the boat. Numerical simulations are presented and validate the proposed algorithm under various wind conditions. Field trials eventually illustrate the efficiency of this navigation technique using a reduced-scale autonomous sailboat prototype. © 2012 Elsevier B.V. All rights reserved.
1. Introduction During recent years considerable progress has been observed in the development and use of autonomous surface vehicles (ASV) [1]. Applications for such vehicles include marine environment monitoring [2–12], bathymetry [13], inspection [14], mine countermeasure and port protection [15] either alone or as part of a sensor network. Among the aforementioned ASV, autonomous sailing robots, since they rely on renewable solar and wind energies, provide a promising solution for long-term missions and semi-persistent presence in the oceans, see [16,17] for a comprehensive survey on recent developments in robotic sailing. In our framework it is assumed that the mission planning task has previously been performed and that a list of waypoints has already been selected. In this context, numerous projects have been launched in Europe and in USA, see for example [18–26]. Autonomous sailing robotics is currently receiving growing attention, however, it is faced with two inherent difficulties. The uncontrollable and partially unpredictable nature of thrust forces (wind direction and wind speed) on one hand and the complex kinematics of a sailboat (aero and hydrodynamic properties of sails and hull) on the other hand. The main contribution of this paper is to propose a reactive navigation approach that addresses these
✩ This work has been supported by the French National Research Agency under the ASAROME project (Autonomous SAiling Robot for Oceanographic MEasurements, Num. ANR-07-ROBO-0009). ∗ Corresponding author. E-mail addresses: [email protected], [email protected] (C. Pêtrès), [email protected] (M.-A. Romero-Ramirez), [email protected] (F. Plumet).
0921-8890/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.robot.2012.08.004
two problems simultaneously. This navigation method, based on artificial potential fields, is designed to react in real-time to changes in the environment on one hand and to suit the specific kinematic constraints of sailboats on the other hand. Changes of wind direction and detected obstacles are addressed by updating a local potential around the boat location to periodically compute an optimal heading for the boat. The specific kinematics of the sailboat is modeled into a speed polar diagram that affects the characteristics of the local potential in order to guarantee the exhibition of a feasible heading for the boat. The paper is organized as follows. First, our navigation method based on artificial potential fields is described. This section explains how to build a local potential relative to the wind direction and a global potential relative to obstacles and goal locations. Second, a set of simulations is presented, which validates this navigation technique under variable wind conditions. Examples of upwind and downwind trajectories are commented upon as well as a simulation under a spatially varying wind chart. Third, the sailboat prototype developed in the lab is presented. This autonomous sailing robot is then used to test our navigation approach under realistic conditions on a lake near Paris, France. Results of these successful field trials are finally presented. 2. Potential based path planning approach During the past decade, numerous methods have been proposed to address the navigation and obstacle avoidance issue of autonomous sailing robots. Raytracing techniques have been proposed in [27,28], the use of a state machine in [29,30], dynamic programming in [31], modified A∗ algorithm in [18], fuzzy logic in [32], interval analysis in [33], Voronoi diagrams in [34] and optimization of the time-derivative of the distance between boat and
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target in [35]. The latest reference is close in spirit to our method (previously investigated in [36,37]) because it is a reactive navigation technique that explicitly uses the speed polar diagram of the sailing boat and a hysteresis condition. In this section our potential field based navigation technique will be described. The main advantage of this potential field approach is to be a unified framework that naturally integrates all the components of interest involved in the navigation process. Goal and obstacle locations, speed characteristics of the boat, costs of tack and gybe manoeuvres and danger of obstacles are all taken into account under the form of an attractive or a repulsive potential. The overall potential field is simply derived from the spatial sum of all these components. Moreover, potential field based algorithms are fast, reliable and easy to tune once implemented on real platforms because there are only a few independent parameters to set up. Besides, the simplicity of potential field techniques is attractive for robotic projects with tight power budgets. They can run on very limited micro-controllers, which is also an asset for low power consumption and energetic autonomy. Potential field methods, due to Khatib [38] and Krogh and Thorpe [39], have been widely and successfully employed for control and motion planning of mobile robots for decades, see for example [40–42] among many others. In artificial potential fields methods, movements of the robot (represented as a particle) are governed by a field, which is usually composed of two components, an attractive potential drawing the robot towards the goal and a repulsive potential pushing the robot away from obstacles. The main drawback with potential field techniques is their susceptibility to local minima. However, typical marine environments are sparse and local minima in our open water context are not an issue. The originality of our method is to build a so-called local potential around the boat location to take upwind and downwind sailing constraints into account. Moreover, an hysteresis potential relative to the cost of tacking and gybing is also proposed, which makes our method easy to tune according to the vehicle specifications. Our potential field approach is decomposed into two parts, a global potential field and a local potential field. The global potential field is relative to the target and to the obstacles. The local potential field is relative to the boat kinematics, the wind direction and the latest tack. 2.1. Global potential The global potential is built on the complete map once for all at the beginning of the planning process. It aims at attracting the vehicle towards the goal point and repulsing the vehicle away from obstacles. 2.1.1. Potential relative to the goal In order to attract the vehicle towards the goal point Pgoal a linear potential Pg is built for every point P of the map as follows: Pg = Gg · dist (P , Pgoal )
(1)
where Gg is the desired attractive gradient and dist (P , Pgoal ) is the Euclidean distance between P and Pgoal . Since Gg is a constant, the potential Pg looks like a cone centered on Pgoal , see Fig. 1. 2.1.2. Potential relative to the obstacles A repulsive potential Po relative to the obstacles located in Pobst is built for every point P of the map as follows: Po =
k dist (P , Pobst )
(2)
where k is a tunable scalar. This potential tends to infinity as we come close to the obstacles, which prevents the vehicle from
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Fig. 1. Illustration of the overall potential relative to three obstacles and to a goal point located at the northeast corner of the map.
Fig. 2. Scheme of the upwind and downwind no-go zones. The dotted region corresponds to the region where Ph ̸= 0.
going through the obstacles. The position of each obstacle can be known in advance or can be updated in real time by on-board navigation sensors. To avoid local minima issues, it is assumed in this framework that the obstacles (surrounding boats, islands) have been overestimated by their convex hull. 2.2. Local potential The local potential handles the specific kinematic constraints of a sailboat. It integrates three components, the so-called upwind, downwind and hysteresis potentials. The hysteresis potential is introduced to prevent the boat from tacking or gybing too frequently. The upwind and downwind components are relative to the upwind and downwind no-go zones defined as follows. 2.2.1. No-go zones To take the specific kinematic constraints of autonomous sailing robots, the so-called upwind and downwind no-go zones are defined, see Fig. 2. These two zones are exhibited respectively up to the wind direction (sector defined by the angle φup ) and down to the wind direction (sector defined by the angle φdown ). For the sake of simplicity, we assume an ideal speed polar diagram (represented by the dotted circle in Fig. 2) for the considered vehicle. This corresponds to a constant speed for the boat in all directions except in the no-go zones, where the speed is assumed to be zero. In the following definition of the local potential, it is
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Fig. 3. Close-up on the local potential around the boat. In this case, the upwind no-go zone is pointing up because the wind is coming from north.
straightforward to adapt upwind, downwind and hysteresis potentials to match a more realistic speed polar diagram. Constant coefficients Gup , Gdown and Gh respectively have only to be functions of the angle φ to respect the real shape of the speed diagram of the vehicle. 2.2.2. Upwind potential In order to take the upwind no-go zone into account the upwind potential Pup is built dynamically for each point Pw inside a window (size Wsize ) centered on the boat location P, see Fig. 2. The magnitude of Pup is a function of the angle φ between the direction
−→
of PPw and the wind direction TWA. It is linear inside the upwind no-go zone and zero outside:
Pup = Gup · dist (Pw , P ) Pup = 0
if 0 < |φ| < φup elsewhere
(3)
where Gup is the desired gradient inside the upwind no-go zone sector (see Fig. 3). 2.2.3. Downwind potential In order to take the downwind no-go zone into account the downwind potential Pdown is built dynamically for each point Pw inside the same window centered on the boat location P, see Fig. 2. The magnitude of Pdown is a function of the angle between the boat direction φ and the wind direction. It is linear inside the downwind no-go zone and zero outside:
Pdown = Gdown · dist (Pw , P ) Pdown = 0
if 0 < |φ − π | < φdown elsewhere
(4)
where Gdown is the desired gradient inside the downwind no-go zone sector. 2.2.4. Hysteresis potential In order to take the cost of gybing and tacking into account the hysteresis potential Ph is built dynamically for each point Pw inside the window centered on the boat location P. The magnitude of Ph is a function of the angle φ , the latest tack and the ability of the boat to tack or gybe. For instance, if the boat navigates with the wind coming from port, Ph will be defined at the right side of the wind direction, see Fig. 2. In this example, Ph is defined as follows:
Ph = Gh · dist (Pw , P ) Ph = 0
if φup < φ < π − φdown elsewhere
(5)
where Gh is the desired gradient of Ph . This way, only one parameter has to be set up to fit the cost of gybing and tacking.
2.2.5. Practical considerations Once the local potential has been built and added to the global potential, a gradient descent is classically carried out on the overall potential Pt = Pg + Po + Pup + Pdown + Ph to find the new heading for the boat. In practice, a profile Pp : [0, 360] → R corresponding to the potential Pt around the boat location P is directly computed along a ring of radius R centered in P, without the use of the square window previously described. This window has been introduced for the sake of clarity in order to match the potential field framework, which usually uses a potential function defined on the whole map. From now on, we will only refer to the profile function Pp to compute the optimal heading ϕ . Logically, the optimal heading ϕ for the next move is the angle corresponding to the global minimum of Pp . Note that the radius R of the ring is defined as a function of the expected size of obstacles. It is chosen to be smaller than the minimum size of possible obstacles. In simulation, the navigation process is stopped when the boat arrives in the vicinity of the goal point. Precisely, the stop criteria is defined as follows: dist (P , Pgoal ) ≤ R. In experimentations, the profile Pp and the optimal heading ϕ are continuously computed. As a precaution, the heading ϕ is smoothed to minimize the influence of sensor noise before being sent to the control system. 2.3. Conclusion The algorithm is based on the extensively used artificial potential field method, which we adapted to take the so-called upwind and downwind no-go zones into account. These specific sailing constraints are handled by a so-called local potential. This mathematical construction is built in the neighborhood of the boat location and it is rebuilt after each displacement of the boat according to the wind direction and the latest tack. This updating strategy for the local potential gives the whole navigation algorithm the property to be truly reactive to changes in the (perception of) the environment. The presented navigation algorithm is a standalone method. It will be implemented on its own on simulated environments as well as on a real experimental platform in the next sections. 3. Simulation results In this section, our navigation method will be tested under various scenarios using numerical simulations. First, the influence of static wind configurations will be analyzed assuming the presence of obstacles. Second, navigation under variable wind conditions will be simulated. The coherence and realism of the resulting trajectories will eventually be discussed. 3.1. Simulated environment For the sake of clarity, the simulated environment is assumed to be static (obstacles are fixed) and completely known (obstacles are mapped without uncertainty). Besides, the wind is assumed to be constant in direction as well as in velocity. However, since our local potential is incrementally built as a function of the visible wind and obstacles around the boat location, this reactive navigation approach holds for dynamic environments and can be implemented without any change on real systems (this will actually be the subject of the next section). In the following simulations, the default parameters for the potential have been set up as follows: Gg = 3, k = 100, Gup = 10, Gdown = 5, Gh = 2, φup = 45°, φdown = 30°.
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Fig. 4. Trajectories computed with winds coming from the southwest and west.
Fig. 6. A trajectory computed under spatially variable wind conditions.
Fig. 5. Trajectories computed with the wind coming from the northeast using different hysteresis potentials. In red Gh = 3, in blue Gh = 2, in black Gh = 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. A trajectory computed under spatially variable wind conditions in the presence of obstructing obstacles.
3.2. Downwind and abeam navigation Two trajectories exhibited by the potential field based navigation algorithm for winds coming from the southwest and from west are depicted in Fig. 4. In the trivial case of wind coming from the west, the sailboat navigates abeam and it reaches the target directly while avoiding obstacles without any difficulty. In the case of wind coming from the southwest, the optimal trajectory in respect of the downwind no-go zones is more complex. The boat avoids two obstacles and executes three gybes on its way to the goal point. In both cases, downwind and abeam scenarios, the simulated sailboat successfully reaches the target while respecting the wind-related constraints and circumnavigates the obstacles.
The amplitude and number of gybes and tacks are a function of the cost of these manoeuvres. This cost may vary according to vehicle dynamics, team efficiency, state of the sea, etc. 3.4. Navigation under spatially variable wind conditions In this simulation, the wind direction varies from west to east along the horizontal axis. In the two following figures (Figs. 6 and 7), the wind directions are represented by arrows. The trajectory depicted in Fig. 6 bends to the east as the wind turns from west to north up to a point where a tack becomes necessary to reach the goal point. The trajectory depicted in Fig. 7 is similar to the previous one apart from the fact that, in this case, the boat has to avoid a barrier of obstacles on its way to the target.
3.3. Upwind navigation
3.5. Conclusion
A trajectory solution exhibited by the potential field based navigation algorithm for a wind coming from the northeast is depicted in Fig. 5. Several hysteresis potentials have been tested. The red trajectory has been computed with Gh = 3, the blue trajectory has been computed with Gh = 2 and the black trajectory has been computed with Gh = 1. Two, three and seven tacks have been respectively executed to reach the goal point.
The presented navigation technique provides coherent trajectories in terms of kinematic constraints for a sailboat. Trajectories follow admissible headings regarding the upwind and downwind pre-defined no-go zones. The amplitude and number of tacks and gybes are controlled by the hysteresis potential. This parameter has to be chosen to suit the real cost of these manoeuvres. Besides, in this potential field framework, the attractiveness of the goal point
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Fig. 9. Software architecture of the prototype.
2. a wind vane coupled with an anemometer for wind direction and wind speed, 3. a potentiometer fixed on the mast to measure the mainsail angle. In this hardware architecture, a PC-104 and a microcontroller boards have been used to manage all the electronic devices. Two communication modes are available. A ‘‘manual mode’’, which allows a human operator to remotely control the boat via a radio or a WiFi channel, and an ‘‘autonomous mode’’, which lets the boat navigate on its own. For safety reasons, the boat automatically switches to an emergency state in the case of loss of the radio channel either in manual or in autonomous mode. 4.1.2. Software architecture From a software point of view, the architecture of our robot can be split in four parts as depicted into Fig. 9:
• a high-level navigation module, where our potential based Fig. 8. The reduced-scale autonomous sailboat prototype of the laboratory.
and repulsiveness of obstacles are easy to tune using only two independent parameters. 4. Experimental results In this section, our path planning approach will be tested under realistic conditions on a lake using a reduced-scale autonomous sailboat. First, we will describe both the hardware and software architecture of this sailboat prototype and, second, a sample run performed during these trials will be presented. 4.1. Sailboat prototype To carry out the following field trials, an autonomous sailboat prototype has been built. We started from an existing off-the-shelf reduced-scale model of a sailboat, which we have equipped with sensors and computers to make it fully autonomous. 4.1.1. Hardware architecture The prototype is depicted in Fig. 8. It is a reduced-scale sailboat with the following specification: 1.38 m long, 2.20 m high and 0.36 m wide. The main advantage of this vehicle is to behave similarly to a real boat while being easy to deploy in the test field. The original rudder and sail actuators of this boat have been kept and some electronic devices and sensors have been added for our robotic purposes. The sensors we used are: 1. an inertial measurement unit (IMU) coupled with a GPS receiver to provide heading, roll and pitch of the boat along with its GPS coordinates,
algorithm has been implemented. Parameters of the algorithm are: Gg = 3, k = 100, Gup = 10, Gdown = 5, Gh = 2, φup = 60°, φdown = 15°; • a low-level control module that controls rudder and sail angles according to the heading reference coming from the navigation module; • the sailboat reacts to the actuators (rudder and sails) and to the environment (wind, state of the water surface for instance); • a so-called perception module, which gathers both internal and environmental data. Internal data include sail and rudder angles, heading, roll, pitch and absolute position of the boat, some status data such as battery, sensor and actuator states. Environmental data include wind direction and wind speed. The closed-loop control of the vehicle is achieved by the lowlevel module. This system controls the rudder angle using a classical PI algorithm. The control algorithm for the sails is more complex because we only control the length of the mainsheet, so we only control the maximum angle of the sails (the mainsail and the headsail are linked together in our boat). However, since the attitude and speed of the boat, the wind characteristics and the mainsail angle are known (respectively thanks to an IMUGPS, a wind vane-anemometer and a potentiometer), the control algorithm for the sails has been empirically tuned to maximize the speed of the boat while guaranteeing a safety roll margin to prevent the boat from capsizing. In the following experiments, the roll amplitude is not supposed to exceed 40°. 4.2. Field trials A series of field trials have been carried out on a lake near Paris, France. Fig. 10 shows a trajectory corresponding to an autonomous navigation of our sailboat prototype for seven and a half minutes. This run has been selected amongst many others because it
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Fig. 10. Example of a run during the field trials at Creteil near Paris, France. Fig. 12. Comparison between actual heading and heading reference.
Fig. 11. Apparent wind speed (top) and apparent wind angle (bottom) during the run.
illustrates all the cases of interest in autonomous sailing: upwind, downwind and sidewind navigations. The boat was launched from the pier and had to reach the first waypoint (WP1) located on the northeast corner of the figure. During this test, the direction of the prevailing wind was westnorthwest, this is the reason why one tack was necessary to reach the first admissible area. Admissible areas have been defined as 10 m discs around the waypoints to take GPS uncertainty into account. On Fig. 10, they are represented by blurred surfaces around the waypoints. After reaching WP1, the boat automatically turned towards WP2. This navigation configuration is trivial because WP2 does not lie in any of the no-go zones of the robot. After reaching WP2, the boat headed back to the pier by pointing towards WP3 with the wind on the beam. One can notice that the boat slightly veered off course to starboard at mid-distance between WP2 and WP3. This is due to a wind shift at this moment of the navigation, see the apparent wind speed (AWS) on top of Fig. 11. Besides, Fig. 11 shows that AWS does not exceed 2 m/s during the run. It is 1.1 m/s on average. Fig. 11 also gives an insight of the apparent wind angle (AWA) during the run. In Fig. 12, the actual heading of the boat is compared to the heading reference computed by the navigation module. The heading follows the reference well, with a small delay of one to ten seconds. The first waypoint is reached at time t = 289 s, WP2 at t = 375 s and WP3 at t = 451 s.
Fig. 13. Close-up on the tack manoeuvre between 270 and 280 s and on some heading reference variations around 300 s.
A close-up of heading versus heading reference between 265 and 310 s is given in Fig. 13. A tack is performed exactly between 270 and 280 s. This means that the control system needed ten seconds at this moment of the navigation to complete this manoeuvre. Around t = 300 s some fluctuations of the heading reference can be observed. These are due to the variations of AWA at the same period, see Fig. 14. Fig. 15 shows that the boat behaves safely because the roll amplitude never exceeds 40° and the pitch amplitude never exceeds 27°. 4.3. Conclusion A reduced-scale prototype has been developed and allowed us to carry out some experimental tests under real wind conditions. Our navigation algorithm successfully achieved its task, which was to safely drive the boat to three predefined waypoints without any human intervention. The average wind direction (300°) during this run was not favorable for a direct navigation towards the first waypoint. This explains why the navigation module routed the boat to the north of the target before controlling a tack back to its precise location. Navigation to the second and third waypoints has been performed without any major difficulty apart from a small deviation due to a wind change on the way back to the pier. It
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Fig. 14. Close-up on some variations of AWA around t = 300 s.
Fig. 16. A view of the full-size sailboat prototype during the first trials on the river Erdre near Nantes, France.
Fig. 15. Roll and pitch recorded during the run.
appears that the proposed potential field technique is reliable and robust to wind disturbances. The heading control of the boat is efficient because the reaction time never exceeds ten seconds, even in the worst case of a tack manoeuvre. The boat navigated at 0.4 m/s on average during this run while respecting safety margins for roll and pitch amplitudes. 5. Conclusion and future work In this paper, a novel method for the navigation of autonomous sailboats has been presented. This method, based on the potential field framework, is a truly reactive navigation method as it reacts to spatially and time varying wind conditions as well as detected obstacles in real-time by recalculating an optimal heading periodically. This method has been validated using numerical simulations in the presence of obstacles under various wind configurations. To conclude this work, field trials, carried out on a lake using a reduced-scale prototype, have successfully demonstrated the capabilities of our technique for safely driving autonomous sailing robots. In the perspective of an open water exploitation of this reactive navigation method, some additional tests are already planned. First, we need to test our algorithm in the presence of obstacles. Since our reduced-scale sailboat is not equipped with any visual or acoustic sensors yet, a set of virtual obstacles will be arbitrarily added to the embedded map of the environment. Second, a full-size
prototype is currently under development in cooperation with a fluid mechanics laboratory1 and a robotics company2 (see Fig. 16). This 3.6 m long sailboat is designed to embed navigation sensors (IMU, GPS, acoustic wind vane and anemometer) as well as perception sensors (sonar, hydrophones and panoramic camera) for obstacle detection. It will use a wind turbine and a solar panel to achieve energetic autonomy. Preliminary tests have been carried out on a river near Nantes, France, during which the sailboat has successfully been remotely controlled. References [1] J. Manley, Unmanned surface vehicles, 15 years of development, in: MTS-IEEE Conference OCEANS 2008, Quebec City, Canada, 2008, pp. 1–4. [2] C. Sauzé, M. Neal, A neuro-endocrine inspired approach to long term energy autonomy in sailing robots, Towards Autonomous Robotic Systems, TAROS 2010 (2010) 255–262. [3] A. Pascoal, P. Oliveira, C. Silvestre, L. Sebastiao, M. Rufino, V. Barroso, J. Gomes, G. Ayela, P. Coince, M. Cardew, A. Ryan, H. Braithwaite, N. Cardew, J. Trepte, N. Seube, J. Champeau, P. Dhaussy, V. Sauce, R. Moitie, R. Santos, F. Cardigos, M. Brussieux, P. Dando, Robotic ocean vehicles for marine science applications: the European ASIMOV project, in: MTS-IEEE Conference OCEANS 2000, vol. 1, Providence, RI, USA, 2000, pp. 409–415. [4] J. Almeida, C. Silvestre, A. Pascoal, Cooperative control of multiple surface vessels in the presence of ocean currents and parametric model uncertainty, International Journal of Robust and Nonlinear Control 20 (14) (2010) 1549–1565. [5] M. Caccia, R. Bono, G. Bruzzone, E. Spirandelli, G. Veruggio, A. Stortini, G. Capodaglio, Sampling sea surfaces with SESAMO: an autonomous craft for the study of sea–air interactions, IEEE Robotics and Automation Magazine 12 (3) (2005) 95–105. [6] J. Curcio, J. Leonard, A. Patrikalakis, SCOUT—a low cost autonomous surface platform for research in cooperative autonomy, in: MTS-IEEE Conference OCEANS 2005, vol. 1, 2005, pp. 725–729. [7] P. Mahacek, R. Kobashigawa, A. Schooley, C. Kitts, The WASP: an autonomous surface vessel for the University of Alaska, in: MTS-IEEE Conference OCEANS 2005, vol. 3, 2005, pp. 2282–2291.
1 Fluid Mechanics Laboratory, Ecole Centrale de Nantes, Nantes, France. 2 Robosoft, Bidart, France.
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[32] R. Stelzer, T. Proll, R. John, Fuzzy logic control system for autonomous sailboats, in: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2007, London, UK, 2007, pp. 1–6. [33] P. Herrero, L. Jaulin, J. Vehi, M.A. Sainz, Guaranteed set-point computation with application to the control of a sailboat, International Journal of Control, Automation and Systems 8 (1) (2010) 1–7. [34] K. Xiao, J. Sliwka, L. Jaulin, A wind-independent control strategy for autonomous sailboats based on Voronoi diagram, in: International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, CLAWAR 2011, Paris, France, 2011, pp. 109–123. [35] R. Stelzer, T. Pröll, Autonomous sailboat navigation for short course racing, Robotics and Autonomous Systems 56 (7) (2008) 604–614. [36] M. Romero Ramirez, C. Petres, F. Plumet, Navigation with obstacle avoidance of an autonomous sailboat, in: International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, CLAWAR 2011, 2011, pp. 86–93. [37] C. Petres, M. Romero Ramirez, F. Plumet, B. Alessandrini, Modeling and reactive navigation of an autonomous sailboat, in: IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2011, San Francisco, CA, USA, 2011, pp. 3571–3576. [38] O. Khatib, Real-time obstacle avoidance for manipulators and mobile robots, International Journal of Robotics Research 5 (1) (1986) 90–98. [39] B. Krogh, C. Thorpe, Integrated path planning and dynamic steering control for autonomous vehicles, in: IEEE International Conference on Robotics and Automation, vol. 3, 1986, pp. 1664–1669. [40] J. Barraquand, B. Langlois, J.-C. Latombe, Numerical potential field techniques for robot path planning, IEEE Transactions on Systems, Man and Cybernetics 22 (2) (1992) 224–241. [41] H. Haddad, M. Khatib, S. Lacroix, R. Chatila, Reactive navigation in outdoor environments using potential fields, in: IEEE International Conference on Robotics and Automation, vol. 2, Leuven, Belgium, 1998, pp. 1232–1237. [42] S. Ge, Y. Cui, Dynamic motion planning for mobile robots using potential field method, Autonomous Robots 13 (3) (2002) 207–222.
C. Pêtrès recieved his Ph.D. in Electrical Engineering in 2007 from Heriot–Watt University (Scotland). He worked as a Researcher in machine learning for the NATO Undersea Research Centre (NURC, Italy). He is the inventor of an inertial system that localizes and guides blind people in the subway. This work has been carried out under a post-doctoral contract at the French Atomic Energy Commission (France). He also worked as a post-doctoral Researcher at the Intelligent Systems and Robotics Institute (ISIR-CNRS-UMR 7222, Pierre et Marie Curie University, France) on the navigation of autonomous sailboats. He is currently a Contract Lecturer at Pierre et Marie Curie University. M.-A. Romero-Ramirez received a degree in Electronic Engineering from the Panamericana University (Aguascalientes, Mexico) in 1999, an M.Sc. degree from the Instituto Tecnolgico y de Estudios Superiores de Monterrey (ITESM, Mexico) in 2002 and a Ph.D. from Pierre et Marie Curie University (UPMC, France) in 2012. From October 2007 to February 2012, he was involved in a research project on autonomous sailboat guidance. His primary research interests include artificial potential fields, optimization algorithms, fuzzy logic controllers as well as electronics for on-board systems. F. Plumet is an Associate Professor at University of Versailles St Quentin (UVSQ). He holds his research activities at the Intelligent Systems and Robotics Institute (ISIR-CNRS-UMR 7222, Pierre et Marie Curie University). His research interests are the control of autonomous systems interacting with their environment such as assistive devices for rehabilitation, articulated rovers on rough terrain or robotic sailboats. He received an M.Sc. degree in Electrical Engineering in 1987 and a Ph.D. in Robotics in 1992 from Pierre et Marie Curie University.
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A potential field approach for reactive navigation of autonomous sailboats✩ C. Pêtrès ∗ , M.-A. Romero-Ramirez, F. Plumet Intelligent Systems and Robotics Institute, (ISIR-CNRS-UMR 7222, Pierre et Marie Curie University), France
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Article history: Received 20 May 2012 Received in revised form 3 August 2012 Accepted 17 August 2012 Available online 23 August 2012 Keywords: Reactive navigation Artificial potential field Autonomous sailboat
abstract Navigation techniques for autonomous sailboats are faced with two inherent difficulties. The uncontrollable and partially unpredictable nature of thrust forces on one hand and the complex kinematics of sailboats on the other hand. This paper proposes a new reactive navigation approach, based on artificial potential fields, that addresses these two problems simultaneously. Environment and specific sailboat navigation constraints are represented by a local potential built around the vehicle location. Changes of wind direction and detected obstacles affect this periodically updated potential, which guarantees the real-time computation of a feasible heading for the boat. Numerical simulations are presented and validate the proposed algorithm under various wind conditions. Field trials eventually illustrate the efficiency of this navigation technique using a reduced-scale autonomous sailboat prototype. © 2012 Elsevier B.V. All rights reserved.
1. Introduction During recent years considerable progress has been observed in the development and use of autonomous surface vehicles (ASV) [1]. Applications for such vehicles include marine environment monitoring [2–12], bathymetry [13], inspection [14], mine countermeasure and port protection [15] either alone or as part of a sensor network. Among the aforementioned ASV, autonomous sailing robots, since they rely on renewable solar and wind energies, provide a promising solution for long-term missions and semi-persistent presence in the oceans, see [16,17] for a comprehensive survey on recent developments in robotic sailing. In our framework it is assumed that the mission planning task has previously been performed and that a list of waypoints has already been selected. In this context, numerous projects have been launched in Europe and in USA, see for example [18–26]. Autonomous sailing robotics is currently receiving growing attention, however, it is faced with two inherent difficulties. The uncontrollable and partially unpredictable nature of thrust forces (wind direction and wind speed) on one hand and the complex kinematics of a sailboat (aero and hydrodynamic properties of sails and hull) on the other hand. The main contribution of this paper is to propose a reactive navigation approach that addresses these
✩ This work has been supported by the French National Research Agency under the ASAROME project (Autonomous SAiling Robot for Oceanographic MEasurements, Num. ANR-07-ROBO-0009). ∗ Corresponding author. E-mail addresses: [email protected], [email protected] (C. Pêtrès), [email protected] (M.-A. Romero-Ramirez), [email protected] (F. Plumet).
0921-8890/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.robot.2012.08.004
two problems simultaneously. This navigation method, based on artificial potential fields, is designed to react in real-time to changes in the environment on one hand and to suit the specific kinematic constraints of sailboats on the other hand. Changes of wind direction and detected obstacles are addressed by updating a local potential around the boat location to periodically compute an optimal heading for the boat. The specific kinematics of the sailboat is modeled into a speed polar diagram that affects the characteristics of the local potential in order to guarantee the exhibition of a feasible heading for the boat. The paper is organized as follows. First, our navigation method based on artificial potential fields is described. This section explains how to build a local potential relative to the wind direction and a global potential relative to obstacles and goal locations. Second, a set of simulations is presented, which validates this navigation technique under variable wind conditions. Examples of upwind and downwind trajectories are commented upon as well as a simulation under a spatially varying wind chart. Third, the sailboat prototype developed in the lab is presented. This autonomous sailing robot is then used to test our navigation approach under realistic conditions on a lake near Paris, France. Results of these successful field trials are finally presented. 2. Potential based path planning approach During the past decade, numerous methods have been proposed to address the navigation and obstacle avoidance issue of autonomous sailing robots. Raytracing techniques have been proposed in [27,28], the use of a state machine in [29,30], dynamic programming in [31], modified A∗ algorithm in [18], fuzzy logic in [32], interval analysis in [33], Voronoi diagrams in [34] and optimization of the time-derivative of the distance between boat and
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target in [35]. The latest reference is close in spirit to our method (previously investigated in [36,37]) because it is a reactive navigation technique that explicitly uses the speed polar diagram of the sailing boat and a hysteresis condition. In this section our potential field based navigation technique will be described. The main advantage of this potential field approach is to be a unified framework that naturally integrates all the components of interest involved in the navigation process. Goal and obstacle locations, speed characteristics of the boat, costs of tack and gybe manoeuvres and danger of obstacles are all taken into account under the form of an attractive or a repulsive potential. The overall potential field is simply derived from the spatial sum of all these components. Moreover, potential field based algorithms are fast, reliable and easy to tune once implemented on real platforms because there are only a few independent parameters to set up. Besides, the simplicity of potential field techniques is attractive for robotic projects with tight power budgets. They can run on very limited micro-controllers, which is also an asset for low power consumption and energetic autonomy. Potential field methods, due to Khatib [38] and Krogh and Thorpe [39], have been widely and successfully employed for control and motion planning of mobile robots for decades, see for example [40–42] among many others. In artificial potential fields methods, movements of the robot (represented as a particle) are governed by a field, which is usually composed of two components, an attractive potential drawing the robot towards the goal and a repulsive potential pushing the robot away from obstacles. The main drawback with potential field techniques is their susceptibility to local minima. However, typical marine environments are sparse and local minima in our open water context are not an issue. The originality of our method is to build a so-called local potential around the boat location to take upwind and downwind sailing constraints into account. Moreover, an hysteresis potential relative to the cost of tacking and gybing is also proposed, which makes our method easy to tune according to the vehicle specifications. Our potential field approach is decomposed into two parts, a global potential field and a local potential field. The global potential field is relative to the target and to the obstacles. The local potential field is relative to the boat kinematics, the wind direction and the latest tack. 2.1. Global potential The global potential is built on the complete map once for all at the beginning of the planning process. It aims at attracting the vehicle towards the goal point and repulsing the vehicle away from obstacles. 2.1.1. Potential relative to the goal In order to attract the vehicle towards the goal point Pgoal a linear potential Pg is built for every point P of the map as follows: Pg = Gg · dist (P , Pgoal )
(1)
where Gg is the desired attractive gradient and dist (P , Pgoal ) is the Euclidean distance between P and Pgoal . Since Gg is a constant, the potential Pg looks like a cone centered on Pgoal , see Fig. 1. 2.1.2. Potential relative to the obstacles A repulsive potential Po relative to the obstacles located in Pobst is built for every point P of the map as follows: Po =
k dist (P , Pobst )
(2)
where k is a tunable scalar. This potential tends to infinity as we come close to the obstacles, which prevents the vehicle from
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Fig. 1. Illustration of the overall potential relative to three obstacles and to a goal point located at the northeast corner of the map.
Fig. 2. Scheme of the upwind and downwind no-go zones. The dotted region corresponds to the region where Ph ̸= 0.
going through the obstacles. The position of each obstacle can be known in advance or can be updated in real time by on-board navigation sensors. To avoid local minima issues, it is assumed in this framework that the obstacles (surrounding boats, islands) have been overestimated by their convex hull. 2.2. Local potential The local potential handles the specific kinematic constraints of a sailboat. It integrates three components, the so-called upwind, downwind and hysteresis potentials. The hysteresis potential is introduced to prevent the boat from tacking or gybing too frequently. The upwind and downwind components are relative to the upwind and downwind no-go zones defined as follows. 2.2.1. No-go zones To take the specific kinematic constraints of autonomous sailing robots, the so-called upwind and downwind no-go zones are defined, see Fig. 2. These two zones are exhibited respectively up to the wind direction (sector defined by the angle φup ) and down to the wind direction (sector defined by the angle φdown ). For the sake of simplicity, we assume an ideal speed polar diagram (represented by the dotted circle in Fig. 2) for the considered vehicle. This corresponds to a constant speed for the boat in all directions except in the no-go zones, where the speed is assumed to be zero. In the following definition of the local potential, it is
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Fig. 3. Close-up on the local potential around the boat. In this case, the upwind no-go zone is pointing up because the wind is coming from north.
straightforward to adapt upwind, downwind and hysteresis potentials to match a more realistic speed polar diagram. Constant coefficients Gup , Gdown and Gh respectively have only to be functions of the angle φ to respect the real shape of the speed diagram of the vehicle. 2.2.2. Upwind potential In order to take the upwind no-go zone into account the upwind potential Pup is built dynamically for each point Pw inside a window (size Wsize ) centered on the boat location P, see Fig. 2. The magnitude of Pup is a function of the angle φ between the direction
−→
of PPw and the wind direction TWA. It is linear inside the upwind no-go zone and zero outside:
Pup = Gup · dist (Pw , P ) Pup = 0
if 0 < |φ| < φup elsewhere
(3)
where Gup is the desired gradient inside the upwind no-go zone sector (see Fig. 3). 2.2.3. Downwind potential In order to take the downwind no-go zone into account the downwind potential Pdown is built dynamically for each point Pw inside the same window centered on the boat location P, see Fig. 2. The magnitude of Pdown is a function of the angle between the boat direction φ and the wind direction. It is linear inside the downwind no-go zone and zero outside:
Pdown = Gdown · dist (Pw , P ) Pdown = 0
if 0 < |φ − π | < φdown elsewhere
(4)
where Gdown is the desired gradient inside the downwind no-go zone sector. 2.2.4. Hysteresis potential In order to take the cost of gybing and tacking into account the hysteresis potential Ph is built dynamically for each point Pw inside the window centered on the boat location P. The magnitude of Ph is a function of the angle φ , the latest tack and the ability of the boat to tack or gybe. For instance, if the boat navigates with the wind coming from port, Ph will be defined at the right side of the wind direction, see Fig. 2. In this example, Ph is defined as follows:
Ph = Gh · dist (Pw , P ) Ph = 0
if φup < φ < π − φdown elsewhere
(5)
where Gh is the desired gradient of Ph . This way, only one parameter has to be set up to fit the cost of gybing and tacking.
2.2.5. Practical considerations Once the local potential has been built and added to the global potential, a gradient descent is classically carried out on the overall potential Pt = Pg + Po + Pup + Pdown + Ph to find the new heading for the boat. In practice, a profile Pp : [0, 360] → R corresponding to the potential Pt around the boat location P is directly computed along a ring of radius R centered in P, without the use of the square window previously described. This window has been introduced for the sake of clarity in order to match the potential field framework, which usually uses a potential function defined on the whole map. From now on, we will only refer to the profile function Pp to compute the optimal heading ϕ . Logically, the optimal heading ϕ for the next move is the angle corresponding to the global minimum of Pp . Note that the radius R of the ring is defined as a function of the expected size of obstacles. It is chosen to be smaller than the minimum size of possible obstacles. In simulation, the navigation process is stopped when the boat arrives in the vicinity of the goal point. Precisely, the stop criteria is defined as follows: dist (P , Pgoal ) ≤ R. In experimentations, the profile Pp and the optimal heading ϕ are continuously computed. As a precaution, the heading ϕ is smoothed to minimize the influence of sensor noise before being sent to the control system. 2.3. Conclusion The algorithm is based on the extensively used artificial potential field method, which we adapted to take the so-called upwind and downwind no-go zones into account. These specific sailing constraints are handled by a so-called local potential. This mathematical construction is built in the neighborhood of the boat location and it is rebuilt after each displacement of the boat according to the wind direction and the latest tack. This updating strategy for the local potential gives the whole navigation algorithm the property to be truly reactive to changes in the (perception of) the environment. The presented navigation algorithm is a standalone method. It will be implemented on its own on simulated environments as well as on a real experimental platform in the next sections. 3. Simulation results In this section, our navigation method will be tested under various scenarios using numerical simulations. First, the influence of static wind configurations will be analyzed assuming the presence of obstacles. Second, navigation under variable wind conditions will be simulated. The coherence and realism of the resulting trajectories will eventually be discussed. 3.1. Simulated environment For the sake of clarity, the simulated environment is assumed to be static (obstacles are fixed) and completely known (obstacles are mapped without uncertainty). Besides, the wind is assumed to be constant in direction as well as in velocity. However, since our local potential is incrementally built as a function of the visible wind and obstacles around the boat location, this reactive navigation approach holds for dynamic environments and can be implemented without any change on real systems (this will actually be the subject of the next section). In the following simulations, the default parameters for the potential have been set up as follows: Gg = 3, k = 100, Gup = 10, Gdown = 5, Gh = 2, φup = 45°, φdown = 30°.
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Fig. 4. Trajectories computed with winds coming from the southwest and west.
Fig. 6. A trajectory computed under spatially variable wind conditions.
Fig. 5. Trajectories computed with the wind coming from the northeast using different hysteresis potentials. In red Gh = 3, in blue Gh = 2, in black Gh = 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. A trajectory computed under spatially variable wind conditions in the presence of obstructing obstacles.
3.2. Downwind and abeam navigation Two trajectories exhibited by the potential field based navigation algorithm for winds coming from the southwest and from west are depicted in Fig. 4. In the trivial case of wind coming from the west, the sailboat navigates abeam and it reaches the target directly while avoiding obstacles without any difficulty. In the case of wind coming from the southwest, the optimal trajectory in respect of the downwind no-go zones is more complex. The boat avoids two obstacles and executes three gybes on its way to the goal point. In both cases, downwind and abeam scenarios, the simulated sailboat successfully reaches the target while respecting the wind-related constraints and circumnavigates the obstacles.
The amplitude and number of gybes and tacks are a function of the cost of these manoeuvres. This cost may vary according to vehicle dynamics, team efficiency, state of the sea, etc. 3.4. Navigation under spatially variable wind conditions In this simulation, the wind direction varies from west to east along the horizontal axis. In the two following figures (Figs. 6 and 7), the wind directions are represented by arrows. The trajectory depicted in Fig. 6 bends to the east as the wind turns from west to north up to a point where a tack becomes necessary to reach the goal point. The trajectory depicted in Fig. 7 is similar to the previous one apart from the fact that, in this case, the boat has to avoid a barrier of obstacles on its way to the target.
3.3. Upwind navigation
3.5. Conclusion
A trajectory solution exhibited by the potential field based navigation algorithm for a wind coming from the northeast is depicted in Fig. 5. Several hysteresis potentials have been tested. The red trajectory has been computed with Gh = 3, the blue trajectory has been computed with Gh = 2 and the black trajectory has been computed with Gh = 1. Two, three and seven tacks have been respectively executed to reach the goal point.
The presented navigation technique provides coherent trajectories in terms of kinematic constraints for a sailboat. Trajectories follow admissible headings regarding the upwind and downwind pre-defined no-go zones. The amplitude and number of tacks and gybes are controlled by the hysteresis potential. This parameter has to be chosen to suit the real cost of these manoeuvres. Besides, in this potential field framework, the attractiveness of the goal point
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Fig. 9. Software architecture of the prototype.
2. a wind vane coupled with an anemometer for wind direction and wind speed, 3. a potentiometer fixed on the mast to measure the mainsail angle. In this hardware architecture, a PC-104 and a microcontroller boards have been used to manage all the electronic devices. Two communication modes are available. A ‘‘manual mode’’, which allows a human operator to remotely control the boat via a radio or a WiFi channel, and an ‘‘autonomous mode’’, which lets the boat navigate on its own. For safety reasons, the boat automatically switches to an emergency state in the case of loss of the radio channel either in manual or in autonomous mode. 4.1.2. Software architecture From a software point of view, the architecture of our robot can be split in four parts as depicted into Fig. 9:
• a high-level navigation module, where our potential based Fig. 8. The reduced-scale autonomous sailboat prototype of the laboratory.
and repulsiveness of obstacles are easy to tune using only two independent parameters. 4. Experimental results In this section, our path planning approach will be tested under realistic conditions on a lake using a reduced-scale autonomous sailboat. First, we will describe both the hardware and software architecture of this sailboat prototype and, second, a sample run performed during these trials will be presented. 4.1. Sailboat prototype To carry out the following field trials, an autonomous sailboat prototype has been built. We started from an existing off-the-shelf reduced-scale model of a sailboat, which we have equipped with sensors and computers to make it fully autonomous. 4.1.1. Hardware architecture The prototype is depicted in Fig. 8. It is a reduced-scale sailboat with the following specification: 1.38 m long, 2.20 m high and 0.36 m wide. The main advantage of this vehicle is to behave similarly to a real boat while being easy to deploy in the test field. The original rudder and sail actuators of this boat have been kept and some electronic devices and sensors have been added for our robotic purposes. The sensors we used are: 1. an inertial measurement unit (IMU) coupled with a GPS receiver to provide heading, roll and pitch of the boat along with its GPS coordinates,
algorithm has been implemented. Parameters of the algorithm are: Gg = 3, k = 100, Gup = 10, Gdown = 5, Gh = 2, φup = 60°, φdown = 15°; • a low-level control module that controls rudder and sail angles according to the heading reference coming from the navigation module; • the sailboat reacts to the actuators (rudder and sails) and to the environment (wind, state of the water surface for instance); • a so-called perception module, which gathers both internal and environmental data. Internal data include sail and rudder angles, heading, roll, pitch and absolute position of the boat, some status data such as battery, sensor and actuator states. Environmental data include wind direction and wind speed. The closed-loop control of the vehicle is achieved by the lowlevel module. This system controls the rudder angle using a classical PI algorithm. The control algorithm for the sails is more complex because we only control the length of the mainsheet, so we only control the maximum angle of the sails (the mainsail and the headsail are linked together in our boat). However, since the attitude and speed of the boat, the wind characteristics and the mainsail angle are known (respectively thanks to an IMUGPS, a wind vane-anemometer and a potentiometer), the control algorithm for the sails has been empirically tuned to maximize the speed of the boat while guaranteeing a safety roll margin to prevent the boat from capsizing. In the following experiments, the roll amplitude is not supposed to exceed 40°. 4.2. Field trials A series of field trials have been carried out on a lake near Paris, France. Fig. 10 shows a trajectory corresponding to an autonomous navigation of our sailboat prototype for seven and a half minutes. This run has been selected amongst many others because it
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Fig. 10. Example of a run during the field trials at Creteil near Paris, France. Fig. 12. Comparison between actual heading and heading reference.
Fig. 11. Apparent wind speed (top) and apparent wind angle (bottom) during the run.
illustrates all the cases of interest in autonomous sailing: upwind, downwind and sidewind navigations. The boat was launched from the pier and had to reach the first waypoint (WP1) located on the northeast corner of the figure. During this test, the direction of the prevailing wind was westnorthwest, this is the reason why one tack was necessary to reach the first admissible area. Admissible areas have been defined as 10 m discs around the waypoints to take GPS uncertainty into account. On Fig. 10, they are represented by blurred surfaces around the waypoints. After reaching WP1, the boat automatically turned towards WP2. This navigation configuration is trivial because WP2 does not lie in any of the no-go zones of the robot. After reaching WP2, the boat headed back to the pier by pointing towards WP3 with the wind on the beam. One can notice that the boat slightly veered off course to starboard at mid-distance between WP2 and WP3. This is due to a wind shift at this moment of the navigation, see the apparent wind speed (AWS) on top of Fig. 11. Besides, Fig. 11 shows that AWS does not exceed 2 m/s during the run. It is 1.1 m/s on average. Fig. 11 also gives an insight of the apparent wind angle (AWA) during the run. In Fig. 12, the actual heading of the boat is compared to the heading reference computed by the navigation module. The heading follows the reference well, with a small delay of one to ten seconds. The first waypoint is reached at time t = 289 s, WP2 at t = 375 s and WP3 at t = 451 s.
Fig. 13. Close-up on the tack manoeuvre between 270 and 280 s and on some heading reference variations around 300 s.
A close-up of heading versus heading reference between 265 and 310 s is given in Fig. 13. A tack is performed exactly between 270 and 280 s. This means that the control system needed ten seconds at this moment of the navigation to complete this manoeuvre. Around t = 300 s some fluctuations of the heading reference can be observed. These are due to the variations of AWA at the same period, see Fig. 14. Fig. 15 shows that the boat behaves safely because the roll amplitude never exceeds 40° and the pitch amplitude never exceeds 27°. 4.3. Conclusion A reduced-scale prototype has been developed and allowed us to carry out some experimental tests under real wind conditions. Our navigation algorithm successfully achieved its task, which was to safely drive the boat to three predefined waypoints without any human intervention. The average wind direction (300°) during this run was not favorable for a direct navigation towards the first waypoint. This explains why the navigation module routed the boat to the north of the target before controlling a tack back to its precise location. Navigation to the second and third waypoints has been performed without any major difficulty apart from a small deviation due to a wind change on the way back to the pier. It
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Fig. 14. Close-up on some variations of AWA around t = 300 s.
Fig. 16. A view of the full-size sailboat prototype during the first trials on the river Erdre near Nantes, France.
Fig. 15. Roll and pitch recorded during the run.
appears that the proposed potential field technique is reliable and robust to wind disturbances. The heading control of the boat is efficient because the reaction time never exceeds ten seconds, even in the worst case of a tack manoeuvre. The boat navigated at 0.4 m/s on average during this run while respecting safety margins for roll and pitch amplitudes. 5. Conclusion and future work In this paper, a novel method for the navigation of autonomous sailboats has been presented. This method, based on the potential field framework, is a truly reactive navigation method as it reacts to spatially and time varying wind conditions as well as detected obstacles in real-time by recalculating an optimal heading periodically. This method has been validated using numerical simulations in the presence of obstacles under various wind configurations. To conclude this work, field trials, carried out on a lake using a reduced-scale prototype, have successfully demonstrated the capabilities of our technique for safely driving autonomous sailing robots. In the perspective of an open water exploitation of this reactive navigation method, some additional tests are already planned. First, we need to test our algorithm in the presence of obstacles. Since our reduced-scale sailboat is not equipped with any visual or acoustic sensors yet, a set of virtual obstacles will be arbitrarily added to the embedded map of the environment. Second, a full-size
prototype is currently under development in cooperation with a fluid mechanics laboratory1 and a robotics company2 (see Fig. 16). This 3.6 m long sailboat is designed to embed navigation sensors (IMU, GPS, acoustic wind vane and anemometer) as well as perception sensors (sonar, hydrophones and panoramic camera) for obstacle detection. It will use a wind turbine and a solar panel to achieve energetic autonomy. Preliminary tests have been carried out on a river near Nantes, France, during which the sailboat has successfully been remotely controlled. References [1] J. Manley, Unmanned surface vehicles, 15 years of development, in: MTS-IEEE Conference OCEANS 2008, Quebec City, Canada, 2008, pp. 1–4. [2] C. Sauzé, M. Neal, A neuro-endocrine inspired approach to long term energy autonomy in sailing robots, Towards Autonomous Robotic Systems, TAROS 2010 (2010) 255–262. [3] A. Pascoal, P. Oliveira, C. Silvestre, L. Sebastiao, M. Rufino, V. Barroso, J. Gomes, G. Ayela, P. Coince, M. Cardew, A. Ryan, H. Braithwaite, N. Cardew, J. Trepte, N. Seube, J. Champeau, P. Dhaussy, V. Sauce, R. Moitie, R. Santos, F. Cardigos, M. Brussieux, P. Dando, Robotic ocean vehicles for marine science applications: the European ASIMOV project, in: MTS-IEEE Conference OCEANS 2000, vol. 1, Providence, RI, USA, 2000, pp. 409–415. [4] J. Almeida, C. Silvestre, A. Pascoal, Cooperative control of multiple surface vessels in the presence of ocean currents and parametric model uncertainty, International Journal of Robust and Nonlinear Control 20 (14) (2010) 1549–1565. [5] M. Caccia, R. Bono, G. Bruzzone, E. Spirandelli, G. Veruggio, A. Stortini, G. Capodaglio, Sampling sea surfaces with SESAMO: an autonomous craft for the study of sea–air interactions, IEEE Robotics and Automation Magazine 12 (3) (2005) 95–105. [6] J. Curcio, J. Leonard, A. Patrikalakis, SCOUT—a low cost autonomous surface platform for research in cooperative autonomy, in: MTS-IEEE Conference OCEANS 2005, vol. 1, 2005, pp. 725–729. [7] P. Mahacek, R. Kobashigawa, A. Schooley, C. Kitts, The WASP: an autonomous surface vessel for the University of Alaska, in: MTS-IEEE Conference OCEANS 2005, vol. 3, 2005, pp. 2282–2291.
1 Fluid Mechanics Laboratory, Ecole Centrale de Nantes, Nantes, France. 2 Robosoft, Bidart, France.
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C. Pêtrès recieved his Ph.D. in Electrical Engineering in 2007 from Heriot–Watt University (Scotland). He worked as a Researcher in machine learning for the NATO Undersea Research Centre (NURC, Italy). He is the inventor of an inertial system that localizes and guides blind people in the subway. This work has been carried out under a post-doctoral contract at the French Atomic Energy Commission (France). He also worked as a post-doctoral Researcher at the Intelligent Systems and Robotics Institute (ISIR-CNRS-UMR 7222, Pierre et Marie Curie University, France) on the navigation of autonomous sailboats. He is currently a Contract Lecturer at Pierre et Marie Curie University. M.-A. Romero-Ramirez received a degree in Electronic Engineering from the Panamericana University (Aguascalientes, Mexico) in 1999, an M.Sc. degree from the Instituto Tecnolgico y de Estudios Superiores de Monterrey (ITESM, Mexico) in 2002 and a Ph.D. from Pierre et Marie Curie University (UPMC, France) in 2012. From October 2007 to February 2012, he was involved in a research project on autonomous sailboat guidance. His primary research interests include artificial potential fields, optimization algorithms, fuzzy logic controllers as well as electronics for on-board systems. F. Plumet is an Associate Professor at University of Versailles St Quentin (UVSQ). He holds his research activities at the Intelligent Systems and Robotics Institute (ISIR-CNRS-UMR 7222, Pierre et Marie Curie University). His research interests are the control of autonomous systems interacting with their environment such as assistive devices for rehabilitation, articulated rovers on rough terrain or robotic sailboats. He received an M.Sc. degree in Electrical Engineering in 1987 and a Ph.D. in Robotics in 1992 from Pierre et Marie Curie University.