Jurnal Teknologi A MODIFIED ATIFICIAL POTENTIAL FIELD METHOD FO IVEINE OBSTACLES AVOIDANCE Mei Jian Hong, M.. Arshad* Underwater, Control and obotics esearch Group (UCG), School of Electrical and Electronic Engineering, Engineering Capus, Universiti Sains Malaysia(USM), Penang, Malaysia Full Paper Article history eceived 15 Noveber 216 eceived in revised for 2 March 216 Accepted 5 April 216 *Corresponding author eerizal@us.y Graphical abstract Abstract This paper presents a odified artificial potential field (APF) based ethod for an Autonoous Surface Vessel (ASV) obstacles avoidance in a dynaic riverine environent. The APF ethod is cobined with a balance control schee to achieve river tracking and obstacles avoidance siultaneously. The APF ethod is further odified odification to coply with arine collision avoidance regulations (COLEGs). The overtaking and head-on scenarios are siulated in MATLAB platfor. The siulation results are copared with other APF ethods to prove that the proposed ethod is efficient for the ASV riverine navigation. Keywords: Artificial potential field; autonoous surface vessel; obstacles avoidance; COLEGs 216 Penerbit UTM Press. All rights reserved 1. INTODUCTION Sae as other unanned systes, Autonoous Surface Vessels (ASVs) are used to accoplish tedious or dangerous tasks in environents that are not suitable for huan. They are able to perfor long tie, wide area and low cost ocean engineering research, coercial and ilitary work instead of people, such as reote sensing, ocean surveillance, ocean apping, weather prediction, etc. The autonoy level of the ASV is deterined by the navigation, guidance and control (NGC) syste. Since the working environent of the ASV is generally with unknown or dynaic factors, obstacles detection and avoidance (ODA) syste plays an indispensable role in the NGC syste. Collision avoidance (CA) is the first priority requireent of the full autonoy ASV. It is orted that huan error operations are the ain reasons of the incidents, which were preventable. Thus the collision avoidance syste is essential for both anned and unanned surface vessels. On one hand, it is necessary for ASV to sense the environent and plan a collision free path; on the other hand, it is able to work as an ai or warning syste to advise crew the potential collision. Path planning ethods can be divided into three classes, i.e. global path planning, local path planning and hybrid path planning. Global path planning refers to the prior known environent inforation, in which the path is planned offline to find an optial or suboptial path. Local path planning refers to the unknown or partially known environent inforation, which eans that all the environental inforation is obtained by onboard sensors. The path is planned online with a reactive way. The third class is hybrid ethods, which refers to the rough known environent with dynaic or uncertain objects. The path is first planned offline based on the prior known inforation to guide the robot. eactive obstacles avoidance ethods will work when the robot encounters dynaic objects. The local path planner is necessary for the unanned syste that works in a dynaic environent, which eans that it is able to avoid both static and dynaic obstacles. Artificial potential field (APF) ethod, proposed by Khatib in1986 [1], is one of the ost widely applied local path planning ethods because of its siplicity and effectiveness. It uses the virtual ulsive and attractive potential field to achieve obstacles avoidance and goal tracking. To ake this ethod applicable to the dynaic obstacles avoidance, Ge and Cui [2] took into account the relative velocities to perfor dynaic obstacles avoidance and soft 78: 6-13 (216) 67 73 www.jurnalteknologi.ut.y eissn 218 3722
68 Mei Jian Hong & M.. Arshad / Jurnal Teknologi (Sciences & Engineering) 78: 6-13 (216) 67 73 landing. Jaradat M A K et al. proposed a fuzzy logic expert syste to realize the static and dynaic obstacles avoidance with only relative position inforation [3], which reduced the requireent of onboard sensors. This ethod also solved the local inia proble of APF. Yu et al. odified the APF ethod by using potential field intensity to lace force vector and they proposed an added potential field to solve the local inia proble [4-6]. To iprove the autonoy level of ASV, soe scholars incorporated the arine traffic rules - The International egulations for Preventing Collisions at Sea 1972 (COLEGs) into the NGC syste. Naee et al. Designed guidance syste by line of sight coupled with a anual biasing schee to generate COLEGs copliant routes [7]. This ethod is applied to a dynaic odel of the ASV and the siulation results are copared with a DPSS algorith in an environent with both static and dynaic obstacles. Benjain et al. developed an interval prograing based ultiobjective optiization approach in a behaviourbased control fraework to resent the COLEGs rules, and this ethod is ipleented and verified with ultiple ASVs [8]. The ai of this paper is to develop an obstacle avoidance algorith that copliant with COLEGs for the riverine ASV syste. The ASV is expected to track along the centerline of the river with the ability of obstacles avoidance, as illustrated in Figure 1. The riverbank lines are extracted with iage processing approach and used to navigate the ASV by a balance control schee to ake it track along the centerline of the river, which were discussed in previous papers [9-11]. Dynaic obstacles avoidance is achieved by applying the ethod proposed by Ge and Cui [2]. Moreover, we odified Ge and Cui s ethod to integrate COLEGs into the path planner. Maritie Organization (IMO) as navigation rules to be followed by ships and other vessels at sea to prevent collisions between two or ore vessels [12]. Both the anned and unanned ships should fulfill the arine traffic rules when travelling on the waterway. The COLEGs consists of five parts and 38 rules. Part A: General is the regulations on the application and responsibility. Part B: Steering and sailing regulates the rules of arine crafts navigation. Part C: Lights and shapes regulates the use of lighting signals. Part D is Sound and light signals and Part E is Exeption. ules 13-15 in Part B regulate three scenarios, i.e. overtaking, head-on and crossing, which are as follows [12]. ule 13. : An overtaking vessel ust keep out of the way of the vessel being overtaken. ule 14. situations: When two power-driven vessels are eeting head-on both ust alter course to starboard so that they pass on the port side of the other. ule 15. Crossing situations: When two power-driven vessels are crossing, the vessel which has the other on the starboard side ust give way and avoid crossing ahead of her. Besides, ule 9 regulates the narrow canal waterway, such as riverine environent. ule 9. Narrow channels: A vessel proceeding along a narrow channel ust keep to starboard. Sall vessels or sailing vessels ust not ipede (larger) vessels which can navigate only within a narrow channel. Ships ust not cross a channel if to do so would ipede another vessel which can navigate only within that channel. In suary, the ASV has to ake an evasive anoeuvre and avoid the encountered obstacles fro starboard side. 3. MODIFIED ATIFICIAL POTENTIAL FIELD METHOD FO ASV OBSTALCES AVOIDANCE 3.1 Artificial Potential Field Figure1 View of Kerian iver fro Google Map Organization of the paper is as follows. The COLEGs rules are introduced in the second section. The odified APF ethod for ASV navigation is presented in section 3. The siulation results and discussions are addressed in section 4. The final section presents conclusions and future work. 2. MAINE TAFFIC ULES - COLEGS The International egulations for Preventing Collisions at Sea 1972 (COLEGs) is established by the International The artificial potential field ethod is illustrated in Figure 2. obot F Fatt Obstacle Figure 2 Artificial potential field illustration Goal The robot is attracted by the goal and ulsed by the obstacles. Equations resenting the virtual attractive and ulsive force are as follows.
69 Mei Jian Hong & M.. Arshad / Jurnal Teknologi (Sciences & Engineering) 78: 6-13 (216) 67 73 1 1 Kr ( ) d d ( ) 2 2 F X ( d( X, Xo) d) ( d d) d d Fatt ( X) Ka d( X, XG) (2) where F is ulsive force, d( X, ) X is distance fro o obstacle to robot, d is a distance threshold which only works when d( X, X ) d, d is the iniu safety o distance to avoid collision, K is a ulsive potential r field constant; F att is attractive force, and K is attractive a potential field constant, d( X, X ) is the distance fro robot to the goal. Therefore the resultant force is Fres F ( X) Fatt ( X) (3) Ge and Cui [2] proposed a odified APF ethod to ipleent dynaic obstacles avoidance, which involved relative velocity in the ulsive potential equation. F (, ) p v (4) where F, (, ) ( ) 1 F 2 p pobs vo o and vo notdefined, vo and s( p, pobs) ( vo) F F vo (1 ) n p p V a 1 2 ( s(, obs) ( O)) v v G ax O O 2 2 O s( p, pobs ) aax ( s( p, pobs ) ( vo)) where P denotes the position, V denotes the velocity, ρ denotes the obstacle influence range, and η denotes a constant paraeter. 3.2 Balance-APF Hybrid Method For the case in this paper, there is no goal for ASV to track and the ASV is expected to track along the centerline of the river. The ASV should be attracted by the centerline of the river. However, the centerline of the river is virtual and cannot be detected by ASV. Therefore, the balance control schee is eployed to lace the attractive potential in Equation (2) to perfor river tracking. The principle of the balance control schee is denoted in Equation (7), which uses a coparison of distances fro left and right side riverbanks to ake sure that the ASV track along the centerline of the river. turnleft, ( DL D) (7) turnright, ( DL D) keepcourse, ( DL D) where D L is distance fro ASV to left riverbank, and D is the distance fro ASV to right riverbank, K is a distance coefficient. Equation (7) shows that, if ASV is on the centerline of the river ( ( D L D ) ), it will keep the course; if the ASV is closer to the left side of riverbank ( ( D L D ) ), it will turn left; if the ASV is closer to the right side of the riverbank, it will turn right. The ASV in this paper is oving with a constant speed of 2/s, which eans that the speed of ASV is not controlled by the ulsive and attractive force. The river tracking and obstacles avoidance are perfored by changing the heading of the ASV. Therefore the direction of ulsive force and attractive force is O n att (1) (5) (6) extracted to control the heading of ASV, while the agnitudes of the forces are abandoned. As presented above, the river centerline tracking is achieved by the balance control schee. The heading control law is expressed in Equation (8), which can be used to lace the Equation (2) to perfor river tracking and obstacles avoidance task. In this way, the resultant heading of ASV is deterined by the direction of the resultant force of Equation (3). K ( D D ) (8) att att L 3.3 COLEGs Copliant Path Planning Since the ASV is travelling with a constant speed, only the heading angle is affected by ulsive force. The Equation (1) and Equation (7) are cobined to guide the ASV in the river. Katt ( DL D ) angle( F ( X)) d d (9) heading Katt ( DL D ) d d where angle( F ( X )) is the direction extracted fro the ulsive potential; d is the distance fro ASV to the obstacle; d is an influence range of obstacle, which eans that the obstacles will ulse the ASV away if and only if the distance d d. Otherwise, the obstacles will not affect the ASV. It can be seen fro Equation (9) that when ASV is out of the influence range of obstacles, it is navigated by the balance control schee. When ASV enters the influence range of obstacles, heading angle of ASV is the resultant of balance control and ulsive function. The direction angle extracted fro Equation (1) can be negative or positive depending on the location of the obstacle. When the ulsive direction angle is positive, the ASV will pass by the obstacle fro port side; when the ulsive direction angle is negative, the ASV will pass by the obstacle fro starboard side. Thus we can force the ulsive direction angle to be negative, then the ASV will turn starboard side when enters influence range of obstacle, which is indicated in Equation (1). K ( D D ) abs( angle( F ( X ))) d d (1) att L heading Katt ( DL D ) d d where abs is the absolute value of angle( F ( X )). In addition, Equation (1) is an iterative process to generate an evasive aneuver action until satisfied COLEGs. 4. ESULTS AND DISCUSSIONS The proposed odified COLEGs copliant APF ethod is ipleented in MATLAB environent and Marine Syste Siulator GNC toolbox which is developed by Fossen and Perez [13]. Two scenarios of head-on and overtaking are perfored for ASV path planning in a riverine environent with both static and dynaic obstacles. In addition, the new proposed ethod is copared with the existing ethod (Ge and Cui) [2] to verify the perforance of the proposed ethod.
7 Mei Jian Hong & M.. Arshad / Jurnal Teknologi (Sciences & Engineering) 78: 6-13 (216) 67 73 As discussed above, (Ge and Cui) [2] proposed a odified APF ethod which took into account the relative velocities between robot and obstacles and goal. The results showed that this ethod was suitable for obstacles avoidance in a dynaic environent. However, the direction of evasive anoeuvre is uncertain when the robot avoids the obstacles, which does not fulfil the arine traffic rules. Thus we odify the ethod to ake it copliant with arine traffic of COLEGs. Figures 3 to 6 present the coparison of the siulation results of Ge and Cui s ethod and the proposed ethod in this paper. In general, the three priary rules in COLEGs ust be integrated in NGC syste are ule 13: overtaking, ule 14, and ule 15 Crossing. However, the ule 9 regulates a situation that Ships ust not cross a channel if to do so would ipede another vessel which can navigate only within that channel, which is exactly a regulation for narrow channel waterway, such as a river. Thus, only two scenarios, head-on and overtaking scenarios are discussed in this paper. To ake the siulation ore practical, we choose a part of a real river ap as the riverine environent. This river is located in Nibong Tebal, Penang, Malaysia. It is near to Engineering Capus, Universiti Sains Malaysia, with the nae of Sungai Kerian. The length of this part of the river is 1, with the axiu width of 166 and iniu width of 56. View of the river is obtained fro Google ap and the riverbank lines are extracted by iage processing approach. The ASV is expected to be navigated by the proposed path planning ethod with capability of keeping in the center of the river and obstacles avoidance. The siulation sapling tie is.1s. The ASV is designed with constant speed of 2.5/s, thus only heading angle is changed by the proposed path planner. The ASV platfor and odel has been discussed in previous paper [11]. 4.1 Coparision of Scenario Figures 3(a) to (c) show the overtaking scenario of ASV navigation process in the river by Ge and Cui s ethod. There are one static obstacle and one dynaic target ship in the river, which the ASV needs to avoid the. The blue line in Figure 3 is the trajectory of ASV, and the red circle is static obstacle, and the red line is the trajectory of target ship. The static obstacle is circle shape with a diaeter of 1 and located on (44, -215). The target ship has the sae size with the ASV starts fro (2, - 24) and it oves with a constant speed of.7/s. Both the ASV and the target ship are guided by balance control schee to track along the centerline of the river fro west to east, but the ASV is able to avoid encountered obstacles while the target ship is not. The ASV starts fro the position of (, 1) and its initial heading angle is. At the beginning, the ASV is far fro the static obstacle and target ship, thus its heading angle is deterined by the balance control. Figure 3 (a) shows the navigation state when t=1s. We can see that the ASV is tracking along the centerline of the river and not affected by the static obstacle and target ship. At tie t=17.5s, the ASV encounters the target ship and needs to overtake the target ship. As discussed above, the evasive anoeuvre is not certain to ake the decision that the ASV should bypass the obstacle on port or starboard side. The evasive anoeuvre depends on the position of the obstacle. In this case, the ASV overtakes the target ship on port side. However, this does not obey the arine traffic rules of COLEGs. After overtaking the target ship, the ASV oves on until it encounters the static obstacle. Sae with the case that the ASV encounters the target ship, the ASV also bypasses the static obstacle on the port side and then oves on. As shown in Figure 3(c), the static obstacle is on the path of ASV and target ship, however, the target ship has no ability of obstacles avoidance. This causes a collision when the target ship encounters the static obstacle. 1-1 -2-3 1 2 3 4 5 6 7 8 9 1 1-1 -2 (a) t=1s -3 1 2 3 4 5 6 7 8 9 1 1-1 -2 (b) t=17.5s -3 1 2 3 4 5 6 7 8 9 1 (c) Coplete navigation (d) Figure 3 scenario of ASV navigating in river with ethod in [2] Figure 4 shows the siulation results of the proposed APF ethod which is copliant with COLEGs. All the paraeters and condition are sae with the results of Figure 3 but the evasive anoeuvre is forced to be
71 Mei Jian Hong & M.. Arshad / Jurnal Teknologi (Sciences & Engineering) 78: 6-13 (216) 67 73 certain to turn starboard side when ASV encounters obstacles, which is deterined by Equation (1). The initial states of Figure 4 are exactly sae with Figure 3, which can be seen in Figure 4(a). As shown in Figure 4(b), at tie t= 17.5s, the ASV encounters the target ship. Since the arine traffic rules of COLEGs are incorporated in the path planner, the ASV overtakes the target ship on starboard side. After overtaking the target ship, the ASV oves on and also bypasses the static obstacle on the starboard side, which is shown in Figure 4(c). Sae with Figure 3, the siulation stops when the target ship collides with the static obstacle. 1-1 -2-3 1 2 3 4 5 6 7 8 9 1 1-1 -2 (a) t=1s -3 1 2 3 4 5 6 7 8 9 1 1-1 -2 (b) t=17.5s -3 1 2 3 4 5 6 7 8 9 1 (c) Coplete navigation (d) Figure 4 scenario of ASV navigating in river with proposed ethod ASV tracks along the centerline of river fro west to east with constant speed of 2.5/s. Since the ASV and the target ship track along the centerline of the river with opposite direction, the paths of the ASV and the target ship are syetrical about the centerline of the river. The heading controller in this paper is a PD controller, thus the ASV and the target ship are roughly tracking along the centerline of the river, and the trajectories of the ASV and target ship are not overlapped. For this reason, the target ship is on the port side the ASV when they encounters. The ASV will autoatically ake the evasive anoeuvre fro starboard side. To ake a ore obvious coparison, we changed both of the trajectories of ASV and target ship. The path of the ASV is oved above with 3 eters and the path of the target ship is oved below with 2 eters to create a ore challenging situation. In such way, the target ship will be on the exact opposite direction when they encountered. Besides, the trajectories of the ASV and target ship are partially overlapped. As shown in Figure 5(a), at tie t=23s, the ASV first encounters the static obstacle and bypasses the static obstacle fro port side. At t=29.7s, the ASV encounters the target ship, and the ASV bypasses the target ship fro port side due to the relative location. Fro Figure 5(c) we can see that the evasive anoeuvre of ASV appears overshoot when ASV avoids the target ship. This is because the relative velocity of head-on scenario is greater than the relative velocity of overtaking. Therefore the second ite of Equation (4) is greater, which causes a bigger evasive anoeuvre. The static obstacle is on the path of the target ship, thus the siulation stops when the target ship collides with the static obstacle. Figure 6 presents the siulation results to copare with Figure 5. Sae as stated above, the ASV akes a starboard evasive anoeuvre when it encounters the static obstacle at t=23s, which is shown in Figure 6(a). At tie t= 3s, the ASV encounters the target ship and bypasses it fro starboard side. The siulation also stops when the target ship collides with the static obstacle. Coparison of the siulation results in overtaking and head-on scenarios shows that the proposed APF ethod integrates the arine traffic rule-colegs in the path planner. This path planner guarantees that the ASV is able to avoid both of the static and dynaic obstacles. 4.2 Coparision of Scenario Figures 5 to 6 show the coparison of the siulation results of head-on scenario with Ge and Cui s ethod and the proposed ethod in this paper, respectively. The static obstacle locates on (44, -215). The target ship starts fro the location of (1, -13) and tracks along the centerline of the river fro east to west with a constant speed of 1.5/s. The initial pose of ASV is still in the position of (, 1) and heading angle of. The
72 Mei Jian Hong & M.. Arshad / Jurnal Teknologi (Sciences & Engineering) 78: 6-13 (216) 67 73 1 1-1 -1-2 -2-3 1 2 3 4 5 6 7 8 9 1 (a) t=23s -3 1 2 3 4 5 6 7 8 9 1 (c) Coplete navigation 1 Figure 6 scenario of ASV navigating in river with proposed ethod -1 4.3 Discussions -2-3 1 2 3 4 5 6 7 8 9 1 1-1 -2 (b) t=29.7s -3 1 2 3 4 5 6 7 8 9 1 (c) Coplete navigation Figure 5 scenario of ASV navigating in river with ethod in [2] 1-1 -2-3 1 2 3 4 5 6 7 8 9 1 1 (a) t=23s The proposed ethod in this paper is to realize siultaneous river centerline tracking and obstacles avoidance that coplies with COLEGs. This strategy is different fro other path following and obstacles avoidance ethods. The orted paths following ethods, such as in paper [7], are based on the GPS and other global inforation to track a planned path. However, in this paper the path that the ASV needs to follow is unknown, and only the local distances fro riverbanks are used to perfor river tracking. The existing orted COLEGs copliant obstacles avoidance ethods are applied in the open sea environent. These ethods are not suitable for the riverine or the other corridor environent. The proposed approach in this paper, the balance control cobined with APF ethod, is firstly presented in riverine environent to achieve siultaneous river tracking and obstacles avoidance. In addition, this ethod can also be applied to the other corridor type environent. Fro the results we can see that, the accuracy of the river tracking is different in different parts. Fro the siulation results we cans see that the accuracy of river tracking depends on the trend of the river. For exaple, the accuracy of tracking is poor in the parts (-4) and (8-1). This is because that the river is ore curved in these two parts. In contrast, the accuracy of tracking is uch better in part (4-8) since the river is kind of straight in this part. Thus, the accuracy of tracking depends on the river environent. In addition, the arine traffic rules-colegs is regulated for navigation safety but not copulsory. The navigator of ships should judge the situation to ake sure that collisions can never occur, even when it has to breach the COLEGs rules [14]. -1-2 -3 1 2 3 4 5 6 7 8 9 1 (b) t=3s 5. CONCLUSION This paper presents a COLEGs copliant path planning ethod based on the artificial potential field for an ASV navigating in the dynaic riverine environent. The APF ethod is cobined with a balance control schee to perfor river tracking. The
73 Mei Jian Hong & M.. Arshad / Jurnal Teknologi (Sciences & Engineering) 78: 6-13 (216) 67 73 arine collision regulations COLEGs are incorporated as well in the NGC syste. Two scenarios of overtaking and head-on are siulated in MATLAB. Siulation results are copared with other existing APF ethod and it proves that the proposed ethod has a better perforance. Future work will focus on path planning in the riverine environent with ulti dynaic obstacles and the experiental ipleentation. Acknowledgeent The authors would like to express sincere thanks for the support given to this research by Hebei University, China and Universiti Sains Malaysia (USM). eferences [1] Khatib, Oussaa. 1986. eal-tie Obstacle Avoidance for Manipulators and Mobile obots. The International Journal Of obotics esearch. 5(1): 9-98. [2] Ge, Shuzhi S., and Yun J. Cui. 22. Dynaic Motion Planning for Mobile obots using Potential Field Method. Autonoous obots. 13(3): 27-222. [3] Jaradat, M. A. K., Garibeh, M. H., & Feilat, E. A. 212. Autonoous Mobile robot dynaic otion Planning Using Hybrid Fuzzy Potential Field. Soft Coputing. 16: 1153-164. [4] Yu, Z. Z., Yan, J. H., Zhao, J., Chen, Z. F., & Zhu, Y. H. 211. Mobile obot Path Planning Based on Iproved Artificial Potential Field Method. Harbin Gongye Daxue Xuebao (Journal of Harbin Institute of Technology). 43(1): 5-55. [5] Azzeri, M. N., Adnan, F. A., & Zain, M. M. 215. eview of Course Keeping Control Syste for Unanned Surface Vehicle. Jurnal Teknologi. 74(5): 11-2. [6] Oar, F. S., Isla, M. N., & Haron, H.. 215. Shortest Path Planning For Single Manipulator In 2d Environent Of Deforable Objects. Jurnal Teknologi. 75(2): 33-37. [7] Naee, W., Irwin, G. W., & Yang, A.. 212. COLEGs-based Collision Avoidance Strategies for Unanned Surface Vehicles. Mechatronics. 22(6): 669-678. [8] Benjain, M.., Leonard, J. J., Curcio, J. A., & Newan, P. M. 26. A Method for Protocol Based Collision Avoidance Between Autonoous Marine Surface Craft. Journal of Field obotics. 23(5): 333-346. [9] Jianhong, M., & Arshad, M... 213. Adaptive Shorelines Detection for Autonoous Surface Vessel Navigation. In Control Syste, Coputing and Engineering (ICCSCE). 213 IEEE International Conference on. 221-225. [1] Mei, Jian Hong and Mohd izal Arshad. 215. Modeling and Visual Navigation of Autonoous Surface Vessels. In Handbook of esearch on Advanceents in obotics and Mechatronics. IGI Global. 25 Jun 215. 662-696. [11] Hong, M. J., & Arshad, M... 215. Modeling And Motion Control Of A iverine Autonoous Surface Vehicle (ASV) With Differential Thrust. Jurnal Teknologi. 74(9): 137-143. [12] Coandant U C G.. 1999. International egulations for Prevention of Collisions at Sea, 1972 (72 COLEGS). US Departent of Transportation, US Coast Guard. Coandant Instruction M. [13] MSS. Marine Systes Siulator. 21. Viewed 51/12/15. http://wwwarinecontrolorg. [14] Capbell, S., Abu-Tair, M., & Naee, W. 213. An Autoatic COLEGs-copliant Obstacle Avoidance Syste for an Unanned Surface Vehicle. In Part M: Journal of Engineering for the Maritie Environent. Proceedings of the Institution of Mechanical Engineers. 1475921349822.