Applied Mechanics and Materials Vol

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1 Applied Mechanics and Materials Online: ISSN: , Vol. 532, pp doi: / Trans Tech Publications, Switzerland A Practical Real-time Motion Cueing Algorithm for Crane Simulator Zhu Ze 1, a *, Xiao Hanbin 1,b,Wang Guoxian 1,c, Hu Kan 2,d 1 Key Laboratory of Port Cargo Handling Technology with Ministry of Communications, PRC, Wuhan University of Technology, Wuhan , China 2 Wuhan Kema Software Company Ltd., Wuhan , China a ze_zhu@163.com, b xhbchina@126.com, c wanggx@whut.edu.cn, d hukan008@qq.com Keywords: Crane simulator; Dynamical model; Motion cueing; Real-time control Algorithm Abstract: This paper addresses motion simulation issues involved in a crane simulator with a 6-Degree-Of-Freedom platform. The crane dynamical models in terms of a range of motion equations are built for the operator cab in various main operating conditions. The ways to make the motion to be reproduced are investigated and the corresponding real-time motion cueing algorithm is proposed based on a special curve-merging approach. The algorithm is of simplified form and the needed computing time is very short, which makes it very practicable. The crane simulation system with this algorithm being adopted has been successfully developed and put into practice. The field application showed that the algorithm is able to ensure achievement of satisfied motion cueing effects. The proposed motion simulation models and the corresponding algorithm will provide significant reference value for developing similar motion simulation systems for all types of large-scale cranes or construction machinery. 0 Introduction High-performance motion simulation systems play a very important role in creating an adequate practice environment for trainees on training simulators. As one of the earliest application examples of motion control system, crane simulator can only provide simple motion simulation functions like some symbolic turbulence, tilt and shaking, with lack of complete motion control models and algorithms consistent with the visual system. With the integrated large crane simulator system [2] collaboratively developed by School of Logistics Engineering, Wuhan University of Technology and Wuhan Kema Software Co., LTD being used as the background, this paper starts from creating the dynamic model of the crane and analyzing the kinematics characteristics related to the dynamic behaviors. Then according to the basic motion cueing principles, the quayside bridge crane is then used as the investigation object to establish a range of real-time motion simulation models and develop a real-time motion simulation algorithm accordingly. It is well solved the conflict between the complexity of the models and algorithm and the real-time instant requirements of the system. 1 The operation principle of the motion simulation system In the process, time management engine is responsible for propulsion of the real-time simulation system according to the unified time slices in order to achieve the coordination of each simulation subsystem. The motion behavior of the crane operator cab is portrayed as the linear superposition of independence movements caused by the driver's various operations and random factors. The crane dynamical model and dynamical equivalent translation units generate the response curve of each All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-13/05/16,03:17:37)

2 Applied Mechanics and Materials Vol independent movement, and the time engine, within each frame, calls motion control for once to determine whether the response curve series need to be adjusted, and then inform the client via network communication. The client completes the fusion of the motion curves first, and then makes them discretized to promote the platform moving according to its own rhythm. The discretized motion curve is converted to the length change of the electric cylinders of the 6-Degree-Of-Freedom motion platform through forward and reverse solution algorithm of 6-Degree-Of-Freedom motion position [1]. 2 Analysis of the motion ingredients and modelization 2.1 The coordinate system As shown in figure 1, regarding the virtual guayside container crane as the entity, its coordinate system OXYZ of dynamic movement takes the mass of operator cab center as the origin of coordinates, the trolley walk direction as the X axis direction, the gantry walk as the Y direction, and the vertical direction as the Z axis direction. By using the plane centroid motion of 6-Degree-Of-Freedom motion platform to replace the operator cab centroid movement, we establish the needed simulation motion in the 6-Degree-Of-Freedom motion platform at reproduce reference coordinate system, in order to put the dynamic simulation in harmony with the visual output. 2.2 The dynamic model of the main motion ingredients The position change process of the crane operator cab in the virtual environment can be described as several limited alternate execution or cycle of operational condition which is determined by the loading and unloading process. The operational conditions are mainly divided into gantry walking, trolley walking, cargo lifting or falling, and down and pitch of boom, etc [3]. The position change in all kinds of working Fig. 1 Coordinate system of crane driver cabin and motion platform conditions can be viewed as the linear superposition of several limited movement ingredients. These motion ingredients can be roughly divided into two kinds. One is a kind of movement generated by starting and braking, conduct by related operating organization according to loading and unloading process, and alternating collaborative work of positive and negative directions. This movement, mainly low frequency motion, features large space scale. The other one is high-frequency vibration of small space scale. It is generated by all kinds of vibration source along with the above process or even under the condition of relative rest like standstill. (1) Big scale motion Big scale motion, in the operational process of quayside container crane, happens at the two kinds of working conditions, namely the trolley walking and gantry walking. That means walking on the X and Y directions, and it will not happen at the same time. The speed-time curve of the movement is trapezoidal curve, as shown in figure 2, which is divided into 3 segments :accelerating section (1), constant velocity section (2) and deceleration section (3). The duration of the process that starting to add (subtract) speed, stopping plus (minus) speed and of plus (minus) speed is controlled by a plus (minus) speed controller through driver's operation. In accordance with the relevant design handbook [3], the largest acceleration(deceleration)of the trolley can be 0.67 m/s 2,

3 282 Mechatronics and Applied Mechanics III and the plus (minus) speed time is about 6s;the largest acceleration(deceleration)of the gantry can be 0.15 m/s 2, and the plus (minus) speed time is approximate 8s, thus the position change of the operator cab caused by the big scale motion can be entirely confirmed. Fig. 2 Velocity and the acceleration curves of big scale motion (2)Small scale high-frequency vibration According to the dynamics analysis of the crane, by the frequency from high to low, the operator cab will slightly vibrate when encountering the following situations in the process of actual operation : (1) when running acceleration of the trolley or gantry have greatly changed; (2) when loading container lifting from the ground, a tight stop lifting and unloading; (3) when down and pitch of boom; (4) when wind has a large effects; (5) when there is a large collision, such as spreader run into gantry. Below it is the analysis of the vibration model of the operator cab when the operational gantry or trolley acceleration greatly changed, the others are similar. The operator can be regarded as doing damping vibration according to natural frequency during acceleration of starting or deceleration of stopping. Since the size of quayside container crane is large and the structure is complex, it is difficult to calculate the actual situation of this kind of damping vibration. Therefore, we consider the quayside container crane as a whole when the gantry starts or stops, and fix it with the ground. The natural frequency is calculated by gantry, as shown in figure 3. Calculate the damping motion equation assumption: the resistance is proportional to the dy velocity. That is fr v dt Application of Newton's second law: kx y my Fig.3 Simplified mechanics model of quayside container crane k 2 let m, 2,so 2 y 2 0 o 0 y y m In general, this kind of vibration is underdamping, the vibration displacement equation as: t y ( t) Ae cos( t ), ' 2 2 (1) o When it is accelerated in the equation 0, When it is slowdown 180 ; The parameter A is connected with the opening of the plus (minus) speed controller, A of the biggest plus (minus) speed and parameters are measured by the actual vibration of the quayside container crane and when the opening of the plus (minus) speed handle is not the biggest, it is discount according to the opening percentage. The gantry must be simplified as the form of figure 4, estimates K value in accordance with the relevant steel parameters and dimension of the quayside container crane, then

4 Applied Mechanics and Materials Vol Y O β=0.7 Fig 4 Under damping vibration curve for gantry acceleration process calculated o, and finally solve β. The vibration curve is shown in figure 4. The vibration displacement equation x(t) when the trolley starts or stops is the same in the form of equation(1), and parameter calculation is relatively simple, we can only take the operator cab's natural frequency. 2.3 Equivalent conversion of individual movement ingredients According to "method of oblique coordinate" [2] of the dynamic simulation algorithm, we can rely on the gravity crane trolley cart s continuous process of acceleration or deceleration, which is also of low frequency and large scale, through the rotary motion platform. If the simulated low frequency linear acceleration at X and Y plane are a x and a y, respectively, the corresponding platform Angle γ(around Y axis) and β(around the X axis)are: a arcsin( x ) arcsin( a y ) (2) g g cos Because the gantry and trolley cannot exercise at the same time, and the trolley s biggest acceleration(deceleration)is 0.67m/s2, the gantry s biggest acceleration(deceleration)is 0.15 m/s 2, and then we calculate the corresponding γ and β are about 4 and 1, respectively. In order not to let the human body detect rotating, it is needed to make the rotation speed in the human body feeling threshold value less than 3 /s [5]. Thus, if the trolley accelerates with the maximum acceleration directly, let the rotation speed as 2 /s, its motion curve can approximately using the following formula: = 2t 0<t 2 t = 4 2<t< the stop time of accelerate t1 γ= (3) = 4-2(t-t1) t1<t<t1+2 =0 t>t1+2 Fig. 5 Equivalent transformation for trolley motion curves In this way, the curve of motion curve shown in figure 3 can be equivalently replaced in figure 5. In a similar way, we can get the curve of the replacement when the gantry accelerates. 3 The real-time dynamic simulation algorithm based on curve fusion 3.1Motion commands based on the curve of the fusion When the time engine in the real-time control computer capture from the input signal that the operation condition of the crane is going to change, it will trigger an order of changing movements. Eventually the operator cab tracking combination

5 284 Mechatronics and Applied Mechanics III of the motion curve is like superposition and blend together layer by layer. And then we can define the key operating commands of the real-time operation environment to notify movement control module to start or stop one or a set of curves. Instruction form: AddLayer (a,a[],b) A is the curve type, a total of three, as described above. Array A []are all the parameters of the curve required. b is seven 0/1 label code, The first bit 0 means stopping this or that group existing curve, 1 means increase; 2 to 7 means whether this kind of curve are respectively applied to some one or a few of 6-Degree-Of-Freedom X,Y,Z,α,β and γ. 3.2 The comprehensive dynamic simulation algorithm Put the analysis above in order, and form the core algorithm of the crane dynamic simulation. This algorithm belongs to one part of of the process of the real-time control according to the beat (frame) by the main time engine. Start a new time frame; Read data from the DAQ Unit; Renew the status of the simulated crane; { Renew rendering status; Render; } { Renew audio output status; Output audio;} {Renew motion cueing status; Do case; case IsCase1=TRUE; AddLayer(2,A1[], ); case IsCase2=TRUE; case IsCase9=TRUE; AddLayer(1,A8[], ); Endcase;} if TimeIsUp=FALSE; Then Nooperation; Else Return; 3.3 Effect of algorithm implementation The algorithm above was realized on a large-scale crane operation training integrated simulation system in a company and put it into the experimental application. Practice shows that the algorithm on the precision has ensured the enough fidelity of the dynamic simulation, fully met the practical requirements of the training effect, making the simulator can replace physical crane used for the training of the new driver. 4. Conclusions Based on the configuration and operation principle of the crane motion simulator system, this paper investigates how to use the motion simulator to provide the fidelity motion cues for crane drivers when they operate the virtual crane as if it is in the actual environment. The proposed motion simulation models and the corresponding algorithm are mainly applied to the quayside crane simulators, but they will also provide significant reference value for developing similar motion simulation systems for all types of large-scale cranes or construction machinery. Reference [1] GAN Hongsheng,YIN Yuehong, LIU Weiwei, YIN Song. The design of control system of 6DOF motion platform in virtual reality environment[j]. Mechanical & Electrical Engineering Magazine, 2003,20(04): [2] DONG Xichen, ZHU Ze, WANG Guoxian, ZHOU Qiang, HU Kan. Crane Simulator Development Based on Open System and COTS Technology [J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2012,36(4): [3] Department of water transportation, Ministry of transport of the people s republic. Port machinery design manual [M]. Beijing: China Communications Press, 2001.

6 Mechatronics and Applied Mechanics III / A Practical Real-Time Motion Cueing Algorithm for Crane Simulator /