- Email: [email protected]
Generalised Steering Strategy for Vehicle Navigation on Sloping Ground
ARTICLE IN PRESS Available online at www.sciencedirect.com
Biosystems Engineering (2003) 86 (3), 267–273 doi:10.1016/S1537-5110(03)00140-5 AE}Automation and Emerging Technologies
Generalised Steering Strategy for Vehicle Navigation on Sloping Ground M.A. Ashraf; J. Takeda; H. Osada; S. Chiba Faculty of Agriculture, Iwate University, Morioka 020-8550, Japan; e-mail of corresponding author: [email protected] (Received 25 October 2002; accepted in revised form 16 July 2003; published online 13 September 2003)
An autonomous tractor guidance system for vehicle navigation on sloping ground was developed by extending a previous study in which navigation was limited to a specific gradient. A previously developed neural network vehicle model was trained along the contour lines of 0, 5, 11 and 158 sloping terrain. Using the trained models and a cost function, optimal steering angles for different ranges of deviations were sought by genetic algorithm and the optimal values were arranged in separate matrix-form reference table for each slope. The optimal steering values of the four reference tables were expressed by a third-order polynomial equation so that the equation can provide an optimal steering value for any inclination. The coefficients of the equations were tabulated in a matrix form, which is designated as a ‘general reference table’. If the slope inclination and vehicle attitude can be determined, real-time navigation of the tractor is possible using this table. An autonomous travel test was conducted on inclined surface. It was found that the developed guidance system could precisely navigate the tractor along a rectilinear contour path on 208 sloping terrain, where the mean offset was 005 m and its standard deviation was 0044 m. # 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd
1. Introduction Much of the grassland in Japan and other countries are in hilly areas where the farm tractor is used for various tasks. However, working on hilly terrain can cause discomfort to the operator, due to the effects on body alignment. This also increases the fatigue of the operator and thereby decreases the work efficiency with time. Although much research has been conducted on automatic guidance system for the farm tractor, most is concerned with flat land (Torii, 2000; Keicher & Seufert, 2000; Reid et al., 2000; Noguchi et al., 1997). Tamaki et al. (2001) studied an automatic crawler guidance system using internal sensors, on 118 sloping terrain. The lateral deviation of the crawler from the target path was less than 25 m. Bell (2000) devised an automatic tractor guidance system using a kinematic model. A biased estimation method was incorporated into the control software to compensate the effect of the slope on the vehicle motion. Torisu et al. (2002) and Ashraf et al. (2002) also conducted experiments on the automatic tractor guidance on sloping terrain. Since the vehicle dynamics on sloping ground is highly non-linear, a neural network vehicle model was used instead of a 1537-5110/$30.00
conventional mathematics-based vehicle model. The model was trained for a specific inclined surface and used a genetic algorithm to develop a steering controller. However, a neural network model can represent the vehicle motion only for that particular gradient for which it is trained. Consequently, the controller can only be used to navigate the tractor on that slope. It would be an impractical, uneconomic and time-consuming task to train a model for every variation. To produce an accurate but more generalised steering strategy, this paper deals with the development of a navigation planner, which includes: (1) development of navigation planner for different gradients, (2) development of the corresponding steering controller, and (3) generalisation of the controller.
2. Navigation planner 2.1. Vehicle model for varying gradients The structure of the neural network vehicle model developed by Torisu et al. (2002) has six input and three output variables with two hidden layers. Each hidden 267
# 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd
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pe
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Output variables
Input layer
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Nn
Fig. 1. A typical neural network model and its weight distribution: wpq ij , weight between two neurons; p & q, consecutive layer numbers; i & j, row numbers; Npi , neuron number
layer has six neurons. Each neuron remains connected with all other neurons of next layer by means of weights (synapses) (Wasserman, 1989). The behaviour of the network is determined by the strength or weights of the interconnecting neurons. A typical neural network model is shown in Fig. 1 where the weight w for each pair of interconnecting neurons is prompted. Unlike a mathematical model, the structure of a neural network model cannot itself express the system behaviour. It entails just the arrangement of the input–output variables and the interconnecting neurons of the network. A neural network must be ‘trained’ before being of use as a practical model. When it is trained for a specific gradient of land, a constant value is determined for each weight. Then the trained model can be used to express the vehicle behaviour but only for land of that specific gradient. From this view point Torisu’s model cannot represent the tractor behaviour for the slopes of varying gradients. Therefore, to develop a generalised navigation planner the neural network model was trained for the sloping land of 0, 5, 11 and 158 (Torisu et al., 2002).
2.2. Optimisation of the quadratic form cost function by genetic algorithm In automatic vehicle guidance systems, a controller is essential to guide the vehicle along desired path. Torisu et al. (2002) used the optimal control method for this purpose and designed a quadratic form cost function (Dutton et al., 1997). The optimal control masses for each slope were determined by simulation. Prior to the simulation different ranges of offset y and heading angle y were considered as the measurable system errors (Fig. 2). The weight vectors of the trained vehicle model and the cost function were used in the simulation to find the best possible (optimal) control mass for each range of error. Genetic algorithms were used as the tool of
⊗
Desired path α y θ
Fig. 2. Vehicle deviations from the desired path: y, heading angle; a, steering angle; f, slope angle; y, lateral deviation (offset)
simulation to find the optimal control mass (Torisu et al. 2002). The simulated optimal control masses (steering angle) for different sets of lateral deviation and heading angle were arranged in a matrix form reference table. This table can be used for real-time navigation of the vehicle on sloped terrains where inclinations are similar to that terrain on which the model was trained. Therefore, the optimal steering angle a was expressed as: Z a ¼ ðy; yÞ ð1Þ The choice of selecting the range of offset and heading angle is optional. Before choosing the range of deviations, however, it was assumed that: (a) when the lateral and heading deviations of the vehicle are more than 04 m and 208 respectively from the desired course, a poorly optimised steering value will not affect the system performance significantly; (b) when the range of lateral deviation is within 01–04 m and that of the heading deviation is within 5–208, a moderately optimised steering value will be rational for the system performance; (c) but when the vehicle is very near to the desired course, i.e., within 01 m lateral and 58 heading deviation, a small variation in the optimal steering value will significantly affect the system performance. Therefore, the ranges of lateral and heading deviations were chosen in three different intervals, and three separate reference tables were prepared for each gradient. The reference table, prepared for the range of 01 m lateral and 58 heading deviation, is introduced as precise; the one, prepared for the range of 03 m lateral and 158 heading deviation, is introduced as normal; and the one, prepared for beyond these ranges of deviations, is introduced as the rough reference table.
2.3. Generalisation of reference tables Without further field experiment a generalised navigation planner was developed. For this purpose the precise, normal and rough reference tables, prepared for each slope with the optimal steering angle, were collated
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into a single reference table. The collated reference table for 58 sloping terrain is shown in Fig. 3. Similar ones were also prepared for 0, 11 and 158 slopes. Table cells were numbered sequentially, each number representing a specific range of lateral and heading deviations. Focusing on part of this table, Fig. 4 shows how the table was converted into a row matrix. The row matrixes
Lateral deviation y, m 0.0
2
<-40 -40 -20
-10 -5
28 20
-21
-30 -38
-13 0.1 0.2
-21 -30
-16 -19
-13 -8
-14 -16 -13 -21
-0.06 -0.03 0.03 0.06 3 1 0 -3 -5 -7 -8 -14 6 3 1 0 -3 -5 9 7 4 3 1 -3
11 7 13 12
0
20 13
-10 -4
2 -5 7
5
Heading angle θ, deg
10
20
4
3
12
0.4 0.8 >0.8
-13 -6 -0.2 -0.1
-3
40 >40
<-0.8 -0.8 -0.4 3 -6
-4 -8
11 10 8 5 3
17 14 20 17
11
8
15
11
1
-3 -1
-6 -13
1
8
35
28
20
13
4
-6
36
34
28
20
13
4
a19 ¼ 00032f3 þ 0057f2 þ 03947f þ 8
Fig. 3. A collated reference table of optimised steering angles for 58 slope
θ° -0.1-0.06 -0.03 0.00.03 0.06 0.1 4 1 2 3 5 6 5 1 2 6 5 3 4 3 1 0 -3 -5 -7 3 1 0 -3 -5 -7 7 8 9 10 11 12 3 7 8 9 12 10 11 6 3 1 0 -3 -5 0 -3 -5 3 1 6 y, m 13 14 15 16 17 18 0 13 14 15 16 17 18 3 7 1 -3 4 9 9 7 4 3 1 -3 -3 20
21
22
23
24
11 10
19
8
5
3
1
19
20
21
22
of 0, 5, 11 and 158 slopes were arranged together and shown in Table 1. In this table, there is no information about the optimal steering values for the land, whose inclinations are in between 0–58, 5–118, 11–158 and above 158. Optimal steering values for the intermediate inclinations can be obtained by developing mathematical relationship between the existing optimal-steering values with the slope inclinations. Therefore, for each column of Table 1, a mathematical expression was derived by interpolating a cubic-polynomial (Wylie & Barrett, 1995) between the optimal steering values of the four inclined surfaces. Values of the unknown polynomial coefficients were derived by linear algebra. From each equation, a pattern of optimal steering angle with the variation of slope was obtained. Therefore, using these polynomial equations, optimal steering values for other inclined surfaces can be determined. For instance, in cell number 19 of Table 1, the optimal steering values for 0, 5, 11 and 158 sloped terrains are 8, 11, 15 and 168, respectively. These values are plotted in Fig. 5, where the polynomial line interpolating these values is also shown. Equation (2) is derived for this polynomial line:
23
24
-5 11 10 8 5 3 Cell number Optimal steering angle 19 20 21 22 23 24 5 6 α° 1 2 3 4 3 1 0 -3 -5 -7 ………… 11 10 8 5 3 1
1
Fig. 4. The precise reference table for a 58 slope and its converted row-matrix form: y, heading angle; y, lateral deviation
ð2Þ
where a is the optimal steering angle, the subscript ‘19’ is the cell number and f is the slope angle. Since the polynomial coefficients are known, for any value of f the optimal steering angle a for the deviations represented by the cell no. 19 (Table 1) can be obtained from this equation. The cubic-polynomial equation to represent the optimal steering angle for any cell can, therefore, be expressed by ae ¼ ae f3 þ be f2 þ ce f þ de
ð3Þ
where a, b, c and d are the polynomial coefficients, and the subscript e is the cell number. Therefore, the optimal steering angle is a function of the gradient, offset and heading deviation, which is
Table 1 Combined row matrices of the optimal steering angle for the reference tables of 0, 5, 11 and 158 slopes Slope angle, deg
Optimal steering angle, degree Cell number
0 5 11 15
1
2
3
4
5
6
. . ..
19
20
21
22
23
24
2 3 4 5
0 1 2 3
2 0 1 2
4 3 2 1
6 5 4 3
8 7 7 6
. . .. . . .. . . .. . . ..
8 11 15 16
6 10 12 13
4 8 9 10
2 5 6 7
0 3 4 5
2 1 2 3
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shown by a¼
e¼
Z Z
ðf; eÞ
ð4Þ
ðy; yÞ
ð5Þ
where, e2 ð1, 2, 3; :::Þ. The derived polynomial-coefficient values for all cell numbers are arranged in a single reference table, which
is known as general reference table. The general reference table prepared for the range of 01 m offset and 58 heading deviation is shown in Table 2. The value indicated inside the square brackets is the cell number e and the rest four rows in each cell of the general reference table are the values of the polynomial coefficients a, b, c and d respectively. During real-time navigation the coefficient values will be used for a known cell number e.
Steering angle , deg
3. Autonomous travel test 17 16 15 14 13 12 11 10 9 8 7
3.1. The test tractor and equipment Polynomial line
0
2
4
6 8 10 Slope angle , deg
12
14
16
Fig. 5. Generalisation of optimal steering angle for specific ranges of deviations
In this experiment an 18 kW, four wheel drive (4WD) Mitsubishi MT2501D model tractor was used as the prototype test vehicle. Total mass, wheelbase and width of the tractor were 1125 kg, 1595 m and 131 m, respectively. The equipment and sensors used in this experiment are shown in Table 3. In this study no on-line slope measuring equipment was used. Therefore, prior to the test, inclinations of the predetermined travel paths were measured by the Total Station.
Table 2 General reference table with values in columns for polynomial coefficients a, b, c and d, respectively, to determine the optimal steering angle for navigating a tractor on slopes of any inclination; cell number in square brackets [ ] Heading angle (y), deg
Polynomial coefficients Offset (y), m 010 to 006
006 to 003
003 to 00
00 to 003
003 to 006
006 to 010
3 to 5
[1] 00008 0015 02568 2
[2] 00008 0015 02568 0
[3] 0002 0053 0615 2
[4] 00041 0069 00440 4
[5] 00008 0015 0257 6
[6] 00029 0064 04492 8
0 to 3
[7] 00036 0079 07061 4
[8] 00041 0069 04402 2
[9] 00008 0015 02568 0
[10] 0002 0053 0615 2
[11] 00024 0042 03485 4
[12] 00008 0015 02568 6
3 to 0
[13] 0001 00079 05871 6
[14] 0003 0090 0972 4
[15] 0000 0004 0422 2
[16] 00032 0090 0972 0
[17] 00032 0090 0972 2
[18] 00041 0069 04402 4
5 to 3
[19] 0003 0057 0395 8
[20] 00023 0079 11371 6
[21] 00044 0128 133 4
[22] 00032 0090 0972 2
[23] 00032 0090 0972 0
[24] 00032 0090 0972 2
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Table 3 Equipment used in the experiment and their working principles Name of equipment 100 MHz Pentium personal computer (PC) Total Station (TS) and a prism Wireless modem AD/DA converter Fibre optic gyroscope (FOG) Linear potentiometer Magnetic sensor DC motor
Working principle The PC was mounted on the tractor. From the sensor signals it calculates the lateral and heading deviations and then determines the optimal steering angle from the general reference table. The prism is mounted on the rear of the tractor and the TS detects the prism by reflecting laser beam. It transmits the vehicle positioning signals from the Total Station to the PC. It converts the analogue signals to digital and digital to analogue. The FOG remains fixed on the tractor body. It measures the heading angle of tractor in the form of voltage, which is then converted into digital value by the AD converter. It is fixed with the front axle and measures the steering angle. The wire of the potentiometer is hinged with one of the front wheels. It is fixed near the flywheel and measures the engine speed in digital form, which is then used to calculate the vehicle velocity. The optimal steering value is converted into analogue voltage by the DA converter and according to the voltage the DC motor makes rotation the steering wheel.
AD, analogue to digital; DA, digital to analogue.
3.2. Travel course and navigation In most of the field operations, tractors travel repeatedly along rectangular path. Therefore, a rectangular travel course was chosen for this study. The course had four rectilinear paths and four quarter turns. The developed table was used to navigate the tractor along the rectilinear portions of the travel course. The navigation procedure for the rectilinear motion is shown in Fig. 6. On flat land, vehicle motion is similar for each respective 908 turn around a rectangular course. However, on sloping ground vehicle motion is different for each of the four turns. Therefore, it is very difficult to develop a feedback control method for a vehicle along curved path on sloping ground. The feedforward control method developed by Ashraf et al. (2002) was used in this study to guide the tractor along four quarter-turn of the rectangular path. In that method when the tractor reaches a pre-determined distance from the end of linear path, the steering angle a begins to increase and when it reaches the maximum (408), it remains constant until the heading angle of the tractor reaches a predetermined turning angle. Just after reaching this turning limit, the feed-forward control switches over to the feedback control for the next linear path.
Start
Slope information Detection of heading angle by total station Measurement of heading angle by fibre optic gyro Measurement of steering angle by potentiometer Measurement of engine speed by magnetic sensor Determination of the cell no. from the general reference table on the basis of lateral and heading deviations Picking up the polynomial coefficients from the cell of general reference table Calculation of the optimal steering angle with the coefficients and slope angle Execution of steering by the DC motor No
3.3. Test field The autonomous travel tests were conducted on a meadow of the Iwate University Omyojin Research
End of travel? Yes Stop
Fig. 6. Flow diagram of the navigation procedure for rectilinear motion
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Path 3
Path 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -1
Path 4
Farm in Japan. The field surface was covered with grass and from eye observation the soil was slightly moist. The prototype test tractor travelled along a predetermined 30 m by 15 m rectangular path. The test was conducted twice. In navigation, the general reference table was applied for one test and the separate reference tables, prepared for each slope, were used for the other test. The travel direction of path 1 was along a contour line of 118 average slope and that of path 3 was along a contour line of 208 average slope. The travel direction of path 2 was towards uphill and that of path 4 was towards downhill. Throughout the test the tractor velocity was 05 m/s in both cases.
Width, m
M.A. ASHRAF ET AL.
Path 1 3
7
11
15
19
23
27
31
Travel length, m
Fig. 8. Autonomous travel trajectory for tractor navigation by separate reference table
4. Results and discussion
Path 3
Path 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -1
Path 4
Width, m
The autonomous travel trajectory of the tractor for navigation by the general reference table is shown in Fig. 7 and the trajectory for navigation by the separate reference table is shown in Fig. 8. The longitudinal travel paths (path 1 and path 3) were towards the contour lines, and the lateral travel paths (path 2 and path 4) were uphill and downhill, respectively. Since the aim of this study was to attain a precise navigation along the contour paths, comparison between the navigation performances of the general reference table and separate reference table for tracking paths 1 and 3 is accentuated here. The reference table, prepared for an 118 slope, was used to navigate the tractor along this path. For that reason in Figs. 7 and 8, no significant difference is found in the trajectories along path 1. In Table 4, it is also found that in case of navigation with general reference table, the mean and standard deviations of the vehicle offsets along path 1 were 00267 and 00338 m, respectively; and those of the heading deviations were
Path 1 3
7
11
15
19
23
27
31
Travel length, m
Fig. 7. Autonomous travel trajectory for tractor navigation by the general steering strategy
309 and 1428, respectively. For navigation with the separate reference table, however, the mean and standard deviations of the vehicle offsets were 00028 and 00297 m, respectively, and those of heading deviations were 214 and 1128, respectively. While preparing the reference table for a 158 slope, it was assumed that this table would be used to navigate the tractor on sloped terrains of 138 and above inclinations. Therefore, for navigation with separate reference table along path 3, this table was used. From Figs. 7 and 8, and also from Table 4, the performances of the two navigation methods in tracking path 3 are clearly apparent. For navigation with the general reference table, as shown in Table 4, the mean and standard deviations of the vehicle offsets were 005 and 00439 m, respectively, and those of heading deviations were 269 and 1548, respectively. Whereas for navigation with separate reference table, the mean and standard deviations of the vehicle offsets were 01464 and 00667 m, respectively, and heading deviations were 327 and 2548, respectively. These differences occurred as the reference table (prepared for a 158 slope) used in the separate reference table navigation could not provide the appropriate optimal-steering angles required for the deviations on a 208 slope; whereas the general reference table could sufficiently provide it. When the tractor travels along the contour direction, the magnitude of the optimal steering angle needed for the deviations on the valley side is obviously larger than that of for similar deviations on the hillside. For uphill and downhill motion, the effects of the slope on the vehicle deviation in both sides of the travel path are assumed to be similar. Therefore, the optimal steering angle for a 08 slope was used for the navigation along these two paths. However, in preparing the optimal steering angle for a 08 slope, there was no concern about the effect of the slope. Therefore, the deviations of the
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Table 4 Comparative navigation performance of general and separate reference tables in tracking the rectilinear paths General reference table
Path Path Path Path
1 2 3 4
Separate reference table
Mean (y), m
STD (y), m
Mean (y), deg
STD (y), deg
Mean (y), m
STD (y), m
Mean (y), deg
STD (y), deg
00267 00511 00500 00086
00338 00515 00439 00419
309 279 269 502
142 345 154 363
00028 00457 01464 00023
00297 00604 00667 00452
214 190 327 315
112 296 254 227
STD, standard deviation.
vehicle along these two paths were great in comparison to the deviations along the contour lines. Figures 7 and 8 also show that although feed-forward control method was applied for the quarter turns, the convergences of the turns were fairly good.
5. Conclusion A general steering strategy was developed to navigate the tractor on sloping terrain, where a neural network model was trained for four slopes of different gradients, respectively. The corresponding steering controllers were then developed but were generalised for the sloping grounds of any inclination. From an autonomous travel test it was found that for the tractor navigation by the developed guidance system, the mean and standard deviation in tracking a contour path on 208 sloping ground were 005 and 00439 m, respectively, whereas that for the navigation by separate reference table method were 01464 and 00667 m, respectively. It was also found that the mean and standard deviation in tracking the contour path of 118 sloping ground by the separate reference table were 00267 and 00338 m, respectively, whereas those by the general reference table method were 0028 and 00297 m, respectively. From the results it is proved that the developed guidance system can precisely navigate the prototype tractor along rectilinear contour paths on sloped terrains of any inclination, whereas the separate reference table method gives better results on specific trained slope. The general reference table method could save time to attain a total navigation on sloping environment.
References Ashraf M A; Torisu R; Takeda J (2002). Autonomous traveling of off-road vehicles along rectangular path on slope terrain. Proceedings of the 26–27 July conference on Automation Technology for Off-Road Equipment, Chicago, IL, pp. 412–421 Bell T (2000). Automatic tractor guidance using carrier-phase differential GPS. Computers and Electronics in Agriculture, 25, 53–66 Dutton K; Thompson S; Barraclough B (1997). The Art of Control Engineering. Addison-Wesley Longman Limited, England Keicher R; Seufert H (2000). Automatic guidance for agricultural vehicles in Europe. Computers and Electronics in Agriculture, 25, 169–194 Noguchi N; Ishii K; Terao H (1997). Development of an agricultural mobile robot using a geomagnetic direction sensor and image sensors. Journal of Agricultural Engineering Research, 67, 1–15 Reid J F; Zhang Q; Noguchi N; Dicson M (2000). Agricultural automatic guidance research in North America. Computers and Electronics in Agriculture, 25, 155–167 Tamaki K; Segawa T; Shibuya Y; Iijima W (2001). [Development of autonomous running technique for wide fertilizer spreading in sloping grasslands (part 1)]. Journal of the Japanese Society of Agricultural Machinery, 63(5), 109–115 (in Japanese, abstract in English) Torii T (2000). Research in autonomous agricultural vehicles in Japan. Computers and Electronics in Agriculture, 25, 133–153 Torisu R; Hai S; Takeda J; Ashraf M A (2002). Automatic tractor guidance on sloped terrain (Part 1), formulation of neural network vehicle model and design of control law for contour line travel. Journal of the Japanese Society of Agricultural Machinery, 64(6), 88–95 Wasserman P D (1989). Neural Computing, Theory and Practice. Van Nostrand Reinhold, New York Wylie C R; Barrett L C (1995). Advanced Engineering Mathematics. McGraw-Hill, Inc, New York
Biosystems Engineering (2003) 86 (3), 267–273 doi:10.1016/S1537-5110(03)00140-5 AE}Automation and Emerging Technologies
Generalised Steering Strategy for Vehicle Navigation on Sloping Ground M.A. Ashraf; J. Takeda; H. Osada; S. Chiba Faculty of Agriculture, Iwate University, Morioka 020-8550, Japan; e-mail of corresponding author: [email protected] (Received 25 October 2002; accepted in revised form 16 July 2003; published online 13 September 2003)
An autonomous tractor guidance system for vehicle navigation on sloping ground was developed by extending a previous study in which navigation was limited to a specific gradient. A previously developed neural network vehicle model was trained along the contour lines of 0, 5, 11 and 158 sloping terrain. Using the trained models and a cost function, optimal steering angles for different ranges of deviations were sought by genetic algorithm and the optimal values were arranged in separate matrix-form reference table for each slope. The optimal steering values of the four reference tables were expressed by a third-order polynomial equation so that the equation can provide an optimal steering value for any inclination. The coefficients of the equations were tabulated in a matrix form, which is designated as a ‘general reference table’. If the slope inclination and vehicle attitude can be determined, real-time navigation of the tractor is possible using this table. An autonomous travel test was conducted on inclined surface. It was found that the developed guidance system could precisely navigate the tractor along a rectilinear contour path on 208 sloping terrain, where the mean offset was 005 m and its standard deviation was 0044 m. # 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd
1. Introduction Much of the grassland in Japan and other countries are in hilly areas where the farm tractor is used for various tasks. However, working on hilly terrain can cause discomfort to the operator, due to the effects on body alignment. This also increases the fatigue of the operator and thereby decreases the work efficiency with time. Although much research has been conducted on automatic guidance system for the farm tractor, most is concerned with flat land (Torii, 2000; Keicher & Seufert, 2000; Reid et al., 2000; Noguchi et al., 1997). Tamaki et al. (2001) studied an automatic crawler guidance system using internal sensors, on 118 sloping terrain. The lateral deviation of the crawler from the target path was less than 25 m. Bell (2000) devised an automatic tractor guidance system using a kinematic model. A biased estimation method was incorporated into the control software to compensate the effect of the slope on the vehicle motion. Torisu et al. (2002) and Ashraf et al. (2002) also conducted experiments on the automatic tractor guidance on sloping terrain. Since the vehicle dynamics on sloping ground is highly non-linear, a neural network vehicle model was used instead of a 1537-5110/$30.00
conventional mathematics-based vehicle model. The model was trained for a specific inclined surface and used a genetic algorithm to develop a steering controller. However, a neural network model can represent the vehicle motion only for that particular gradient for which it is trained. Consequently, the controller can only be used to navigate the tractor on that slope. It would be an impractical, uneconomic and time-consuming task to train a model for every variation. To produce an accurate but more generalised steering strategy, this paper deals with the development of a navigation planner, which includes: (1) development of navigation planner for different gradients, (2) development of the corresponding steering controller, and (3) generalisation of the controller.
2. Navigation planner 2.1. Vehicle model for varying gradients The structure of the neural network vehicle model developed by Torisu et al. (2002) has six input and three output variables with two hidden layers. Each hidden 267
# 2003 Silsoe Research Institute. All rights reserved Published by Elsevier Ltd
ARTICLE IN PRESS 268
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2 N1
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wn341
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1
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2
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N m4
φ
w1212
Output layer
pe
Input variables
Hidden layer 2 o Sl
1 N1
Hidden layer 1
Output variables
Input layer
3
Nn
Fig. 1. A typical neural network model and its weight distribution: wpq ij , weight between two neurons; p & q, consecutive layer numbers; i & j, row numbers; Npi , neuron number
layer has six neurons. Each neuron remains connected with all other neurons of next layer by means of weights (synapses) (Wasserman, 1989). The behaviour of the network is determined by the strength or weights of the interconnecting neurons. A typical neural network model is shown in Fig. 1 where the weight w for each pair of interconnecting neurons is prompted. Unlike a mathematical model, the structure of a neural network model cannot itself express the system behaviour. It entails just the arrangement of the input–output variables and the interconnecting neurons of the network. A neural network must be ‘trained’ before being of use as a practical model. When it is trained for a specific gradient of land, a constant value is determined for each weight. Then the trained model can be used to express the vehicle behaviour but only for land of that specific gradient. From this view point Torisu’s model cannot represent the tractor behaviour for the slopes of varying gradients. Therefore, to develop a generalised navigation planner the neural network model was trained for the sloping land of 0, 5, 11 and 158 (Torisu et al., 2002).
2.2. Optimisation of the quadratic form cost function by genetic algorithm In automatic vehicle guidance systems, a controller is essential to guide the vehicle along desired path. Torisu et al. (2002) used the optimal control method for this purpose and designed a quadratic form cost function (Dutton et al., 1997). The optimal control masses for each slope were determined by simulation. Prior to the simulation different ranges of offset y and heading angle y were considered as the measurable system errors (Fig. 2). The weight vectors of the trained vehicle model and the cost function were used in the simulation to find the best possible (optimal) control mass for each range of error. Genetic algorithms were used as the tool of
⊗
Desired path α y θ
Fig. 2. Vehicle deviations from the desired path: y, heading angle; a, steering angle; f, slope angle; y, lateral deviation (offset)
simulation to find the optimal control mass (Torisu et al. 2002). The simulated optimal control masses (steering angle) for different sets of lateral deviation and heading angle were arranged in a matrix form reference table. This table can be used for real-time navigation of the vehicle on sloped terrains where inclinations are similar to that terrain on which the model was trained. Therefore, the optimal steering angle a was expressed as: Z a ¼ ðy; yÞ ð1Þ The choice of selecting the range of offset and heading angle is optional. Before choosing the range of deviations, however, it was assumed that: (a) when the lateral and heading deviations of the vehicle are more than 04 m and 208 respectively from the desired course, a poorly optimised steering value will not affect the system performance significantly; (b) when the range of lateral deviation is within 01–04 m and that of the heading deviation is within 5–208, a moderately optimised steering value will be rational for the system performance; (c) but when the vehicle is very near to the desired course, i.e., within 01 m lateral and 58 heading deviation, a small variation in the optimal steering value will significantly affect the system performance. Therefore, the ranges of lateral and heading deviations were chosen in three different intervals, and three separate reference tables were prepared for each gradient. The reference table, prepared for the range of 01 m lateral and 58 heading deviation, is introduced as precise; the one, prepared for the range of 03 m lateral and 158 heading deviation, is introduced as normal; and the one, prepared for beyond these ranges of deviations, is introduced as the rough reference table.
2.3. Generalisation of reference tables Without further field experiment a generalised navigation planner was developed. For this purpose the precise, normal and rough reference tables, prepared for each slope with the optimal steering angle, were collated
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into a single reference table. The collated reference table for 58 sloping terrain is shown in Fig. 3. Similar ones were also prepared for 0, 11 and 158 slopes. Table cells were numbered sequentially, each number representing a specific range of lateral and heading deviations. Focusing on part of this table, Fig. 4 shows how the table was converted into a row matrix. The row matrixes
Lateral deviation y, m 0.0
2
<-40 -40 -20
-10 -5
28 20
-21
-30 -38
-13 0.1 0.2
-21 -30
-16 -19
-13 -8
-14 -16 -13 -21
-0.06 -0.03 0.03 0.06 3 1 0 -3 -5 -7 -8 -14 6 3 1 0 -3 -5 9 7 4 3 1 -3
11 7 13 12
0
20 13
-10 -4
2 -5 7
5
Heading angle θ, deg
10
20
4
3
12
0.4 0.8 >0.8
-13 -6 -0.2 -0.1
-3
40 >40
<-0.8 -0.8 -0.4 3 -6
-4 -8
11 10 8 5 3
17 14 20 17
11
8
15
11
1
-3 -1
-6 -13
1
8
35
28
20
13
4
-6
36
34
28
20
13
4
a19 ¼ 00032f3 þ 0057f2 þ 03947f þ 8
Fig. 3. A collated reference table of optimised steering angles for 58 slope
θ° -0.1-0.06 -0.03 0.00.03 0.06 0.1 4 1 2 3 5 6 5 1 2 6 5 3 4 3 1 0 -3 -5 -7 3 1 0 -3 -5 -7 7 8 9 10 11 12 3 7 8 9 12 10 11 6 3 1 0 -3 -5 0 -3 -5 3 1 6 y, m 13 14 15 16 17 18 0 13 14 15 16 17 18 3 7 1 -3 4 9 9 7 4 3 1 -3 -3 20
21
22
23
24
11 10
19
8
5
3
1
19
20
21
22
of 0, 5, 11 and 158 slopes were arranged together and shown in Table 1. In this table, there is no information about the optimal steering values for the land, whose inclinations are in between 0–58, 5–118, 11–158 and above 158. Optimal steering values for the intermediate inclinations can be obtained by developing mathematical relationship between the existing optimal-steering values with the slope inclinations. Therefore, for each column of Table 1, a mathematical expression was derived by interpolating a cubic-polynomial (Wylie & Barrett, 1995) between the optimal steering values of the four inclined surfaces. Values of the unknown polynomial coefficients were derived by linear algebra. From each equation, a pattern of optimal steering angle with the variation of slope was obtained. Therefore, using these polynomial equations, optimal steering values for other inclined surfaces can be determined. For instance, in cell number 19 of Table 1, the optimal steering values for 0, 5, 11 and 158 sloped terrains are 8, 11, 15 and 168, respectively. These values are plotted in Fig. 5, where the polynomial line interpolating these values is also shown. Equation (2) is derived for this polynomial line:
23
24
-5 11 10 8 5 3 Cell number Optimal steering angle 19 20 21 22 23 24 5 6 α° 1 2 3 4 3 1 0 -3 -5 -7 ………… 11 10 8 5 3 1
1
Fig. 4. The precise reference table for a 58 slope and its converted row-matrix form: y, heading angle; y, lateral deviation
ð2Þ
where a is the optimal steering angle, the subscript ‘19’ is the cell number and f is the slope angle. Since the polynomial coefficients are known, for any value of f the optimal steering angle a for the deviations represented by the cell no. 19 (Table 1) can be obtained from this equation. The cubic-polynomial equation to represent the optimal steering angle for any cell can, therefore, be expressed by ae ¼ ae f3 þ be f2 þ ce f þ de
ð3Þ
where a, b, c and d are the polynomial coefficients, and the subscript e is the cell number. Therefore, the optimal steering angle is a function of the gradient, offset and heading deviation, which is
Table 1 Combined row matrices of the optimal steering angle for the reference tables of 0, 5, 11 and 158 slopes Slope angle, deg
Optimal steering angle, degree Cell number
0 5 11 15
1
2
3
4
5
6
. . ..
19
20
21
22
23
24
2 3 4 5
0 1 2 3
2 0 1 2
4 3 2 1
6 5 4 3
8 7 7 6
. . .. . . .. . . .. . . ..
8 11 15 16
6 10 12 13
4 8 9 10
2 5 6 7
0 3 4 5
2 1 2 3
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shown by a¼
e¼
Z Z
ðf; eÞ
ð4Þ
ðy; yÞ
ð5Þ
where, e2 ð1, 2, 3; :::Þ. The derived polynomial-coefficient values for all cell numbers are arranged in a single reference table, which
is known as general reference table. The general reference table prepared for the range of 01 m offset and 58 heading deviation is shown in Table 2. The value indicated inside the square brackets is the cell number e and the rest four rows in each cell of the general reference table are the values of the polynomial coefficients a, b, c and d respectively. During real-time navigation the coefficient values will be used for a known cell number e.
Steering angle , deg
3. Autonomous travel test 17 16 15 14 13 12 11 10 9 8 7
3.1. The test tractor and equipment Polynomial line
0
2
4
6 8 10 Slope angle , deg
12
14
16
Fig. 5. Generalisation of optimal steering angle for specific ranges of deviations
In this experiment an 18 kW, four wheel drive (4WD) Mitsubishi MT2501D model tractor was used as the prototype test vehicle. Total mass, wheelbase and width of the tractor were 1125 kg, 1595 m and 131 m, respectively. The equipment and sensors used in this experiment are shown in Table 3. In this study no on-line slope measuring equipment was used. Therefore, prior to the test, inclinations of the predetermined travel paths were measured by the Total Station.
Table 2 General reference table with values in columns for polynomial coefficients a, b, c and d, respectively, to determine the optimal steering angle for navigating a tractor on slopes of any inclination; cell number in square brackets [ ] Heading angle (y), deg
Polynomial coefficients Offset (y), m 010 to 006
006 to 003
003 to 00
00 to 003
003 to 006
006 to 010
3 to 5
[1] 00008 0015 02568 2
[2] 00008 0015 02568 0
[3] 0002 0053 0615 2
[4] 00041 0069 00440 4
[5] 00008 0015 0257 6
[6] 00029 0064 04492 8
0 to 3
[7] 00036 0079 07061 4
[8] 00041 0069 04402 2
[9] 00008 0015 02568 0
[10] 0002 0053 0615 2
[11] 00024 0042 03485 4
[12] 00008 0015 02568 6
3 to 0
[13] 0001 00079 05871 6
[14] 0003 0090 0972 4
[15] 0000 0004 0422 2
[16] 00032 0090 0972 0
[17] 00032 0090 0972 2
[18] 00041 0069 04402 4
5 to 3
[19] 0003 0057 0395 8
[20] 00023 0079 11371 6
[21] 00044 0128 133 4
[22] 00032 0090 0972 2
[23] 00032 0090 0972 0
[24] 00032 0090 0972 2
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Table 3 Equipment used in the experiment and their working principles Name of equipment 100 MHz Pentium personal computer (PC) Total Station (TS) and a prism Wireless modem AD/DA converter Fibre optic gyroscope (FOG) Linear potentiometer Magnetic sensor DC motor
Working principle The PC was mounted on the tractor. From the sensor signals it calculates the lateral and heading deviations and then determines the optimal steering angle from the general reference table. The prism is mounted on the rear of the tractor and the TS detects the prism by reflecting laser beam. It transmits the vehicle positioning signals from the Total Station to the PC. It converts the analogue signals to digital and digital to analogue. The FOG remains fixed on the tractor body. It measures the heading angle of tractor in the form of voltage, which is then converted into digital value by the AD converter. It is fixed with the front axle and measures the steering angle. The wire of the potentiometer is hinged with one of the front wheels. It is fixed near the flywheel and measures the engine speed in digital form, which is then used to calculate the vehicle velocity. The optimal steering value is converted into analogue voltage by the DA converter and according to the voltage the DC motor makes rotation the steering wheel.
AD, analogue to digital; DA, digital to analogue.
3.2. Travel course and navigation In most of the field operations, tractors travel repeatedly along rectangular path. Therefore, a rectangular travel course was chosen for this study. The course had four rectilinear paths and four quarter turns. The developed table was used to navigate the tractor along the rectilinear portions of the travel course. The navigation procedure for the rectilinear motion is shown in Fig. 6. On flat land, vehicle motion is similar for each respective 908 turn around a rectangular course. However, on sloping ground vehicle motion is different for each of the four turns. Therefore, it is very difficult to develop a feedback control method for a vehicle along curved path on sloping ground. The feedforward control method developed by Ashraf et al. (2002) was used in this study to guide the tractor along four quarter-turn of the rectangular path. In that method when the tractor reaches a pre-determined distance from the end of linear path, the steering angle a begins to increase and when it reaches the maximum (408), it remains constant until the heading angle of the tractor reaches a predetermined turning angle. Just after reaching this turning limit, the feed-forward control switches over to the feedback control for the next linear path.
Start
Slope information Detection of heading angle by total station Measurement of heading angle by fibre optic gyro Measurement of steering angle by potentiometer Measurement of engine speed by magnetic sensor Determination of the cell no. from the general reference table on the basis of lateral and heading deviations Picking up the polynomial coefficients from the cell of general reference table Calculation of the optimal steering angle with the coefficients and slope angle Execution of steering by the DC motor No
3.3. Test field The autonomous travel tests were conducted on a meadow of the Iwate University Omyojin Research
End of travel? Yes Stop
Fig. 6. Flow diagram of the navigation procedure for rectilinear motion
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Path 3
Path 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -1
Path 4
Farm in Japan. The field surface was covered with grass and from eye observation the soil was slightly moist. The prototype test tractor travelled along a predetermined 30 m by 15 m rectangular path. The test was conducted twice. In navigation, the general reference table was applied for one test and the separate reference tables, prepared for each slope, were used for the other test. The travel direction of path 1 was along a contour line of 118 average slope and that of path 3 was along a contour line of 208 average slope. The travel direction of path 2 was towards uphill and that of path 4 was towards downhill. Throughout the test the tractor velocity was 05 m/s in both cases.
Width, m
M.A. ASHRAF ET AL.
Path 1 3
7
11
15
19
23
27
31
Travel length, m
Fig. 8. Autonomous travel trajectory for tractor navigation by separate reference table
4. Results and discussion
Path 3
Path 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -1
Path 4
Width, m
The autonomous travel trajectory of the tractor for navigation by the general reference table is shown in Fig. 7 and the trajectory for navigation by the separate reference table is shown in Fig. 8. The longitudinal travel paths (path 1 and path 3) were towards the contour lines, and the lateral travel paths (path 2 and path 4) were uphill and downhill, respectively. Since the aim of this study was to attain a precise navigation along the contour paths, comparison between the navigation performances of the general reference table and separate reference table for tracking paths 1 and 3 is accentuated here. The reference table, prepared for an 118 slope, was used to navigate the tractor along this path. For that reason in Figs. 7 and 8, no significant difference is found in the trajectories along path 1. In Table 4, it is also found that in case of navigation with general reference table, the mean and standard deviations of the vehicle offsets along path 1 were 00267 and 00338 m, respectively; and those of the heading deviations were
Path 1 3
7
11
15
19
23
27
31
Travel length, m
Fig. 7. Autonomous travel trajectory for tractor navigation by the general steering strategy
309 and 1428, respectively. For navigation with the separate reference table, however, the mean and standard deviations of the vehicle offsets were 00028 and 00297 m, respectively, and those of heading deviations were 214 and 1128, respectively. While preparing the reference table for a 158 slope, it was assumed that this table would be used to navigate the tractor on sloped terrains of 138 and above inclinations. Therefore, for navigation with separate reference table along path 3, this table was used. From Figs. 7 and 8, and also from Table 4, the performances of the two navigation methods in tracking path 3 are clearly apparent. For navigation with the general reference table, as shown in Table 4, the mean and standard deviations of the vehicle offsets were 005 and 00439 m, respectively, and those of heading deviations were 269 and 1548, respectively. Whereas for navigation with separate reference table, the mean and standard deviations of the vehicle offsets were 01464 and 00667 m, respectively, and heading deviations were 327 and 2548, respectively. These differences occurred as the reference table (prepared for a 158 slope) used in the separate reference table navigation could not provide the appropriate optimal-steering angles required for the deviations on a 208 slope; whereas the general reference table could sufficiently provide it. When the tractor travels along the contour direction, the magnitude of the optimal steering angle needed for the deviations on the valley side is obviously larger than that of for similar deviations on the hillside. For uphill and downhill motion, the effects of the slope on the vehicle deviation in both sides of the travel path are assumed to be similar. Therefore, the optimal steering angle for a 08 slope was used for the navigation along these two paths. However, in preparing the optimal steering angle for a 08 slope, there was no concern about the effect of the slope. Therefore, the deviations of the
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Table 4 Comparative navigation performance of general and separate reference tables in tracking the rectilinear paths General reference table
Path Path Path Path
1 2 3 4
Separate reference table
Mean (y), m
STD (y), m
Mean (y), deg
STD (y), deg
Mean (y), m
STD (y), m
Mean (y), deg
STD (y), deg
00267 00511 00500 00086
00338 00515 00439 00419
309 279 269 502
142 345 154 363
00028 00457 01464 00023
00297 00604 00667 00452
214 190 327 315
112 296 254 227
STD, standard deviation.
vehicle along these two paths were great in comparison to the deviations along the contour lines. Figures 7 and 8 also show that although feed-forward control method was applied for the quarter turns, the convergences of the turns were fairly good.
5. Conclusion A general steering strategy was developed to navigate the tractor on sloping terrain, where a neural network model was trained for four slopes of different gradients, respectively. The corresponding steering controllers were then developed but were generalised for the sloping grounds of any inclination. From an autonomous travel test it was found that for the tractor navigation by the developed guidance system, the mean and standard deviation in tracking a contour path on 208 sloping ground were 005 and 00439 m, respectively, whereas that for the navigation by separate reference table method were 01464 and 00667 m, respectively. It was also found that the mean and standard deviation in tracking the contour path of 118 sloping ground by the separate reference table were 00267 and 00338 m, respectively, whereas those by the general reference table method were 0028 and 00297 m, respectively. From the results it is proved that the developed guidance system can precisely navigate the prototype tractor along rectilinear contour paths on sloped terrains of any inclination, whereas the separate reference table method gives better results on specific trained slope. The general reference table method could save time to attain a total navigation on sloping environment.
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